JOKER'S VAULT MATH QUESTION

There is this new progressive video poker game, Joker's Vault, that I'm trying to analyze. You can bet up to $2 a hand but the optimum bet is just 50 cents. The main game is Two Pair Jokers. Here's the payscale:

RF..........800
5k..........240
JR..........110
SF............35
4K............12
FH.............8
FL........ .....5
ST.............4
3K.............1
2P.............1

I ran it on WVP, 73.588%

When you make a Full House, either natural or joker, you get 10 free games. The payscale remains the same but there are TWO JOKERS in the deck. I ran it on WVP, 109.189%. The frequency on making the Full House is 67.7. The free games add 10.9189 bets per 67.7 games. That brings the payback up to 89.72%.

There is a progressive meter that starts at $100 and runs 2%. If you win 8 out of the ten free games you win the progressive meter. This is the math I'm stuck on. I have a vague idea of how to do it but I'm not really sure. The WVP game stats for Double Joker shows that you will make a garbage hand 64.2% of the time. Which means your chances of winning your next hand is 35.8%.

There are also questions about a strategy shift but I will save that for later. Can anyone show me how to calculate winning 8 out of the ten games. Any help is greatly appreciated.

Quote: mickeycrimm

There is this new progressive video poker game, Joker's Vault, that I'm trying to analyze. You can bet up to $2 a hand but the optimum bet is just 50 cents. The main game is Two Pair Jokers. Here's the payscale:

RF..........800
5k..........240
JR..........110
SF............35
4K............12
FH.............8
FL........ .....5
ST.............4
3K.............1
2P.............1

I ran it on WVP, 73.588%

When you make a Full House, either natural or joker, you get 10 free games. The payscale remains the same but there are TWO JOKERS in the deck. I ran it on WVP, 109.189%. The frequency on making the Full House is 67.7. The free games add 10.9189 bets per 67.7 games. That brings the payback up to 89.72%.

There is a progressive meter that starts at $100 and runs 2%. If you win 8 out of the ten free games you win the progressive meter. This is the math I'm stuck on. I have a vague idea of how to do it but I'm not really sure. The WVP game stats for Double Joker shows that you will make a garbage hand 64.2% of the time. Which means your chances of winning your next hand is 35.8%.

There are also questions about a strategy shift but I will save that for later. Can anyone show me how to calculate winning 8 out of the ten games. Any help is greatly appreciated.

so your saying its 91.7% only wow that's very low. I prog would need to be fairly high

Quote: mickeycrimm

There is this new progressive video poker game, Joker's Vault, that I'm trying to analyze. You can bet up to $2 a hand but the optimum bet is just 50 cents. The main game is Two Pair Jokers. Here's the payscale:

RF..........800
5k..........240
JR..........110
SF............35
4K............12
FH.............8
FL........ .....5
ST.............4
3K.............1
2P.............1

I ran it on WVP, 73.588%

When you make a Full House, either natural or joker, you get 10 free games. The payscale remains the same but there are TWO JOKERS in the deck. I ran it on WVP, 109.189%. The frequency on making the Full House is 67.7. The free games add 10.9189 bets per 67.7 games. That brings the payback up to 89.72%.

There is a progressive meter that starts at $100 and runs 2%. If you win 8 out of the ten free games you win the progressive meter. This is the math I'm stuck on. I have a vague idea of how to do it but I'm not really sure. The WVP game stats for Double Joker shows that you will make a garbage hand 64.2% of the time. Which means your chances of winning your next hand is 35.8%.

There are also questions about a strategy shift but I will save that for later. Can anyone show me how to calculate winning 8 out of the ten games. Any help is greatly appreciated.

(35.8% ^ 8 * 62.2% ^ 2) to do it in order, multiply by 45 (10C8) ways to do it = .5% That's for EXACTLY 8. Assuming you still get the progressive for 9 or 10, you'd calc those the same way and add 'em up.

Quote: AxelWolf

so your saying its 91.7% only wow that's very low. I prog would need to be fairly high

Yes, it would have to be high. When I'm out making rounds I occasionally see meters in the $300 range. The highest I've seen is $500. I think the reason for this is, while you only have to bet 50 cents to qualify for the meter, many people bet up to $2 per hand. The payscale multiplies up when you are betting more than 50 cents, but the meter stays the same. If the meter is at $200 when you win 8 out of ten hands it doesn't matter if you are betting 50 cents or $2, you get paid $200. If there is an opportunity in this game then it's being created by the $2 bettors who are hammering the meter up at a much faster rate than a 50 cent player.

These are all stand alone progressives. So you don't have to worry about getting picked off. If I can find the breakeven number then the meter alone is worth $12 an hour. But I wouldn't want to fool with it for less than $30 an hour.

Quote: vetsen

(35.8% ^ 8 * 62.2% ^ 2) to do it in order, multiply by 45 (10C8) ways to do it = .5% That's for EXACTLY 8. Assuming you still get the progressive for 9 or 10, you'd calc those the same way and add 'em up.

vetsen, I'm lousy with the code language. But for the first way of getting there, which is winning 8 hands in a row, are you saying that I should multiple 35.8% eight times and then divide one by the decimal?

Quote: mickeycrimm

vetsen, I'm lousy with the code language. But for the first way of getting there, which is winning 8 hands in a row, are you saying that I should multiple 35.8% eight times and then divide one by the decimal?

.358 to the eighth power, multiplied by .622 squared, multiplied by 45. Should give you .005.

The complete list is

0 of 10 0.011894612
1 of 10 0.06632821
2 of 10 0.166440416
3 of 10 0.247500182
4 of 10 0.24152471
5 of 10 0.161618404
6 of 10 0.075103049
7 of 10 0.023931368
8 of 10 0.00500434
9 of 10 0.000620129
10 of 10 0.000034580

Quote: vetsen

.358 to the eighth power, multiplied by .622 squared, multiplied by 45. Should give you .005.

The complete list is

0 of 10 0.011894612
1 of 10 0.06632821
2 of 10 0.166440416
3 of 10 0.247500182
4 of 10 0.24152471
5 of 10 0.161618404
6 of 10 0.075103049
7 of 10 0.023931368
8 of 10 0.00500434
9 of 10 0.000620129
10 of 10 0.000034580

Thank you so much, vetsen. I like to study stuff like this so I know how to do it next time. So I take it that the chances are one in 200. Which would mean 200 X 67.7 = a 13,540 game cycle.

You also need to consider that you can re-initiate free spins, so you will get to play 12.17 free games on average. If you do re-initiate the bonus, your win meter resets for any additional sets of 10 games.

I calculate, without shifting any strategy, that the meter must reach $345 to break even, not including the progressive contribution. But... It will take 8.25 hours, on average, to hit, given 1200 hands per hour.

I'm guessing this will almost never hit the $36/hour mark, plus you run the risk of not cashing in, unless you leave at closing time and show back up at opening time.

Also, a friend sent me some screen shots which claim a progressive contribution of 1.5%. That might be configurable on the machine, though.

Quote: CrystalMath

You also need to consider that you can re-initiate free spins, so you will get to play 12.17 free games on average. If you do re-initiate the bonus, your win meter resets for any additional sets of 10 games.

I calculate, without shifting any strategy, that the meter must reach $345 to break even, not including the progressive contribution. But... It will take 8.25 hours, on average, to hit, given 1200 hands per hour.

I'm guessing this will almost never hit the $36/hour mark, plus you run the risk of not cashing in, unless you leave at closing time and show back up at opening time.

Also, a friend sent me some screen shots which claim a progressive contribution of 1.5%. That might be configurable on the machine, though.

Thanks, Crystal. I totally forgot that you can trigger more free games in Double Joker mode. I think you are right about the meter too. Thanks everyone for all the help.

Just out of curiosity, is this a Spielo GTECH machine of some kind? Spielo's have the only machines I have ever seen that have Progressives that do not require that a player Max bet, specifically, the bet only need be $0.50. The games I have seen such as this have all been Video Keno games, though.

Quote: Mission146

Just out of curiosity, is this a Spielo GTECH machine of some kind? Spielo's have the only machines I have ever seen that have Progressives that do not require that a player Max bet, specifically, the bet only need be $0.50. The games I have seen such as this have all been Video Keno games, though.

Yes, this is a Spielo game.

Quote: Mission146

Just out of curiosity, is this a Spielo GTECH machine of some kind? Spielo's have the only machines I have ever seen that have Progressives that do not require that a player Max bet, specifically, the bet only need be $0.50. The games I have seen such as this have all been Video Keno games, though.

Yes, they are Spielo machines that are called "Power Station Five's." They have about a dozen keno games, about 8 video poker games, and a few line games on them. Spielo is on the Wiz's blacklist for writing an online game that defrauded players but I would have to give up income to quit playing them. So far there are four games I exploit. Perhaps Crystalmath could get his buddy to send him some screen shots of a keno game called Hot "n Hotter. Especially the 6-spot and 9-spot. It's a progressive/banking game. I'd like to get his take on the game. I put the cost at about $350 on the game, but my math may be faulty.

On the games I play the betting is 50 cents to qualify for the meter, except one game is just 40 cents to qualify for the meter, but you can bet as high as $2.

One of the quirks of Montana video poker is you get penalized for betting higher. Betting a dollar or less the royal pays 800 for 1. But Montana Law is $800 max jackpot. Betting $1 the royal pays $800. But if you are betting $1.25, $1.50, $1.75, or $2 the royal still pays just $800.

It's the same thing with the Spielo machines I have seen at Wheeling Island Hotel, Casino, Racetrack in West Virginia, except the ones I have seen operate just as strangely. It's the same thing with the Progressives, you qualify for them by betting anywhere from $0.50-$2.00, however, $2.00 is not the highest possible Max bet in West Virginia, and you can bet more than $2.00 on these machines, but the Progressive turns off if you do!

Furthermore, there is no Maximum Jackpot in West Virginia that I'm aware of, and you can certainly win more than $800 on these machines.

I don't understand the people that bet more than $0.50 on the Progressive Keno Games (Big Catch Keno, Frost N' Fire Keno, Lucky Bells Keno) because, even if a person is not Math inclined, wouldn't you notice when it says, "Jackpot," for so many balls hit that the Jackpot amount isn't changing as you increase your bet? It's just really difficult to believe that someone could play that stupidly. I personally have no problem with playing -EV games, as I will play them for small amounts, but I'm not going to go out of my way to make the game even worse paying!!! You reach a point sometimes, betting more than $0.50 with that Progressive Jackpot, that the ER was better betting less than $0.50 and just taking the Base Pay!!!

Mission, I think it's because the conventional wisdom is to always max bet a slot. People don't look to see if the jackpot increases, or do the math to realize they can't get full odds because of state caps or aggregate table rules on the big bonus pays. For example, I have enjoyed playing LIR from time to time, especially after they added the PP pays on the front, but the gamblling boat I play on has a 10K table aggregate cap on the payout. That means that, even at $5 minimum, they won't pay the full Royal if you win it. So I don't play it at all.

I wouldn't play that game, either. I have no problem with Maximum Aggregate so long as it is the player's mistake by betting an amount in excess of the Maximum amount that would result in the full jackpot...based on Odds...because that is the player's mistake and a fail to play Optimally. However, to advertise Jackpot Odds against a Maximum Aggregate payout such that the casino's minimum makes payout at the true Odds impossible for anyone playing should be illegal as it amounts to a false advertisement.

If you want to do that, just change the return table!!!

Quote: mickeycrimm

Perhaps Crystalmath could get his buddy to send him some screen shots of a keno game called Hot "n Hotter. Especially the 6-spot and 9-spot. It's a progressive/banking game. I'd like to get his take on the game. I put the cost at about $350 on the game, but my math may be faulty.

I made a mistake here. It should read "I put the cost at about $350 when there is just one symbol to go to win the progressive meter."

According to the website, you only get 8 free games during the Fever Games Bonus, all of which must be winners to collect the progressive. Also, if these are VLT's, then isn't strategy moot?

http://www.spielo.com/games/vlt-public-gaming/jokers-vaulttm-poker

Quote: camapl

According to the website, you only get 8 free games during the Fever Games Bonus, all of which must be winners to collect the progressive. Also, if these are VLT's, then isn't strategy moot?

http://www.spielo.com/games/vlt-public-gaming/jokers-vaulttm-poker

The Joker's Vault game you are reading about online has a different configuration than the game in Montana.

Quote: mickeycrimm

The Joker's Vault game you are reading about online has a different configuration than the game in Montana.

That's excellent news (because it can be calculated)!

Quote: mickeycrimm

...If you win 8 out of the ten free games you win the progressive meter. This is the math I'm stuck on. I have a vague idea of how to do it but I'm not really sure. The WVP game stats for Double Joker shows that you will make a garbage hand 64.2% of the time. Which means your chances of winning your next hand is 35.8%...

You might want to consider your strategy shift(s) prior to calculating this value, as the chance of winning/losing a hand can be (slightly) affected. Nevertheless, here is one way to calculated it without double counting.

Exactly 8 winners in 8 hands:
Take 0.358 to the power of 8 and multiply it by the 1 way it may occur.

Exactly 8 winners in 9 hands with a winner on the 9th:
Take 0.358 to the power of 8, multiply it by 0.642, and multiply the result by the 8 ways that it may occur.

Exactly 8 winner in 10 hands with a winner on the 10th:
Take 0.358 to the power of 8, multiply it by 0.642 twice, and multiply the result by the 36 ways that it may occur.

Finally, add the three results above together to get the chance of hitting the jackpot once you are in the bonus. Once you determine the chance of playing the bonus, you can determine the overall chance of hitting the progressive. This would be the chance of getting a full house in regular mode times the chance of winning 8 hands during the bonus. CORRECTION: the chance of getting any Full House times...


As for the strategy during the bonus, treat it like the initial hand in Multi-Strike. Determine a value to add to each winning hand (based on either the current or seed value of the progressive) and re-analyze the paytable for Double Joker. Determine the return of the bonus round (including progressive) in order to determine the value of a Full House in normal mode. These calculations would resemble those for Shockwave Poker. Considering the recursive nature (triggering a bonus within a bonus) gets tricky, especially if bonuses are awarded for multiple Full Houses during bonus play. You could disregard this in your calculation to determine progressive frequency and overall return, and just eat them up as gravy!

Quote: camapl

That's excellent news (because it can be calculated)!



You might want to consider your strategy shift(s) prior to calculating this value, as the chance of winning/losing a hand can be (slightly) affected. Nevertheless, here is one way to calculated it without double counting.

Exactly 8 winners in 8 hands:
Take 0.358 to the power of 8 and multiply it by the 1 way it may occur.

Exactly 8 winners in 9 hands with a winner on the 9th:
Take 0.358 to the power of 8, multiply it by 0.642, and multiply the result by the 8 ways that it may occur.

Exactly 8 winner in 10 hands with a winner on the 10th:
Take 0.358 to the power of 8, multiply it by 0.642 twice, and multiply the result by the 36 ways that it may occur.

Finally, add the three results above together to get the chance of hitting the jackpot once you are in the bonus. Once you determine the chance of playing the bonus, you can determine the overall chance of hitting the progressive. This would be the chance of getting a full house in regular mode times the chance of winning 8 hands during the bonus.


As for the strategy during the bonus, treat it like the initial hand in Multi-Strike. Determine a value to add to each winning hand (based on either the current or seed value of the progressive) and re-analyze the paytable for Double Joker. Determine the return of the bonus round (including progressive) in order to determine the value of a Full House in normal mode. These calculations would resemble those for Shockwave Poker. Considering the recursive nature (triggering a bonus within a bonus) gets tricky, especially if bonuses are awarded for multiple Full Houses during bonus play. You could disregard this in your calculation to determine progressive frequency and overall return, and just eat them up as gravy!

Camapl, thank you, CrystalMath, and vetsen so much for taking me to math class. I might be getting the hang of it. I'm gonna put the equation up long hand and. hopefully, you guys can tell me if I did it right. But first.

Yes, you can retrigger more free games in Double Joker mode. You are eligible to do this up to 9 times. And the Full House frequency is 56.062 in that mode.

For software I have Win, Frugal, and WVP (Wolf Video Poker). I mostly use WVP these days because it has functions I really like, like Tweaking The Strategy Chart. I analyzed the Joker's Vault payscale. The basic chart came up 73.588%. And 67.71 was the Full House frequency. CrystalMath stated that you actually average 12.17 games in Double Joker mode. So I took that number and recalculated the ER of dealt hands that can make a Full House. Then I tweaked the strategy chart, i.e., putting those dealt hands that can make a Full House in their proper places in the strategy chart. Then I analyzed. The new return came up 73.4371%. And 66.4632 was the new Full House frequency.

I calculated the cost to produce a Full House with no strategy shift, 67.71 times 50 cents for a total wager of $33.855, then multiplied that by .73588 for a return of $24.835. So the cost is $9.02.

Then I calculated the cost to produce a Full House with the strategy shift, 66.4632 times 50 cents for a total wager of $33.2316, then multiplied that by .734371 for a return of $24.4043. So the cost is $8.8273. So it's actually 19.27 cents cheaper to make a Full House using the strategy shift.

Now, from reading Mission145's equations I take it that this symbol, *, means times. So here I go making an ass out of myself for all the world to see. But I really want to know how to do this. Hopefully, camapl, I'm interpreting your formula for calculating the frequency of winning at least 8 of ten hands correctly:

.358 * .358 * .358 * .358 * .358 * .358 * .358 * .358 = .0002697 Multiplied by 1 it is still = .0002697

.358 * .358 * .358 * .358 * .358 * .358 * .358 * .358 * .642 = .0001731 Multiplied by 8 = .0013848

.358 * .358 * .358 * .358 * .358 * .358 * .358 * .358 * .642 * .642 = .0001111 Multiplied by 36 = .0039996

Then we add 'em all up. The total is .0056541. Dividing 1 by .0056541 = 176.8628. So with no strategy shift in Double Joker mode I will average winning at least 8 out of ten games every 176.8628 times I get ten free games.

CrystalMath gave the average number of Double Joker games as 12.17. So wouldn't that mean that per 176.8628 times I win ten free games I will get an extra 383.79 games (2.17 times 176.8628)? That equates to 38.379 times I will retrigger 10 free games while in Double Joker mode per 176.8628 times I'm in it. If that is the case then I would have to make a Full House in Single Joker mode an average of only 138.4838 times to take the progressive off. That is, without a strategy shift in Double Joker mode.

So 138.4838 times 66.4632 means a cycle of 9204 Single Joker games to take the progressive off.

If I did everything right then the payback for the game playing straight through would be:

The base game is 73.4371%
12.17 divided by 66.4632 equals an 18.3209% add-on
The $100 already In the meter would add 2.17296% (200 bets divided by 9204)
Plus a 1.6666% meter. (CrystalMath, I went and checked a couple of machines. The help screen said one nickel per $3 wager goes in meter)

Totaling everything up, the payback to this game should be 95.5976% playing straight through. But there is still the question of a strategy shift in Double Joker mode. Oh, well. I'll worry about that after I see whether you guys give me a passing grade on what I've done so far.

Thank you all for the help.

Mickey

One more thing. The strategy shift in Single Joker mode really simplified the strategy chart. Discounting the obvious holds, there are only 14 moves in the non-joker hands, and only 16 moves in the joker hands.

Well, guys. I gotta go to the town just over for a couple of days to see if I can make some money. I'll Catcha when I get back. Take care.

Quote: mickeycrimm

...Hopefully, camapl, I'm interpreting your formula for calculating the frequency of winning at least 8 of ten hands correctly:

.358 * .358 * .358 * .358 * .358 * .358 * .358 * .358 = .0002697 Multiplied by 1 it is still = .0002697

.358 * .358 * .358 * .358 * .358 * .358 * .358 * .358 * .642 = .0001731 Multiplied by 8 = .0013848

.358 * .358 * .358 * .358 * .358 * .358 * .358 * .358 * .642 * .642 = .0001111 Multiplied by 36 = .0039996

Then we add 'em all up. The total is .0056541. Dividing 1 by .0056541 = 176.8628. So with no strategy shift in Double Joker mode I will average winning at least 8 out of ten games every 176.8628 times I get ten free games...

Happy to help mickeycrimm! The analysis of this game peaks my interest! Edit: lol piques...

Your numbers above match fairly closely with mine (I would attribute the difference to rounding):
8 in 8 is 0.0272%
8 in 9 is 0.1393%
8 in 10 is 0.4036%
This give a 0.5706% chance of hitting the progressive during any 10-game bonus round if you don't adjust Dbl Jkr strategy. The expected cycle length is 175.24 10-game bonus rounds to win at least 8 hands and win the progressive.

As for the rest of your analysis, it looked like a very good "back of the envelope" estimate. I'll be curious to see how our "final" number compare to your 95.6%! I am working out (for now in my head) a good way to account for both retriggers and the progressive during any given 10-hand bonus round. Don't think we have to get too fancy, as strategy shifts don't increase Full House frequencies a great deal. The dial just doesn't move like it does for SF's and RF's.

Hope your trip bears success!

Camapl, I just tweaked the strategy chart for the Double Joker phase of the game. The Tweak the Strategy Chart function on WVP is a great tool for trying to solve the puzzle presented by games like Joker's Vault. I don't know if you have WVP. I can move hands up and down the strategy chart then re-analyze to get all the game stats and payback percentage.

All the dealt hands that can make a Full House go up in value. The changes were:

Non-Joker Hands

1. A Pair plays over SF3 +0 and ST4 -1
2. RF2, Ace High plays over FL3

One-Joker Hands

1. W + a Mid-Range Card plays over a SF3 -3
2. SF3 -1, -2, plays over a FL 4
3. 3K plays over SF3 -1, -2

Two-Joker Hands

1. The strategy chart is perfect except for this type of hand: W-W-QH-7H-2H. Believe it or not the W W 7 plays over the pat flush. It has an ER of 5.12 bets compared to the 5 bets that the flush represents. It has to do with the WW7 already being a paying hand and it's possible to make a Full House.

Here's the new stats.

The tweaked chart has a payback of 109.0371%
You make a Full House every 55.2 games
The chances of making a paying hand is 36.1322%

All of the strategy adjustments not only improve the chances of making a Full House, they also improve the chances of making a paying hand. I'm gonna call this strategy the Double Joker Basic Strategy. It's definitely the strategy to use if you have already lost 3 games. But I can see a ton more strategy adjustments coming for when you are still eligible for the progressive meter. I took a look at some hands. I based this off of a $400 (800 bets) progressive meter as I don't think I'll be playing a number lower than that. Some of this stuff is glaringly obvious. And I think you hit the nail on the head when you said one has to use a multi-strike type strategy.

Say I've won 7 out of 9 hands then get dealt a W-5H-6H-7H-7D. Basic strategy calls for playing the SF4. But with W-7-7 you have a paying hand and would take down the progressive. There's no way in hell I would go for the SF. Even if you had only won 6 out of 8 at that point you wouldn't play the SF4 because you have at least a 36.1322% chance of winning the next hand and taking down the $400 meter. And my guess is if you had only won 5 out of 7 at that point you would still probably hold the paying hand, but I'm gonna have to figure out a way to do the math on it.

Because of the new numbers I'm gonna have to start back over and multiply 36.1322% to the 8th power, and so on, to get a new set of numbers.

This is how far I've gotten today. Take care.

Mickeycrimm, looks like you've put some time in... The feature on WVP that allows strategy tweaks looks like it would be very useful! Especially when it comes to simplifying a strategy and seeing how it affects your bottom line. I don't currently have any VP analysis software - just relying on JB's strategy calculator on WoO and pasting into Excel in order to manipulate my calculations. I have considered purchasing the one put out by Dan Paymar, but I don't even recall which one is his... Is this one of the ones you use?

Funny, at first, I thought holding W W Q would be superior to W W 7 in your Two Joker hold example because of the wild royal, but then I realized it's not just the increase in straights, but straight flushes as well that makes W W 7 the most lucrative choice.

As for strategy adjustments, I'm thinking that we have two issues: (1) Determine a somewhat simplified strategy for determining the return of the game, the frequency of the progressive, and thus the play point. (2) Determine a set of strategies to use during the bonus rounds for a given number of wins and losses during each 10-game set and the value of the progressive.

In working towards (1), I've been tweaking a single strategy during the bonus round to maximize the value of a Full House at any time. Thru many iterations, I have narrowed down to a single strategy for Double Joker using the paytable below which is our base paytable with a FH value of 22.9131 and a value of 2.6147 added to each winning hand:

RF..........802.6147
5k..........242.6147
JR..........112.6147
SF............37.6147
4K............14.6147
FH.............25.5278
FL........ .....7.6147
ST.............6.6147
3K.............3.6147
2P.............3.6147

Analyzing this paytable and plugging in our original values with the adjusted FH at 22.9131 results in a Full House with the following value:
Full House pays: 8.0000
Value of 10 free hands: 10 X 135.4672% = 13.5467 (10 hands time the resulting return)
Value of progressive: 200 X 0.6832% = 1.3664 (progressive reset in bets times the probability of hitting during any 10-hand bonus round)
Total: 22.9131

If you play around with the numbers added to each winning combination in the paytable above, you will find that lowering or raising the number will decrease the value of the Full House. Note that the value of a Full House in bonus mode is calculated by pieces of the resulting analysis from using that same value for the Full House, such as the probability of winning or losing a hand and by the overall return. In a manner of speaking, the value of the Full House determines the value of the Full House; thus, the iterative process. I started with 8, and increased as needed based on the resulting calculated value until I found that using 22.9131 resulted in the same value. This requires plugging values into the VP Analyzer, waiting for results, updating the Combinations column, adjusting the value of the Full House, and repeating (then changing the value added to each winning hand and repeating, repeatedly). Seem repetitious? lol

I had originally surmised that the value added to each winning hand would be around 25, the progressive reset value in bets divided by the number of winning hands needed, but that turned out to be way too high. What little you gain in progressive opportunities does not outweigh the harm that you do to the return of the 10 free games. (Of course, this will be different once we are actually playing.) As these are the two variable components that make up the value of the Full House that triggered a new bonus round, it seemed logical to maximize the value of the Full House that resulted in the same value of the Full House, so to speak. Fortunately, this same figure of 22.9131 may be used to express the value of a Full House in regular mode (on the “single” Joker paytable), with the value of the bonus round and progressive all wrapped up in a tidy bundle.

Using the “single” Joker paytable below, I get an overall return for JOKER’S VAULT of 95.9512% (if the jackpot was not a progressive). Keep in mind that this is a close approximation using a single strategy for each bonus hand and that it does not account for the limit on re-triggers.
RF..........800
5k..........240
JR..........110
SF............35
4K............12
FH.............22.9131
FL........ .....5
ST.............4
3K.............1
2P.............1

I think I'll pause here before I continue with the calculation of the progressive frequency and finally, get to the strategies to use during play.

Quote: camapl

Mickeycrimm, looks like you've put some time in... The feature on WVP that allows strategy tweaks looks like it would be very useful! Especially when it comes to simplifying a strategy and seeing how it affects your bottom line. I don't currently have any VP analysis software - just relying on JB's strategy calculator on WoO and pasting into Excel in order to manipulate my calculations. I have considered purchasing the one put out by Dan Paymar, but I don't even recall which one is his... Is this one of the ones you use?

Funny, at first, I thought holding W W Q would be superior to W W 7 in your Two Joker hold example because of the wild royal, but then I realized it's not just the increase in straights, but straight flushes as well that makes W W 7 the most lucrative choice.

As for strategy adjustments, I'm thinking that we have two issues: (1) Determine a somewhat simplified strategy for determining the return of the game, the frequency of the progressive, and thus the play point. (2) Determine a set of strategies to use during the bonus rounds for a given number of wins and losses during each 10-game set and the value of the progressive.

In working towards (1), I've been tweaking a single strategy during the bonus round to maximize the value of a Full House at any time. Thru many iterations, I have narrowed down to a single strategy for Double Joker using the paytable below which is our base paytable with a FH value of 22.9131 and a value of 2.6147 added to each winning hand:

RF..........802.6147
5k..........242.6147
JR..........112.6147
SF............37.6147
4K............14.6147
FH.............25.5278
FL........ .....7.6147
ST.............6.6147
3K.............3.6147
2P.............3.6147

Analyzing this paytable and plugging in our original values with the adjusted FH at 22.9131 results in a Full House with the following value:
Full House pays: 8.0000
Value of 10 free hands: 10 X 135.4672% = 13.5467 (10 hands time the resulting return)
Value of progressive: 200 X 0.6832% = 1.3664 (progressive reset in bets times the probability of hitting during any 10-hand bonus round)
Total: 22.9131

If you play around with the numbers added to each winning combination in the paytable above, you will find that lowering or raising the number will decrease the value of the Full House. Note that the value of a Full House in bonus mode is calculated by pieces of the resulting analysis from using that same value for the Full House, such as the probability of winning or losing a hand and by the overall return. In a manner of speaking, the value of the Full House determines the value of the Full House; thus, the iterative process. I started with 8, and increased as needed based on the resulting calculated value until I found that using 22.9131 resulted in the same value. This requires plugging values into the VP Analyzer, waiting for results, updating the Combinations column, adjusting the value of the Full House, and repeating (then changing the value added to each winning hand and repeating, repeatedly). Seem repetitious? lol

I had originally surmised that the value added to each winning hand would be around 25, the progressive reset value in bets divided by the number of winning hands needed, but that turned out to be way too high. What little you gain in progressive opportunities does not outweigh the harm that you do to the return of the 10 free games. (Of course, this will be different once we are actually playing.) As these are the two variable components that make up the value of the Full House that triggered a new bonus round, it seemed logical to maximize the value of the Full House that resulted in the same value of the Full House, so to speak. Fortunately, this same figure of 22.9131 may be used to express the value of a Full House in regular mode (on the “single” Joker paytable), with the value of the bonus round and progressive all wrapped up in a tidy bundle.

Using the “single” Joker paytable below, I get an overall return for JOKER’S VAULT of 95.9512% (if the jackpot was not a progressive). Keep in mind that this is a close approximation using a single strategy for each bonus hand and that it does not account for the limit on re-triggers.
RF..........800
5k..........240
JR..........110
SF............35
4K............12
FH.............22.9131
FL........ .....5
ST.............4
3K.............1
2P.............1

I think I'll pause here before I continue with the calculation of the progressive frequency and finally, get to the strategies to use during play.

No, it looks like you've put in a lot of work. I'm still studying it but I can answer your simple questions first. First, the W W Q 7 2 hand. The W W Q and
W W 7 are actually tied in ER at 5.12 bets. I went with the W W 7 because it has much lower variance than W W Q. It has 522 combinations out of 1176 to improve, where the W W Q has only 432 combinations to improve.

Re: Software

I bought my first computer in 2002, and quickly bought Bob Dancer's Winpoker. It was great for it's day but doesn't have a strategy generating component. Then I bought Frugal Video Poker, which was developed by Jim Wolf, in order to have a strategy generating component. My next move was to buy Wolf Video Poker, also developed by Jim Wolf. It's a souped up version of Frugal Video Poker. It has more advanced functions. Which means that Frugal is now out of date. However, it can be downloaded for free on the WVP website.

The two analyzers I don't own and have never used are Bob Dancer's Video Poker For Winners and Dan Paymar's Video Poker Optimum Play. I haven't bought them because I figure I don't need them. From what I've been told, on VPFW you can't zero in on a progressive royal. You can analyze for a 4000 coin royal, 5000 coint, etc. But you can't analyze for numbers like 4873, or 5647, etc. That would be to much pain in the ass for me, especially since WVP has that function.

As for Paymar's VPOP, I've heard it has the most advanced bankroll calculator. WVP has a bankroll calculator but I never use it. I'm either over bankrolled for a play or I don't play it. I don't like sweating a play. As for the rest of VPOP's functions, fivecard, who sometimes posts here and also on vpFREE, was not to impressed with it. I know fivecard is an exceptionally talented video poker pro. I'll take his word for it that I don't need it.

I've never used the WOO calculator so I can't comment on it.

But this one function that WVP has, tweaking the strategy chart is the nuts. WVP comes preloaded with games, all the Jacks or Better, Bonus Poker, Kicker Games, Multi Pays, Deuces, Jokers, Deuces and Joker, One Eyed Jacks, and Pickem games. Joker's Vault is a game that can't be fully analyzed by any software on the market. And I've encountered many more games that can't. But this is what I could do with WVP:

I go in, find a single joker game, and pull it up. Then I change the payscale to the Joker's Vault Single Joker's game and analyze. It only takes a few seconds. I get the payback percentage, all the game stats ( how often you make a 3K, ST, FL, etc.), and the strategy. In Joker's Vault all the hands that can make a Full House go up in value. So I determine the true expected value of those hands, then tweak the strategy chart to reflect those values. In essence, I'm moving the hands that make a Full House up in the strategy chart to their proper places.

Then I hit the analyze tab and voila! It spits out the payback percenatage and the game stats. I then give the game a name and save it into the library for future reference. I did the same for the Double Joker phase of the game.

Quote: camapl

Using the “single” Joker paytable below, I get an overall return for JOKER’S VAULT of 95.9512% (if the jackpot was not a progressive). Keep in mind that this is a close approximation using a single strategy for each bonus hand and that it does not account for the limit on re-triggers.
RF..........800
5k..........240
JR..........110
SF............35
4K............12
FH.............22.9131
FL........ .....5
ST.............4
3K.............1
2P.............1

Camapl, this is great news! I recalculated after tweaking the strategy chart on the Double Joker phase of the game. I came up with 95.7133%. I was wondering how close I was. It's very close to your number. With the meter thrown in, 97.38%.

mickeycrimm, thanks for the review of the analysis software out there - it will help me decide if and when I am ready to purchase... It's not that any of them are too expensive, it's just that I have most of what I need for free right now, so it's just a matter of principle. What I need to consider, though, is my time - the ability to tweak the strategy in WVP seems like it would be a time saver, and although I know how to calculate ROR in Excel, it can be time consuming. Both WVP and VPOP might prove to be valuable time savers for me. I guess I could start with Frugal, just in case it offers games that WoO doesn't...

One feature, which I believe is included in VPOP, that I could definitely use is the ability to analyze natural hands in wild games. How often to you see promotions that center around natural 4-of-a-kinds? Another feature that would interest me, for similar reasons, would be customizable paytables, especially for distinguishing certain 4-of-a-kinds from others and possibly even certain full houses. Quite often, the 4-of-a-kind promotions are geared around a certain set of quads, like 4 5's through 10's. Currently, I use SDB to analyze the games, but there are limitations. Kicker games must be tweaked further and wild games are left out completely by me. At one of my local casinos, there is a Double Double Jackpot version of VP Bingo, in which a block of 25 different hands, including certain quads and full houses, comprise a bingo sheet. Depending on how many bingos are one away from winning the 250-coin bonus, the game is definitely playable quite often. Being able to isolate some of the quads and full houses would be useful both for this game and for "Card of the Day" promotions.

As for picking W W 7 over W W Q, I think that is a wise choice. Typically, the analyzers pick the choice with less variance when the expected values are equal. It seems to me that the hold with lower variance would also be the hold that is more likely to yield a winning hand. Would you agree? Since we are rewarded (with the progressive jackpot) for a 8 winning hands out of 10, this strategy would be aligned with two of our objectives: winning the progressive and preserving our bankroll until we do!

As I mentioned above, being able to tweak a strategy by hand could be useful. Bear in mind that making these choices by hand could be sub-optimal. How do you know that you have switched the right items in your list of holds? Also, it might be easy for someone without much experience to overlook a re-ordering that could be advantageous. I am sure this is not the case with you, mickeycrimm, as you have been using the software for quite some time and before that, you were doing your own longhand calculations! (I read and thoroughly enjoyed the "I remember when" thread!) Besides, 95.7133% is not too far from 95.9512%, and your method probably took you a lot less time! Besides, my result is just an estimate based on a flat strategy in bonus mode and I have not accounted for limited retriggers...

Speaking of limited re-triggers, I am assuming that any given bonus round could be extended to a total of 100 hands. If I'm not mistaken, mickeycrimm, you indicated that up to 9 re-triggers are allowed. While it is possible to land a Full House that does not trigger a bonus round, it is very unlikely! Not only would you have to get 10 Full Houses (with an average cycle of around 54 hands) within 100 hands, you would have to have them spread throughout such that each one happens before the previous round(s) had been completed. In other words, you would have to get at least 1 in 10 hands, at least 2 in 20 hands, at least 3 in 30 hands, ...and likewise, all the way up to at least 10 in 100 hands of bonus play! If and when this happens, all Full Houses after the 9th during this long bonus round would still be valued at 8 units (rather than 22.9131), and the overall return of the subsequent hands would potentially be higher, as you would no longer be bending towards hitting a Full House only towards winning the progressive, if it is still in play, during the remaining 10-hand round(s). I think we can safely say that the limit on re-triggers has a very small effect on both the overall return and the progressive frequency, thus there is no dire need to calculate the chances of this event.

Quote: camapl

mickeycrimm, thanks for the review of the analysis software out there - it will help me decide if and when I am ready to purchase... It's not that any of them are too expensive, it's just that I have most of what I need for free right now, so it's just a matter of principle. What I need to consider, though, is my time - the ability to tweak the strategy in WVP seems like it would be a time saver, and although I know how to calculate ROR in Excel, it can be time consuming. Both WVP and VPOP might prove to be valuable time savers for me. I guess I could start with Frugal, just in case it offers games that WoO doesn't...

One feature, which I believe is included in VPOP, that I could definitely use is the ability to analyze natural hands in wild games. How often to you see promotions that center around natural 4-of-a-kinds? Another feature that would interest me, for similar reasons, would be customizable paytables, especially for distinguishing certain 4-of-a-kinds from others and possibly even certain full houses. Quite often, the 4-of-a-kind promotions are geared around a certain set of quads, like 4 5's through 10's. Currently, I use SDB to analyze the games, but there are limitations. Kicker games must be tweaked further and wild games are left out completely by me. At one of my local casinos, there is a Double Double Jackpot version of VP Bingo, in which a block of 25 different hands, including certain quads and full houses, comprise a bingo sheet. Depending on how many bingos are one away from winning the 250-coin bonus, the game is definitely playable quite often. Being able to isolate some of the quads and full houses would be useful both for this game and for "Card of the Day" promotions.

As for picking W W 7 over W W Q, I think that is a wise choice. Typically, the analyzers pick the choice with less variance when the expected values are equal. It seems to me that the hold with lower variance would also be the hold that is more likely to yield a winning hand. Would you agree? Since we are rewarded (with the progressive jackpot) for a 8 winning hands out of 10, this strategy would be aligned with two of our objectives: winning the progressive and preserving our bankroll until we do!

As I mentioned above, being able to tweak a strategy by hand could be useful. Bear in mind that making these choices by hand could be sub-optimal. How do you know that you have switched the right items in your list of holds? Also, it might be easy for someone without much experience to overlook a re-ordering that could be advantageous. I am sure this is not the case with you, mickeycrimm, as you have been using the software for quite some time and before that, you were doing your own longhand calculations! (I read and thoroughly enjoyed the "I remember when" thread!) Besides, 95.7133% is not too far from 95.9512%, and your method probably took you a lot less time! Besides, my result is just an estimate based on a flat strategy in bonus mode and I have not accounted for limited retriggers...

WVP has a function for bonuses on four of a kinds. You can set each and every four of a kind to whatever value you want. And in the wild card games you can split natural and wild payoffs. For instance if you split natural and wild payoffs on FPDW it will show you make 4 Deuces every 4884.7 games and a natural Three's thru Aces every 598.9 games. Then it's just a matter of averaging it to show you will make a natural quad every 533.5 games. The Joker games have the same functions.

I know the Bingo game you are speaking of. I thought they were extinct. It's a Sigma game called Jackpot Card. They used to have multitudes of them in Laughlin. This was before I was computerized. 6/5 DDJB was 94.9%. Dan Paymar used a simple rule of thumb by adding 0.9% for every way you could make a bingo. I played them when they were 9, 10 or 11 ways. On rare occasions I found the game where a certain Full House or certain Flush made a bingo. WVP will serve your purpose on this game as far as the quads go. But I don't know of any software where you can change the value of a certain Full House. I'll get back to you later for the rest of your post.

Quote: camapl

Speaking of limited re-triggers, I am assuming that any given bonus round could be extended to a total of 100 hands. If I'm not mistaken, mickeycrimm, you indicated that up to 9 re-triggers are allowed. While it is possible to land a Full House that does not trigger a bonus round, it is very unlikely! Not only would you have to get 10 Full Houses (with an average cycle of around 54 hands) within 100 hands, you would have to have them spread throughout such that each one happens before the previous round(s) had been completed. In other words, you would have to get at least 1 in 10 hands, at least 2 in 20 hands, at least 3 in 30 hands, ...and likewise, all the way up to at least 10 in 100 hands of bonus play! If and when this happens, all Full Houses after the 9th during this long bonus round would still be valued at 8 units (rather than 22.9131), and the overall return of the subsequent hands would potentially be higher, as you would no longer be bending towards hitting a Full House only towards winning the progressive, if it is still in play, during the remaining 10-hand round(s). I think we can safely say that the limit on re-triggers has a very small effect on both the overall return and the progressive frequency, thus there is no dire need to calculate the chances of this event.

I'm with you on this one. I don't think we need to worry about that frequency of occurrence.

Good to know that WVP handles natural quads as well.

Yeah, Jackpot Card is on a pair of linked quarter machines (sharing the same card) at Cactus Jack's Casino in Carson City (near the restrooms). You are spot on that it is DDJ 6/5; however, the Royal pays off at 959 bets, so the return of the base game is a little higher at 95.2807%. Also, I've seen Paymar's write-up of DB Jackpot Card and his reference to adding 0.9% for every bingo line that is one quad away. In DDJ, the average quad is a bit more likely since trip faces beats dealt Full Houses (in addition to trip Aces), so I add 0.9407% for each quad-away bingo line. Obviously, analyzing the current combination of quads needed would yield different results, depending on which quads are needed and how many bingos a given quad would complete. Also, you could alter your strategy for any given situation on the bingo card as well. Adding 0.9407% makes 5 quad-away bingos just under break-even at 99.9843% (Cactus Jack's has no player's card). As Paymar mentions in his article, any one-away bingos that need a lesser hand would be playable regardless. I've had some not-so-good sessions on these games, as the variance is relatively high any time you're playing a 6-5-4-3-1-1 game.

Frequency of the Progressive Jackpot:

In order to determine the overall frequency of hitting the progressive, I have performed the calculations below:

On average, a Regular Full House occurs once every 66.2531 regular hands.
A Bonus Round occurs exactly once every Regular Full House.
On average, a Bonus Full House occurs once every 53.6677 bonus hands.
The average number of hands during a Bonus Round is 12.3118.
The average number of 10-hand bonus sets per Bonus Round is 1.2312.
On average, the Progressive Jackpot hits once every 146.3695 10-hand bonus sets.

Therefore, on average, the Progressive Jackpot hits once every 7,877 paid hands.

The two Full House frequencies come directly from the respective VP analyses of playing regular hands and bonus hands. Using that of the Bonus Full House, I calculated the average number of hands during a Bonus Round (not too different from 12.17 quoted by CrystalMath). The duration of a Bonus Round is calculated by determining the percent of the rounds that will be 10 hands, 20 hands, 30 hands, ...and so on to 100 hands and taking a weighted average. The calculation for 10 through 90 hands is similar to that of calculating the probability of hitting the progressive during a 10-hand bonus, except we are using the probability to hit or miss Bonus Full Houses rather than to win or lose a bonus hand. For the probability of a 100-hand Bonus Round, I "cheated" and subtracted the other 9 probabilities from 100%. I typically prefer not to do this, and eventually, I will think of a way to calculate this probability without having to calculate the ways of getting from 10 to 100 Full Houses in 100 hands! (As it turns out, the probability of a 100 hand Bonus Round is 0.0575% of all Bonus Rounds, which reinforces the idea that the limit on re-triggers is of little consequence.) The Progressive cycle in paid hands is given by multiplying the number of regular hands per Bonus Round (66.2531) by the number of 10-hand bonus sets per Progressive Jackpot (146.3695) and dividing the result by the number of 10-hand sets per Bonus Round (1.2312).

At first, I mistakenly thought that I needed to calculate the frequencies over all hands played, but in order to calculate the cost of the progressive, and thus the break-even and play points, we only need to consider paid hands. Before I realized this and corrected my calculation, I determined some the following:

The average number of regular and bonus hands per Regular Full House is 78.5649.
The average number of any Full Houses per Regular Full House is 1.2294.
The expected frequency of any Full House is 63.9047 played hands. This is also the expected frequency of any 10-hand bonus set.
The expected frequency of the Progressive Jackpot is 9,354 played hands, including both paid and free hands. This is not the number that we need for our Optimal Play Number.

Quote: camapl

Frequency of the Progressive Jackpot:

In order to determine the overall frequency of hitting the progressive, I have performed the calculations below:

On average, a Regular Full House occurs once every 66.2531 regular hands.
A Bonus Round occurs exactly once every Regular Full House.
On average, a Bonus Full House occurs once every 53.6677 bonus hands.
The average number of hands during a Bonus Round is 12.3118.
The average number of 10-hand bonus sets per Bonus Round is 1.2312.
On average, the Progressive Jackpot hits once every 146.3695 10-hand bonus sets.

Therefore, on average, the Progressive Jackpot hits once every 7,877 paid hands.

The two Full House frequencies come directly from the respective VP analyses of playing regular hands and bonus hands. Using that of the Bonus Full House, I calculated the average number of hands during a Bonus Round (not too different from 12.17 quoted by CrystalMath). The duration of a Bonus Round is calculated by determining the percent of the rounds that will be 10 hands, 20 hands, 30 hands, ...and so on to 100 hands and taking a weighted average. The calculation for 10 through 90 hands is similar to that of calculating the probability of hitting the progressive during a 10-hand bonus, except we are using the probability to hit or miss Bonus Full Houses rather than to win or lose a bonus hand. For the probability of a 100-hand Bonus Round, I "cheated" and subtracted the other 9 probabilities from 100%. I typically prefer not to do this, and eventually, I will think of a way to calculate this probability without having to calculate the ways of getting from 10 to 100 Full Houses in 100 hands! (As it turns out, the probability of a 100 hand Bonus Round is 0.0575% of all Bonus Rounds, which reinforces the idea that the limit on re-triggers is of little consequence.) The Progressive cycle in paid hands is given by multiplying the number of regular hands per Bonus Round (66.2531) by the number of 10-hand bonus sets per Progressive Jackpot (146.3695) and dividing the result by the number of 10-hand sets per Bonus Round (1.2312).

At first, I mistakenly thought that I needed to calculate the frequencies over all hands played, but in order to calculate the cost of the progressive, and thus the break-even and play points, we only need to consider paid hands. Before I realized this and corrected my calculation, I determined some the following:

The average number of regular and bonus hands per Regular Full House is 78.5649.
The average number of any Full Houses per Regular Full House is 1.2294.
The expected frequency of any Full House is 63.9047 played hands. This is also the expected frequency of any 10-hand bonus set.
The expected frequency of the Progressive Jackpot is 9,354 played hands, including both paid and free hands. This is not the number that we need for our Optimal Play Number.

Camapl, I'm still tinkering with the Single Joker strategy chart but so far I have it very close to your number. At this point the strategy produces a Full House every 66.3185 games which is very close to your number of 66.2531 games. I'll put it up when I finish.

Fair enough, mickeycrimm! These numbers do not need to match exactly, as we are only trying to get an idea of the value of the game and the jackpot. It is reassuring to see that our figures are close to each other, even if they are approximations.

As for the value...

If the rate of Meter Rise is 1.5%, then we have the following:

Bet: $0.50
Reset: $100.00
Meter Rise: 1.5%
Exp Cycle: 7,877
Return at Reset: 95.9512%
Total Exp Bet: $3,938.27
Exp Jackpot: $318.53
Exp Cost/Breakeven/Optimal Play Number: $259.45
Exp Profit: $59.07
Profit / Bet: $0.0075
Prob Jpt is Playable: 6.7247%
Playable Jpts: 1 in 14.87
Avg Val All Jpts (V): $3.97


If, however, the rate of Meter Rise is 2%, then we have the following changes:

Meter Rise: 2%
Exp Jackpot: $338.22
Exp Cost/Breakeven/Optimal Play Number: $259.45
Exp Profit: $78.77
Profit / Bet: $0.0100
Prob Jpt is Playable: 13.2055%
Playable Jpts: 1 in 7.57
Avg Val All Jpts (V): $10.40


As the Expected Cycle did not change, neither does the Expected Total Bet Amount nor the Expected Cost/Optimal Play Number. Also, it is no coincidence that the Profit Per Bet is the Meter Rise times the Bet. This is true only if you start playing exactly and the Optimal Play Number (and use the simplified strategies based on my approximations of the value of Bonus Rounds). Some of the numbers at the bottom are meaningless on their own - use them to compare the value of the meter being 2% instead of 1.5%. If the meter moves just a bit faster, the game becomes playable more often AND you expect to earn more each time you play.

Quote: mickeycrimm

...And I think you hit the nail on the head when you said one has to use a multi-strike type strategy.

Say I've won 7 out of 9 hands then get dealt a W-5H-6H-7H-7D. Basic strategy calls for playing the SF4. But with W-7-7 you have a paying hand and would take down the progressive. There's no way in hell I would go for the SF. Even if you had only won 6 out of 8 at that point you wouldn't play the SF4 because you have at least a 36.1322% chance of winning the next hand and taking down the $400 meter. And my guess is if you had only won 5 out of 7 at that point you would still probably hold the paying hand, but I'm gonna have to figure out a way to do the math on it.

...

When it comes to playing the game, clearly we can improve the simplified strategy that I used to calculate the value of the game. I would start by grouping different states within each 10-hand set, much like you started to a few pages ago (above).

Group 0: Regular Hands
Use a strategy for single Joker based on actual payouts, except use 22.9131 for the Full House.
There may be value in playing even stronger towards the Full House in order to gain more frequent access to a high Progressive Jackpot.

Group 1A: You already have 8 winning hands during the current 10-hand bonus set.
Play the remaining hands of the set using a strategy for Double Joker based on actual payouts, except use 22.9131 for the Full House.
Winning hands do not carry a premium for the remainder of this set, as you have just won the required number of hands.
There is little value in playing stronger towards the Full House, as you have just won and reset the Progressive Jackpot.

Group 1B: You already have 3 losing hands during the current 10-hand bonus set.
Play the remaining hands of the set using a strategy for Double Joker based on actual payouts, except use 22.9131 for the Full House.
Winning hands do not carry a premium for the remainder of this set, as you have just won the required number of hands.
There may be value in playing even stronger towards the Full House in order to gain more frequent access to a high Progressive Jackpot.

Groups 2 thru N to come...

Quote: camapl

Fair enough, mickeycrimm! These numbers do not need to match exactly, as we are only trying to get an idea of the value of the game and the jackpot. It is reassuring to see that our figures are close to each other, even if they are approximations.

As for the value...

If the rate of Meter Rise is 1.5%, then we have the following:

Bet: $0.50
Reset: $100.00
Meter Rise: 1.5%
Exp Cycle: 7,877
Return at Reset: 95.9512%
Total Exp Bet: $3,938.27
Exp Jackpot: $318.53
Exp Cost/Breakeven/Optimal Play Number: $259.45
Exp Profit: $59.07
Profit / Bet: $0.0075
Prob Jpt is Playable: 6.7247%
Playable Jpts: 1 in 14.87
Avg Val All Jpts (V): $3.97


If, however, the rate of Meter Rise is 2%, then we have the following changes:

Meter Rise: 2%
Exp Jackpot: $338.22
Exp Cost/Breakeven/Optimal Play Number: $259.45
Exp Profit: $78.77
Profit / Bet: $0.0100
Prob Jpt is Playable: 13.2055%
Playable Jpts: 1 in 7.57
Avg Val All Jpts (V): $10.40


As the Expected Cycle did not change, neither does the Expected Total Bet Amount nor the Expected Cost/Optimal Play Number. Also, it is no coincidence that the Profit Per Bet is the Meter Rise times the Bet. This is true only if you start playing exactly and the Optimal Play Number (and use the simplified strategies based on my approximations of the value of Bonus Rounds). Some of the numbers at the bottom are meaningless on their own - use them to compare the value of the meter being 2% instead of 1.5%. If the meter moves just a bit faster, the game becomes playable more often AND you expect to earn more each time you play.

The help screen states that one nickel per $3 in action goes in the meter, i.e., a 1.6667% meter. At least that's the meter for the Montana version of the game.

Quote: camapl

Mickeycrimm, looks like you've put some time in... The feature on WVP that allows strategy tweaks looks like it would be very useful! Especially when it comes to simplifying a strategy and seeing how it affects your bottom line. I don't currently have any VP analysis software - just relying on JB's strategy calculator on WoO and pasting into Excel in order to manipulate my calculations. I have considered purchasing the one put out by Dan Paymar, but I don't even recall which one is his... Is this one of the ones you use?

Funny, at first, I thought holding W W Q would be superior to W W 7 in your Two Joker hold example because of the wild royal, but then I realized it's not just the increase in straights, but straight flushes as well that makes W W 7 the most lucrative choice.

As for strategy adjustments, I'm thinking that we have two issues: (1) Determine a somewhat simplified strategy for determining the return of the game, the frequency of the progressive, and thus the play point. (2) Determine a set of strategies to use during the bonus rounds for a given number of wins and losses during each 10-game set and the value of the progressive.

In working towards (1), I've been tweaking a single strategy during the bonus round to maximize the value of a Full House at any time. Thru many iterations, I have narrowed down to a single strategy for Double Joker using the paytable below which is our base paytable with a FH value of 22.9131 and a value of 2.6147 added to each winning hand:

RF..........802.6147
5k..........242.6147
JR..........112.6147
SF............37.6147
4K............14.6147
FH.............25.5278
FL........ .....7.6147
ST.............6.6147
3K.............3.6147
2P.............3.6147

Analyzing this paytable and plugging in our original values with the adjusted FH at 22.9131 results in a Full House with the following value:
Full House pays: 8.0000
Value of 10 free hands: 10 X 135.4672% = 13.5467 (10 hands time the resulting return)
Value of progressive: 200 X 0.6832% = 1.3664 (progressive reset in bets times the probability of hitting during any 10-hand bonus round)
Total: 22.9131

If you play around with the numbers added to each winning combination in the paytable above, you will find that lowering or raising the number will decrease the value of the Full House. Note that the value of a Full House in bonus mode is calculated by pieces of the resulting analysis from using that same value for the Full House, such as the probability of winning or losing a hand and by the overall return. In a manner of speaking, the value of the Full House determines the value of the Full House; thus, the iterative process. I started with 8, and increased as needed based on the resulting calculated value until I found that using 22.9131 resulted in the same value. This requires plugging values into the VP Analyzer, waiting for results, updating the Combinations column, adjusting the value of the Full House, and repeating (then changing the value added to each winning hand and repeating, repeatedly). Seem repetitious? lol

I had originally surmised that the value added to each winning hand would be around 25, the progressive reset value in bets divided by the number of winning hands needed, but that turned out to be way too high. What little you gain in progressive opportunities does not outweigh the harm that you do to the return of the 10 free games. (Of course, this will be different once we are actually playing.) As these are the two variable components that make up the value of the Full House that triggered a new bonus round, it seemed logical to maximize the value of the Full House that resulted in the same value of the Full House, so to speak. Fortunately, this same figure of 22.9131 may be used to express the value of a Full House in regular mode (on the “single” Joker paytable), with the value of the bonus round and progressive all wrapped up in a tidy bundle.

Using the “single” Joker paytable below, I get an overall return for JOKER’S VAULT of 95.9512% (if the jackpot was not a progressive). Keep in mind that this is a close approximation using a single strategy for each bonus hand and that it does not account for the limit on re-triggers.
RF..........800
5k..........240
JR..........110
SF............35
4K............12
FH.............22.9131
FL........ .....5
ST.............4
3K.............1
2P.............1

I think I'll pause here before I continue with the calculation of the progressive frequency and finally, get to the strategies to use during play.

Camapl, I took your Full House value, 22.9131, along with the rest of the payscale, and punched it into WVP for the One Joker game. Well, almost. I couldn't punch in a fraction so I rounded up to 23. The strategy it spit out is virtually identical to the one I was working on. The analyzer put the game at 96.0824%. I'm sure the difference from 95.9512% is attributed to the rounding up of the Full House to 23. Then I had to make a choice. WVP actually spits out three strategies for a game, the Penalty Chart, Intermediate Chart and the Basic Chart. I took a look at the difference between the Penalty Chart and the Basic Chart. The Penalty Chart is pretty complicated. The difference between the two charts, .960824 and .960655 is .000169. So, for simplicity, I went with the Basic Strategy Chart. The Full House frequency is 66.2763. This is what the strategy looks like. The ER's are expressed as average coins returned for a five coin bet:


ONE JOKER HANDS

RF4..............................32.4946
FL................................25.0000
SF4+0..........................23.4936
ST................................20.0000
SF4-1...........................19.2396
3K................................16.9814
SF4-2...........................14.8958
RF3, JT..........................8.1955
ST4...............................7.6042
RF3, QX.........................7.4509
SF3+0...........................7.2347
RF3, KX.........................6.6631
SF3-1............................6.4488
FL4...............................6.1458
RF3, AX.........................5.9653
SF3-2............................5.7698
ST3+0...........................5.1009
W+TEN..........................5.0030
SF3-3............................4.9723
W+8,7,6,9,5,J,4,Q..........4.9288

NON JOKER HANDS

RF4............................100.9495
4K................................83.7500
FL................................25.0000
ST................................20.0000
3K................................16.9814
2P................................16.4583
SF4+0,-1,-2..................13.6164
RF3................................6.4133
FL4................................5.2083
ST4+0...........................3.7500
PAIR..............................3.6069
SF3+0,-1,-2...................2.4352
ST4-1............................2.0833
RF2,JT,QX.....................1.5764
FL3...............................1.4184
RF2, KX.........................1.4497
SF2+0...........................1.4018
ST3+0...........................1.3342
RF2,AX..........................1.3277
SF2-1,-2........................1.2128
W+T,8,7,6,9,5,J,4..........1.0997
HOLD NONE..................1.0669

*Hands above RF4 in both charts are pat hands of a Full House or higher and obvious holds.

Quote: mickeycrimm

Camapl, I took your Full House value, 22.9131, along with the rest of the payscale, and punched it into WVP for the One Joker game. Well, almost. I couldn't punch in a fraction so I rounded up to 23. The strategy it spit out is virtually identical to the one I was working on. The analyzer put the game at 96.0824%. I'm sure the difference from 95.9512% is attributed to the rounding up of the Full House to 23. Then I had to make a choice. WVP actually spits out three strategies for a game, the Penalty Chart, Intermediate Chart and the Basic Chart. I took a look at the difference between the Penalty Chart and the Basic Chart. The Penalty Chart is pretty complicated. The difference between the two charts, .960824 and .960655 is .000169. So, for simplicity, I went with the Basic Strategy Chart. The Full House frequency is 66.2763. This is what the strategy looks like. The ER's are expressed as average coins returned for a five coin bet:


ONE JOKER HANDS

RF4..............................32.4946
FL................................25.0000
SF4+0..........................23.4936
ST................................20.0000
SF4-1...........................19.2396
3K................................16.9814
SF4-2...........................14.8958
RF3, JT..........................8.1955
ST4...............................7.6042
RF3, QX.........................7.4509
SF3+0...........................7.2347
RF3, KX.........................6.6631
SF3-1............................6.4488
FL4...............................6.1458
RF3, AX.........................5.9653
SF3-2............................5.7698
ST3+0...........................5.1009
W+TEN..........................5.0030
SF3-3............................4.9723
W+8,7,6,9,5,J,4,Q..........4.9288

NON JOKER HANDS

RF4............................100.9495
4K................................83.7500
FL................................25.0000
ST................................20.0000
3K................................16.9814
2P................................16.4583
SF4+0,-1,-2..................13.6164
RF3................................6.4133
FL4................................5.2083
ST4+0...........................3.7500
PAIR..............................3.6069
SF3+0,-1,-2...................2.4352
ST4-1............................2.0833
RF2,JT,QX.....................1.5764
FL3...............................1.4184
RF2, KX.........................1.4497
SF2+0...........................1.4018
ST3+0...........................1.3342
RF2,AX..........................1.3277
SF2-1,-2........................1.2128
W+T,8,7,6,9,5,J,4..........1.0997
HOLD NONE..................1.0669

*Hands above RF4 in both charts are pat hands of a Full House or higher and obvious holds.

I took the Double Joker game, changed the Full House value to 23, then analyzed to get the strategy. I'm not going to enter the strategy here as I just realized something. The hands that make a Full House have inflated values. What I'm going to do is take the above Single Joker Strategy based on a Full House value of 23, and the Double Joker Strategy based on a Full House value of 23, and tweak the strategy charts of the One Joker and Two Joker games based on a Full House value of 8. That should give me the true numbers.

Quote: mickeycrimm

I took the Double Joker game, changed the Full House value to 23, then analyzed to get the strategy. I'm not going to enter the strategy here as I just realized something. The hands that make a Full House have inflated values. What I'm going to do is take the above Single Joker Strategy based on a Full House value of 23, and the Double Joker Strategy based on a Full House value of 23, and tweak the strategy charts of the One Joker and Two Joker games based on a Full House value of 8. That should give me the true numbers.

To what end, mickeycrimm? Not sure what numbers you are after... As for the correct strategies, you would want to use the 23 (or higher) for the Full House instead of 8. Although you are actually paid 8 units, there is also value in the free games and the progressive opportunity, and 23 represents the 8 units plus a simplified average value of a 10-hand bonus round. You could use a value higher than 23 when the progressive is high. I may need more info to understand the "true numbers" to which you refer above. Perhaps I will understand when you find the answer...

Quote: mickeycrimm

The help screen states that one nickel per $3 in action goes in the meter, i.e., a 1.6667% meter. At least that's the meter for the Montana version of the game.

You may have posted that in an earlier thread... In that case, we have the following:

Bet: $0.50
Reset: $100.00
Meter Rise: 1.667%
Exp Cycle: 7,877
Return at Reset: 95.9512%
Total Exp Bet: $3,938.27
Exp Jackpot: $325.09
Exp Cost/Breakeven/Optimal Play Number: $259.45
Exp Profit: $65.64
Profit / Bet: $0.0083
Prob Jpt is Playable: 8.8086%
Playable Jpts: 1 in 11.35
Avg Val All Jpts (V): $5.78

Quote: camapl

...Groups 2 thru N to come...

So, I've been toying with a way to group the remaining states of a 10-hand bonus set. The following table indicates how many winning hands are still needed (column 1), how many of the 10 hands remain (column 2), and the overall probability of hitting the progressive from each state using the probability of win/loss of a hand using the simplified Double Joker strategy (column 3). Clearly the probability of winning/losing a hand will change slightly as we adjust the strategy for each state. I am providing the list below, sorted by increasing probability of hitting the jackpot, as a tool for us to use in order to group some of the states together (and shorten the list, if possible). For example, it appears that getting 5 wins with 5 remaining hands is about as likely as getting 8 wins with 10 remaining. Also, 4 of 5 and 5 of 7 could be a group, and 2 of 2 and 4 of 6 could be another.

NEED........OUT OF....PROB
8..............8..............0.0334%
7..............7..............0.0909%
8..............9..............0.2024%
6..............6..............0.2471%
7..............8..............0.4930%
5..............5..............0.6720%
8..............10............0.6832%
6..............7..............1.1845%
7..............9..............1.5101%
4..............4..............1.8277%
5..............6..............2.7967%
6..............8..............3.2592%
3..............3..............4.9708%
4..............5..............6.4504%
5..............7..............6.8270%
2..............2..............13.5193%
4..............6..............13.7580%
3..............4..............14.4002%
3..............5..............26.3249%
2..............3..............30.6161%
1..............1..............36.7685%
2..............4..............46.8320%
1..............2..............60.0178%
1..............3..............74.7187%

The reason for looking at the overall probability of hitting the progressive from each state is that in addition to adjusting the value of the Full House, we want to find how much of a premium we should put on winning any given hand. If we overshoot this amount, we eat up the return of the hands in Double Joker bonus mode, and if we under cut it, then our cycle goes too long on a game with a relatively low base return and we may run into time constraints while trying to pull down the meter. For example, in groups 1A and 1B, we don't adjust for the progressive once it has been hit or is out of reach for that set. Likewise, if we find that we need 8 of 8, 7 of 7, 8 of 9, or 6 of 6 wins during a set, we could treat that set as though we already have 3 losses in order to maximize the return and/or the possibility of a re-trigger for the remainder of the Double Joker bonus hands. While this may be sub-optimal, we may find that it is both "close enough" to optimal AND lowers our variance in order to preserve our bankroll.

By the way, wouldn't it be awesome to have 7 wins behind us and more than 1 hand remaining to hit the final win?

Quote: camapl

To what end, mickeycrimm? Not sure what numbers you are after... As for the correct strategies, you would want to use the 23 (or higher) for the Full House instead of 8. Although you are actually paid 8 units, there is also value in the free games and the progressive opportunity, and 23 represents the 8 units plus a simplified average value of a 10-hand bonus round. You could use a value higher than 23 when the progressive is high. I may need more info to understand the "true numbers" to which you refer above. Perhaps I will understand when you find the answer...

I changed the Full House value to 23 for both the One Joker game and the Double Joker game and had WVP analyze and create the strategy charts. The payback percentage for the One Joker game came in at 96%, and the payback for the Double Joker game came in at 136%. I can't use those two numbers together to come up with the payback of the two games combined. But I CAN use the strategy charts.

I inserted the "Full House 23" strategy charts into the "Full House 8" games and had WVP analyze. This was the result:

Payback for the One Joker game..............73.4143%
You make a Full House every...................66.3183 Games

Payback for the Double Joker game........108.9854%
You make a Full House every...................55.0081 games
The chance of making a paying hand is....36.1303%

To get the combined payback I took your number 12.3118 (average number of games in the bonus round) and multiplied it by 1.089854 (the expected return per hand in the Double Joker game) to get 13.4181 bets. I divided 13.4181 by 66.3183 games (Full House frequency in the One Joker game) to get 20.2329%. Then I added 20.2329% to 73.4143% (payback percentage in the One Joker game) to get 93.6472%. This number should represent the payback if there were no meter starting at $100 and running 1.6666%.

Then I used your number of 7822 One Joker games to snap the progressive off. 200 bets divided by 7822 is 2.5569%. I added 2.5569% to the 1.6666% meter to get 4.2235%. Then added 4.2235% to 93.6472% to get an overall payback of 97.8707%.

I subtracted .936472 from 1 to get 6.3528% (the drain between hitting the progressive).
Then I multiplied 7822 * 50 cents * .063528 to get a cost of $248.46 to snap off the progressive. I think your number was $249.25.

Please let me know if you think I'm making a mistake somewhere or I'm on the wrong track. I would rather be corrected than continue to be wrong. I'll put up the Double Joker strategy in the next post.

This is the Double Joker strategy based on a Full House value of 23. Again, I'm putting up the Basic Strategy. The difference between the Penalty Strategy and Basic is 0.000289. The Penalty strategy is much more complicated than basic. At a $500 wager per hour it would cost me only 1.5 cents per hour to use the Basic Strategy and keep it simple, so that's what I went with. The ER's are expressed as coins returned per five-coin bet. If you like percentages instead then divide the ER's by five.

TWO JOKER HANDS

5K.......................................1200.0000
WR........................................550.0000
SF.........................................125.0000
4K.........................................106.5306
RF4.........................................53.8393
SF4+0,-1,-2,-3.........................33.0089
FL...........................................25.0000
WW+T,8,7,6,9,5,J,Q,K,A..........24.7934
HOLD TWO WILD CARDS.........23.4455

ONE JOKER HANDS

RF4........................................43.0560
SF4+0....................................26.5384
FL..........................................25.0000
SF4-1.....................................22.3312
3K.........................................20.6760
ST.........................................20.0000
SF4-2....................................18.1633
RF3, NO ACE...........................9.2342
SF3+0....................................8.5516
ST4........................................7.8571
RF3, AX..................................7.7726
SF3-1,-2.................................7.1508
FL4........................................6.5306
W+TEN..................................6.2921
ST4-1.....................................6.2245
W+8,7,6,9,5,J.........................6.1176
HOLD NONE............................6.0544

NON JOKER HANDS

RF4.....................................110.1138
4K.......................................106.5306
FL.........................................25.0000
3K.........................................20.6760
ST.........................................20.0000
2P.........................................18.4694
SF4+0,-1...............................16.9099
RF3.........................................7.9372
PAIR.......................................4.6659
SF3+0.....................................4.2412
ST4+0.....................................4.0816
SF3-1,-2..................................3.0550
ST4-1......................................2.4490
RF2, NO ACE...........................1.9782
SF2+0....................................1.8264
RF2, AX..................................1.7035
FL3........................................1.6327
SF2-1,-2.................................1.6894
ST3+0....................................1.6071
HOLD TEN..............................1.5465
HOLD NONE...........................1.5465

*The hands above the RF4 in both the One Joker and Non Joker charts are pat hands of a Full House or higher and obvious holds.