Double Up Poker

I noticed this game at the Green Valley Ranch on Monday.


Click any image for larger version.

It plays like regular video poker except:

1. The player bet 15 credits at a time and gets two hands dealt from separate decks.
2. The player is paid based on the the poker value of each final hand as well as a third win based on the value of both hands.

The concept if both hands score high then the player wins a lot on the "parlay" portion. Here is an example.



In the hand above you can see both initial hands. The bottom one is illuminated because I play out that one first.



Here I hold the two pair on the bottom hand and then the top hand is illuminated to direct my attention to playing that one.



I held the pair of aces on the top hand. Then the draw cards are dealt to both hands. I end up with a two pair on both.

From the base pay table I'm paid 10 credits for each two pair. On the parlay pay table I'm paid 15 based on the score of both hands. So, my total win is 10+10+15=35.

My first question is whether this is a new game or has been around for years and I am just seeing it for the first time. As a west side resident, I don't get out to the GVR very often.

It would be easy to analyze with an assumption that the player didn't make any strategy deviations for the parlay portion. However, if one considers this then the analysis really becomes a bear. I get 15,893,347,154,073,300,000,000,000 possible combinations. I tip my hat to whoever did a combinatorial analysis of this one, if anybody.

I've never seen this game in a casino or at G2E. I like it though. I would definitely play it.

You made a mistake in your adding above though. You say "From the base pay table I'm paid 10 credits for each two pair. On the parlay pay table I'm paid 15 based on the score of both hands. So, my total win is 10+10+15=25." 10+10+15 equals 35, which is what is show as the total win in the picture.


ZCore13

Quote: Zcore13

You made a mistake in your adding above though. You say "From the base pay table I'm paid 10 credits for each two pair. On the parlay pay table I'm paid 15 based on the score of both hands. So, my total win is 10+10+15=25." 10+10+15 equals 35, which is what is show as the total win in the picture.

Well, that was embarrassing. Thanks for the correction.

Quote: Wizard

My first question is whether this is a new game or has been around for years and I am just seeing it for the first time. As a west side resident, I don't get out to the GVR very often.

I feel like you should have asked this question for "Extra Action Poker".
http://media.igt.com/marketing/PromotionalLiterature/GamePromoLit_1D58E-201BE.pdf (media sheet copyright in 2011)

You can play the game for "Extra Action Poker" for free at videopoker.com

Media Sheet for "Double Up Parlay" (copyright 2013), and I never saw it even until you posted this.
It also follows the new IGT standard of not permitting 99%+ video poker...grrrrrrrrrrrrrrrrrrrrrrr
http://comebackgaming.com/assets/parlay-video-poker-sales-sheet.pdf

But you can play a free game here:
http://www.advancedgamingsolutions.com/games/Comeback/bundles/parlaypkr/loader.html

I think I might have just changed my mind on this game. Just got my butt handed to me for $250 in about 15 minutes playing the basic Jacks or Better version.

Ouch!

ZCore13

Quote: Zcore13

I think I might have just changed my mind on this game. Just got my butt handed to me for $250 in about 15 minutes playing the basic Jacks or Better version.

Ouch!

ZCore13

I was sitting there watching you. Lol...no, but looking at the timing, we were trying it at the same time. I played even w/max bets in the same time. The best parley hand I had was FH+somethiing smaller (3oak?) for 200, and I had another for 120. Wasn't too bad, but I did get slightly bored with it. And it seemed odd to me that it didn't pay better than a 4000 bonus for royalxroyal. You'd think that would be so improbable they could pay some crazy amount on it like 20000.

Quote: beachbumbabs

And it seemed odd to me that it didn't pay better than a 4000 bonus for royalxroyal. You'd think that would be so improbable they could pay some crazy amount on it like 20000.

There is a law in Nevada that the highest possible prize must have a probability of at least p. I keep forgetting what p is, but something like 1 in 20 million. I'm sure MathExtremist knows. The probability of a double royal is about 1 in 1.6 billion.

I implemented this game about 12 years ago for a company that contracted me to build games for them. Sadly, at about the same time this company sold their slot business to IGT before releasing the game. I enjoyed the game but the volatility was pretty high.

Quote: Wizard

There is a law in Nevada that the highest possible prize must have a probability of at least p. I keep forgetting what p is, but something like 1 in 20 million. I'm sure MathExtremist knows. The probability of a double royal is about 1 in 1.6 billion.

Actually in Nevada you could offer a higher royal/royal payout but you'd have to explicitly write the probability on the glass. Any sane manufacturer would not do this. The threshold for this requirement is 1 in 100 million in Nevada.

Most states outright ban top payouts over the cutoff. This is sorta offhand for some states, particularly CT; I think Crystal Math told me that one.

MS and NJ: 1 in 100 million
Most states and GLI-11 standard: 1 in 50 million
CT: 1 in 17 million?
CO (non network games): 1 in 17 million
CO (network games): 1 in 50 million

So 1 in 17M is the "catch-all" probability. With that in mind, that affects my favorite video poker variant. For Double Super Times Pay, they automatically award 20X the Royal with a dealt Royal and any deal multiplier (~1 in 9.74M). Maybe I'll be lucky enough for this to happen once in my life. ;) If this rule didn't exist, the probability of a 20X Royal is closer to: 1 in 22.7 billion...lol

For regular Super Times Pay, the highest available Double Bonus game I am aware of is 10/6 and not 9/7. With 9/7 the probability of a 10X Royal would be > 1 in 18 million, which would be illegal in a few states at least.

Quote: Wizard

There is a law in Nevada that the highest possible prize must have a probability of at least p. I keep forgetting what p is, but something like 1 in 20 million. I'm sure MathExtremist knows. The probability of a double royal is about 1 in 1.6 billion.

You're looking at it wrong.

Yeah, a double royal is damn rare, but a royal with jacks OR BETTER is far more common. And, since a royal with anything pays the same regardless of what the anything is, it's well within the limit.

Quote: DJTeddyBear

You're looking at it wrong.

Yeah, a double royal is damn rare, but a royal with jacks OR BETTER is far more common. And, since a royal with anything pays the same regardless of what the anything is, it's well within the limit.

I think when we first did this game we were paying 20,000 coins for a royal with a straight or better.

Quote: DRich

I think when we first did this game we were paying 20,000 coins for a royal with a straight or better.

And I think something like that would have better than the current setup, imo. But I guess you get a nice 4000 credit boost roughly 45% of the time.

There are too many gaming companies in Las Vegas with the initials AGS.

I did some more math on Double Up. For the $1 8-6 Jacks game, assuming the player follows optimal 8-5 strategy, here is the return of each component, as well as the average.

Hand	Return
Red	0.983927
Blue	0.983927
Parlay	0.974444
Total	0.980766

So the extra feature lowers the overall return. Now I'm sure with optimal strategy that considers the parlay feature that would go up, but how many people on earth are going to learn such a strategy unless the game gets over 100%, which I'm sure it doesn't?

The next table shows the return table for the parlay portion. The return column is the product of the win, probability, and 0.2. The reason for multiplying by 0.2 is the wins are based on a 5-coin bet.

Parlay Win	Probability	Return
4000	0.000023	0.018014
2000	0.000009	0.003446
1000	0.000241	0.048275
800	0.000405	0.064776
750	0.000019	0.002810
500	0.000375	0.037490
400	0.001625	0.129981
250	0.000075	0.003759
200	0.000259	0.010345
120	0.002088	0.050105
90	0.001640	0.029519
60	0.001672	0.020070
50	0.005543	0.055425
40	0.007917	0.063337
30	0.007575	0.045448
20	0.007725	0.030899
15	0.067912	0.203736
10	0.055481	0.110963
5	0.046046	0.046046
0	0.793372	0.000000
Total	1.000000	0.974444

Quote: Wizard

I did some more math on Double Up. For the $1 8-5 Jacks game, assuming the player follows optimal 8-5 strategy, here is the return of each component, as well as the average.

Hand	Return
Red	0.983927
Blue	0.983927
Parlay	0.974444
Total	0.980766

You mean 8/6 JoB, right? 8/5 JoB is 97.3%.

Quote: Wizard

I did some more math on Double Up. For the $1 8-5 Jacks game, assuming the player follows optimal 8-5 strategy, here is the return of each component, as well as the average.

Hand	Return
Red	0.983927
Blue	0.983927
Parlay	0.974444
Total	0.980766

So the extra feature lowers the overall return. Now I'm sure with optimal strategy that considers the parlay feature that would go up, but how many people on earth are going to learn such a strategy unless the game gets over 100%, which I'm sure it doesn't?

There might be an interesting question for your next FOIA request. I was under the impression that each additional coin wagered in a machine game could not have a lower RTP than the previous coin, and this wouldn't qualify. Am I wrong about that in Nevada?

Quote: tringlomane

You mean 8/6 JoB, right? 8/5 JoB is 97.3%.

Yes, I meant 8/6.

Quote: MathExtremist

There might be an interesting question for your next FOIA request. I was under the impression that each additional coin wagered in a machine game could not have a lower RTP than the previous coin, and this wouldn't qualify. Am I wrong about that in Nevada?

The return only goes down if the player sticks with 8-6 strategy. I assume that a more aggressive strategy, especially on the second hand if the first hand scores high, would increase the return.

Quote: MathExtremist

There might be an interesting question for your next FOIA request. I was under the impression that each additional coin wagered in a machine game could not have a lower RTP than the previous coin, and this wouldn't qualify. Am I wrong about that in Nevada?

Rescanning the NV regulations, I think you're wrong. But I could have missed one legal sentence; I perused pretty fast. You're definitely right about some other states though. Regardless, what Wiz currently shows is likely NOT from optimal strategy. It's entirely possible that correlating the two hands dealt to you optimally will make the combined game pay more than 98.39%. What irks me though is, playing standard strategy does not increase RTP, ala Ultimate X. :( And unlike Ultimate X, I'm not sure if variance/game interest will be enough to cover up this undesirable side effect.

I went to my thoughtful spot and realized an optimal analysis of this game would not be that hard.



For any given win on the first hand there are specified total wins for any given hand on the second hand by summing the win from the second hand itself and the parlay win. For example, if the first hand is a flush, the following would be the pay table for the second hand, considering both the hand itself and the parlay.

Royal flush 1600
Straight Flush 250
Four of a Kind 225
Full House 108
Flush 106
Straight 28
Three of a kind 21
Two pair 8
Pair 7
Nonpaying hand 0

This kind of adjusted pay table would obviously motivate a conservative strategy to win anything.

Putting these wins through my game return calculator results in an expected return of 1.57548.

Then go backwards and consider these expected wins for the second two wins in playing the first hand.

Hand	First Hand Pays	Second and Parlay Pay	Total	Probability	Return
Royal flush	800	383.537701	1,183.54	0.000020	0.008003
Straight Flush	50	39.040890	89.04	0.000107	0.003171
Four of a Kind	25	48.048006	73.05	0.002357	0.057403
Full House	8	10.231967	18.23	0.011475	0.069734
Flush	6	7.877408	13.88	0.012621	0.058382
Straight	4	4.704761	8.70	0.011038	0.032029
Three of a kind	3	3.789850	6.79	0.074101	0.167711
Two pair	2	2.444352	4.44	0.128571	0.190471
Pair	1	2.097817	3.10	0.211511	0.218407
Nonpaying hand	0	0.983927	0.98	0.548199	0.179796
Total	0	-	-	1.000000	0.985107

The return in this table is defined as sum(wins)*probability/3. The reason for dividing by 3 is the player must bet 15 credits, and all these wins are based on 5 coins per win.

So, the total return of 8-6 jacks is 98.51%.

Recall the base game was 98.39%, so optimal strategy (which I'm sure nobody will ever use) will increase the return by 0.12%.

So, you get to resolve the first hand before playing the second? That definitely makes the math easier. At first, I assumed that you had to make all of your holds at the same time.

ME: I don't think NV has that rule, but I'm almost certain that IGT would never put out a video poker that decreased the return for an extra wager. I remember a rule like that for Louisiana Native American, I think, but they would accept the game with a note from GLI. The only time I ever remember running into this was with a game that had expanding wilds. Because of the reel layout, there were certain lines that paid a little less.

Quote: CrystalMath

So, you get to resolve the first hand before playing the second? That definitely makes the math easier. At first, I assumed that you had to make all of your holds at the same time.

From his description,I think you hold both hands first.

Quote: Wizard

I held the pair of aces on the top hand. Then the draw cards are dealt to both hands. I end up with a two pair on both.

Back to your thoughtful spot, Wizard. :+)

Quote: miplet

Back to your thoughtful spot, Wizard. :+)

Oh bother! You're right, the first hand isn't resolved until the player makes the decision on the second hand. I forgot that. My initial thought that analysis would be a bear was right.

I do think this game would be better if the first hand were resolved before the decision made on the second.

Back to the thoughtful spot.

Quote: Wizard

I do think this game would be better if the first hand were resolved before the decision made on the second.

When we first did this game the first hand was played out before you even received cards for the second hand. I am surprised to hear they changed it.

Quote: CrystalMath

ME: I don't think NV has that rule, but I'm almost certain that IGT would never put out a video poker that decreased the return for an extra wager. I remember a rule like that for Louisiana Native American, I think, but they would accept the game with a note from GLI. The only time I ever remember running into this was with a game that had expanding wilds. Because of the reel layout, there were certain lines that paid a little less.

I know IGT won't do it but I always assumed it was for regulatory reasons. But you're right, I can't find any regs that say so. I think IGT applies the rule to all other games too, not just VP. Interesting.

And the piece about expanding wilds is interesting. I would have expected that overwriting a symbol with a wild would always increase the RTP of the line.

Quote: MathExtremist

And the piece about expanding wilds is interesting. I would have expected that overwriting a symbol with a wild would always increase the RTP of the line.

Although it would always increase the RTP, the effective symbol distribution can be different for each position. Consider the following reel layout:
A A A B C W D E F F F

Lines containing the top position on the screen will effectively have the following layout:
A A A W W W D E F F F

Lines containing the center position will have this layout:
A A A B W W W E F F F

Lines containing the bottom position will have this layout:
A A A B C W W W F F F

There are two ways to avoid this that I know of:
1. Always structure the reel so that the symbols above and below the wild are the same, like A A A B C W B C F F F. Regardless of the position on the screen, you will be replacing a B and a C with a Wild.
2. Pay all wins before and after the wild expansion.