Desirable Hit Rate and House Edge

When designing a side bet pay table, it's always a compromise between size of payouts vs. frequency of payouts (hit rate). What is the lowest hit rate that's going to be acceptable to a player? The hit rate is incredibly low in Let it Ride, but that bet is limited to $1 where most are variable. In conversations at games, I've recalled players saying they don't play the side bet because "they never seem to win." So I'll start this discussion by saying that I think the hit rate needs to be higher than 1 in 12 hands (8.3%), and ideally higher than 1 in 10 hands (10%).

With house hedge (HE), what are casinos looking for here? Obviously they want the highest edge possible while still getting as much action as possible. I think I read somewhere that the NV limit is 25%. I would suggest that many of the players that play side bets aren't aware of HE and simply play based on whether they feel that they win or not. So naturally the ideal range is probably 5-15%, but I'd like to hear opinions that might narrow that down a bit.

Pai Gow Poker's is almost 20%. I think that's the perfect amount.

It's not just the hit rate but the tease rate that you need to have. Nothing keeps them betting more than a near miss.
So much so that false near miss options on slots are illegal.

Another reason why Pai Gow's is so great. The game should be called "1 away"

"Oh look, if I just had the Jack of hearts I would have had a royal. Oh wow, it's in the spot right next to me"

Quote: buzzpaff

It's not just the hit rate but the tease rate that you need to have. Nothing keeps them betting more than a near miss.
So much so that false near miss options on slots are illegal.

You should read the Wizard of Odds section on slots. The slot making industry widely encourages the belief that the programming the "near miss" is illegal. They base this on a 30 year old ruling by the gaming commission in Nevada. What that ruling actually said was that one particular technique for creating a "near miss" was illegal. They did not generalize it to any algorithm.

In fact , programming a slot machine to create a "near miss" is a fundamental part of the design of most slot machines.

Since at least 1988, a technique called clustering has been used to create a high number of near misses, failures that are close to wins. The result is that what the player sees does not represent the underlying probabilities and randomness, and this misrepresented outcome will have some effect on the player’s perceptions of the game, which may lead directly to classical and operant conditioning, the frustration effect, the perception of early wins, illusion of control, biased evaluation of outcomes, entrapment, and irrational thinking,

Paper on the Psychology of the Near Miss in journal of gaming behavior.

Once again I bow to superior knowledge! Thanks for the link also

Phosphorous

Side bet (not progressive) on a normal table game eg, blackjack, poker:

I would go for around 1 in 8 (hit rate), it would happened often enough and you can make a decent payout schedule for this frequency.

House edge: no less than 2.5% . No more than 8%.

Quote: FinsRule

Pai Gow Poker's is almost 20%. I think that's the perfect amount.

For the "Table hold," yes it is.
That is the "Table Hold" figure, that's different than HE, or House Edge.

That "Hold" figure is the amount of "buy-in money" kept per shift or per account/tracking period, compared to the drop or buy-in amounts.
A Casino table should hold between 18% and 30% of the cash buy-ins that it sees for a table game. Below that, the house doesn't make much profit over expenses, and above that, the players get rapidly burnt-out and abandon the game.

However, if a house gets a LOT of action on a table game, its hold may be smaller. For example, if a Baccarat table drops $1,000,000 a month and holds only 9% of that, that's $90,000 profit. Not uncommon. And this is better than dropping or "holding" $200,000, but keeping only 25% of it, for $50,000. At the end of the month, a casino would rather deposit $90,000 from one table than $50,000.

What the game designer does is assume that for each percentage on his game's "main bet(s)," or flat bets, that he'll have a House Percentage of 2.0% to 3.5% Roughly, each percentage of table hold on a "flat" even money bet for a game equates to 10% for each percentage. A table game that has a 2.5% house edge on the main bet of the game should hold 25% on average, - very, very roughly.

Blackjack's table hold is about 6% to 12%, because it's house edge is about 0.5% to slightly over 1% with experienced players, depending on rules (DOA, DAS, hit soft 17, split up to four times, etc...). The house doesn't mind the table hold percentage and house edge (HE) being less, because it is made up for by the additional action BJ receives - blackjack tables are generally enourmosly busy.

What the game designer seeks mathematically on his game designs are some standard benchmark House edge figures that are "within range" before a field trial or introduction, as determined by the designer's initial math work math, and verified by the gaming math report (from someone Like Charles Mousseau or Mike Shackleford, etc.) Basially, these ranges are:
1. For a flat "main bet," similar to a Pass-line bet, a BJ main bet, a Pai Gow bet on the hand's win/loss/push, etc, the HE should be around 2.0% to 3.5%, for an expected table hold of about 22%-30%, plus/minus 5 points.
2. For a "bonus" type bet with a low starting payout of 2:1 to 5:1 for most bonuses hits, plus rare windfall payouts, the house edge should be about 7% (Fortune bonus on Pai Gow Poker, Three-card Poker's Pai Plus bet, Bonus bets on Ultimate Hold 'em, etc...)
3. for a progressive type bet, it should actually be in the range of 20% to 50% house edge, to re-seed the jackpot and to pay the house. If a payer hits the jackpot, he's set for the year.
4. For one-shot prop bet wins of 10:1 to 60:1, the house ege should be in the range of 9% to 20% - like the hardways and prop bets on craps, the Dragon bet on EZ Pai Gow or EZ Baccarat, etc.

For games that have optional raise bets on poker games, an element of risk is introduced, where players bet out hands that are apparent winners against the house. This introduces the "Element of risk," where they player may increase his edge by raising his bet when he has a probable or clear winning hand after seeing a part of the community board on a house-banked poker game. The element of risk should be between 0.5% to 2.0% on the main "poker style" bets, such as in Ultimate Texas Hold 'em, Texas Hold 'em Bonus, Let it Ride, etc.

You can look at all the house edge math for each casino game in existence at www.wizardofodds.com, practically, and you will see that the successful table games that are still around with longevity adhere strictly to these guidelines. Games just play very well, better, in this range, assuming that the base game is interesting and fun to play.

That's how table game math design works, in a really short nutshell.

I think that people probably have very different perceptions based on how much you can distract them. While a traditional side bet had only 2 payouts, the newer ones have as many as five. It seems like you have to set out a table like the one below for a Bally Blazing 7's machine.

The core of these slot machine designs is you need some percentage of the coins constantly coming back at you. While you are feeding the machine below at $7.50 per minute, on average every minute one fifty cent and one $2.50 payback is being returned. These two paybacks are the drivers.

But you need a seducer payback. The $50 payback comes every 17 minutes. It's seductive because it might put you in the positive, but it's not enough to make you cash in and go home.

Not that there is a second level seducer. The $250 payback comes in at almost 7 hour intervals, and is much more frequently than the $150, $30, or the $100 payback.

The jackpot arrives at disproportionately large mean time interval. Those people lucky enough to hit the jackpot will probably quit playing the machine.


$7.50 Feed Rate /minute
12.05% Hit Rate
92.70% Payback Rate

Hour:Min:Sec	3 quarters * 10 times /minute	Seconds
0:01:54.92	$0.50	114.92
0:02:08.91	$2.50	60.75
0:11:16.38	$5	55.75
0:17:06.35	$50	52.88
0:36:46.39	$10	51.64
0:45:57.99	$1	50.69
1:51:05.14	$75	50.31
5:08:28.17	$20	50.17
5:45:36.00	$15	50.05
6:45:42.26	$250	49.95
11:06:30.86	$150	49.88
17:16:48.00	$30	49.84
20:44:09.60	$100	49.81
11:31:12 +5 days	$1,250	49.81

There is a good book that Eliot Jacobson wrote on table game development and it discusses house edge, game mathetics, hold, etc. I think it has some really good information and analysis in it relating to the trends in table games over the last 20 years. You can check it out on his site http://www.jacobsongaming.com/

For full disclosure purposes, I am a client of Eliot's and think he does great work!

With an online slot machine, you could give players some alternatives. For instance in the machine below, the player could elect not to receive the 50 cent payouts, in exchange for a much larger jackpot.

$7.50 Feed Rate /minute
12.0467% Standard Hit Rate
12.0456% Alternate Hit Rate
92.70% Standard Payback Rate
91.71% Alternate Payback Rate

Hour:Min:Sec	3 quarters * 10 times /minute	Seconds
0:01:54.92	$0.50 (alternate pays zero)	114.92
0:02:08.91	$2.50	60.75
0:11:16.38	$5	55.75
0:17:06.35	$50	52.88
0:36:46.39	$10	51.64
0:45:57.99	$1	50.69
1:51:05.14	$75	50.31
5:08:28.17	$20	50.17
5:45:36.00	$15	50.05
6:45:42.26	$250	49.95
11:06:30.86	$150	49.88
17:16:48.00	$30	49.84
20:44:09.60	$100	49.81
11:31:12 +6 days	$1,250 (alternate pays $3000)	49.81

Quote: Paradigm

There is a good book that Eliot Jacobson wrote on table game development and it discusses house edge, game mathetics, hold, etc. I think it has some really good information and analysis in it relating to the trends in table games over the last 20 years. You can check it out on his site http://www.jacobsongaming.com/

For full disclosure purposes, I am a client of Eliot's and think he does great work!

Just ordered book from Amazon $20. Only 2 reviews. Both rate it 5 stars, One is Paradigm. You get 2 guesses who the other reviewer
is First guess doesn't count.

Eliot does touch upon a lot of things in his fine book..
- Name must be very good, simple, and inviting. MANY designers screw this simple thing up and insist upon a very off-putting table game name.
- Flexibility with your distributor.
- Being very realistic and avoiding the "Mother's child" syndrome - if your kid is found to be a tad "ugly," then let a make-over happen!
- The Expense involved...
etc., aside from the basic and advanced math.

That's a very concise and 'on target' analysis by main bet type, Paigowdan.

I probably should have joined this conversation sooner.

Frequency and payouts, balanced with an acceptable house edge, are some of the things I juggled when I was creating my Poker For Roulette side bet. I still juggle with it - as I was composing this post, I discovered I do not specify the overall odds of winning. That will be fixed later today.

I can tweak the paytables, and remove winning combinations as the casino desires, but I've come up with is what I beleive is a good balance. The overall odds of winning is about 1 in 3.12 events. My simulations produced house edges between 12.4% and 16.6%.

My simulations also showed me some startling things: As expected with 250,000 spins, I nailed the 1 win in 3.12 events. However, there were times where there were as many as 171 consecutive events without any type of win, and individual numbers with dry spells as long as 767 spins.

Quote: DJTeddyBear

My simulations also showed me some startling things: As expected with 250,000 spins, I nailed the 1 win in 3.12 events. However, there were times where there were as many as 171 consecutive events without any type of win, and individual numbers with dry spells as long as 767 spins.

DJ that result should not be startling, as we have discussed very often that unexpectedly long streaks are actually quite likely to happen given a big enough sample size. What were the other extremes of your simulation? For instance what was your longest winning streak? You should always calculate both extremas.

Yeah, I guess "Startling" was a bit much.


It's hard for me to track winning streaks and clusters because events are overlapping.

I.E.: A "Pair" is any repeat within the five spins. A pair that is consecutive means those two spins counts as a pair, or better, in four overlapping events.

As a result, tracking unique occurances began to give me a headache, so, although I have some data for it, I'm not publishing it yet. I'll let whatever qualified math person I retain figure that stuff out.

For what it's worth, I did my simulations correctly. By that I mean the 250 million event simulations actually consisted of 250,000,004 spins. With each new spin, I retained the 4 previous spins, and evaluated the 5 spin event. I just can't figure out a good way to track / calculate the clusters that use unique spins while ignoring multiples using the same spins.

In looking at the PARS for different slot machines (Table below compares the Red White and Blue machine on Wizard of Odds site with a Bally Blazing 7's machine), you can see that the expected frequency of the individual payouts can be more important than the overall house edge and hit frequency.

The Red White and Blue machine has a very high frequency, but a much lower overall payout. Partly because the jackpots are so very difficult to reach. The two smallest payouts are much more frequent.

Both machines assumed 75 cents per play, 10 plays/ minute, or $450 /hr.
The cumulative seconds column tells you the expected wait time for the payouts up to that point.

RWB	$7.50 /min	$450/hr	Blaze 7	$7.50 /min	$450/hr
Payout/HE	86.58%	13.42%	Payout/HE	92.70%	7.30%
Hit freq	17.35%		Hit freq	12.05%
Return	HH:MM:SS	seconds	Return	HH:MM:SS	seconds
$0.75	0:00:48	48.000	$0.50	0:01:55	114.916
$3.75	0:03:17	38.603	$2.50	0:02:09	60.755
$1.50	0:12:19	36.687	$5.00	0:11:16	55.747
$60.00	0:21:52	35.689	$50.00	0:17:06	52.875
$7.50	1:00:41	35.343	$10.00	0:36:46	51.638
$18.75	1:09:21	35.045	$1.00	0:45:58	50.689
$30.00	2:04:50	34.882	$75.00	1:51:05	50.306
$37.50	2:25:38	34.743	$20.00	5:08:28	50.170
$15.00	3:51:59	34.657	$15.00	5:45:36	50.049
			$250.00	6:45:42	49.946
$150.00	10:24:09	34.625	$150.00	11:06:31	49.884
			$30.00	17:16:48	49.844
$112.50	10:24:09	34.593	$100.00	20:44:10	49.811
$899.25	145:38:08	34.590	$1,250.00	155:31:12	49.806
$1,800.00	436:54:24	34.590

The $50 or $60 payout is the most seductive one for the player. It comes often enough and it is high enough to keep the player interested, but not high enough to encourage the player to quit.

DJ, with your game with a 32.05% hit frequency it would be interesting to see a similar table.

Quote: pacomartin

DJ, with your game with a 32.05% hit frequency it would be interesting to see a similar table.

Your table is based upon a specific speed of play. I would have preferred to see the number of other events between winning events.

Roulette is much slower. The last time I spent any apreciable amount of time at a Roulette table, I was shocked at the lengthy delay between spins. At one point I timed it at SEVEN MINUTES!

When I get the simulations from a math guy, number of events between winning events will be one of the reports I request.



On the other hand, I have no idea what the 'seconds' column is supposed to represent. Those numbers are too similar to be meaningful to me.

Quote: DJTeddyBear

Your table is based upon a specific speed of play. I would have preferred to see the number of other events between winning events.

Roulette is much slower. The last time I spent any apreciable amount of time at a Roulette table, I was shocked at the lengthy delay between spins. At one point I timed it at SEVEN MINUTES!

When I get the simulations from a math guy, number of events between winning events will be one of the reports I request.

On the other hand, I have no idea what the 'seconds' column is supposed to represent. Those numbers are too similar to be meaningful to me.

I set it up as 10 plays per minute so that it would be easy to convert to events. I just found that with very large numbers it is more intuitive to convert to hours, and then to days.

If you prefer I can change it from seconds to frequency of all the payouts on that level or more often. I just find seconds more intuitive.


Overall hit frequency is of limited use since you can always make it relatively high by returning a lot of crappy payouts. The table gives the operator an idea of how long it will be (on average) between certain payouts. It gives you an idea of when the player will get bored and stop playing.


I gave an alternative pay schedule for the blazing 7's. It gives the same hit frequency and payout as the previous schedule, but you must wait longer for bigger infrequent payouts.

RWB	$7.50 /min	$450/hr	Blaze 7	Blaze 7	$7.50 /min	$450/hr
Payout/HE	86.58%	13.42%	Payout/HE	Payout/HE	92.71%	7.29%
Hit freq	17.35%		Hit freq	Hit freq	12.047%
Return	HH:MM:SS	frequency	Return	Return	HH:MM:SS	frequency
$0.75	0:00:48	12.500%		$0.50	0:01:55	5.221%
$3.75	0:03:17	15.543%		$2.50	0:02:09	9.876%
$1.50	0:12:19	16.354%		$5.00	0:11:16	10.763%
$60.00	0:21:52	16.812%	$8.00	$50.00	0:17:06	11.347%
$7.50	1:00:41	16.977%		$10.00	0:36:46	11.619%
$18.75	1:09:21	17.121%	$90.00	$1.00	0:45:58	11.837%
$30.00	2:04:50	17.201%		$75.00	1:51:05	11.927%
$37.50	2:25:38	17.270%		$20.00	5:08:28	11.959%
$15.00	3:51:59	17.313%		$15.00	5:45:36	11.988%
			$300.00	$250.00	6:45:42	12.013%
$150.00	10:24:09	17.329%	$250.00	$150.00	11:06:31	12.028%
				$30.00	17:16:48	12.038%
$112.50	10:24:09	17.345%		$100.00	20:44:10	12.046%
$899.25	145:38:08	17.346%	$3,545.00	$1,250.00	155:31:12	12.047%
$1,800.00	436:54:24

You must think about the frequency of intermediate payouts as well as the overall hit rate and house edge

Notice how the designers of the above slot machines pay very little attention to correlating payouts with the probability of getting a combination. They are more concerned with how the game plays then they are with such a correlation. The player does not know (for instance) that his $1 payout in the Blazing 7's machine is statistically very hard to get.

============
DJ, I would take those rows with extremas out of your website. They don't sell the game. Replace them with values for 1, 2 or 3 or even up to 4 standard deviations.

Because of this post, this thread has been resurrected.

It reminds me that I should update my numbers for my Poker For Roulette side bet.

My 3 spin version has a 12.6% edge and 22.3% hit rate.
My 4 spin version has a 16.1% edge and 39.3% hit rate.
My 5 spin version has a 13.0% edge and 6.1% hit rate.

Note that on my 4 spin version, 35.6 of the 39.3 hit rate is pairs or flushes, which only push.


FYI: My math and paytable page.

I would respectfully suggest reducing the HE, if there is any way possible. For a SB in Roulette, given that the HE is the same for every bet except the basket on the base game, I'd suspect that you'd want the HE to be darn close to the base...under 10% at a minimum.

Quote: Mission146

I would respectfully suggest reducing the HE, if there is any way possible. For a SB in Roulette, given that the HE is the same for every bet except the basket on the base game, I'd suspect that you'd want the HE to be darn close to the base...under 10% at a minimum.

This is a tough issue, and understandably a sore point with gamblers, but for high-payout side bets, the house edge has to be very high in comparison to flat bets offered.

I both agree and disagree. I agree that it needs to be higher than the Base Game, but is not 9-10% a reasonable middleground? I'm supposed to do worse on a SB than virtually any slot machine in the House? Those have high payouts.

9-10% is a reasonable middle ground, and many side bets are in the acceptable 7% to 14% range.
There are many side bets well above this range that are also acceptable and are getting a lot of action.

For what it's worth, I was really just posting the hit rate, but included the edge as a "what the heck."

Additionally, it's easy for the casino or distributor to adjst the edge by changing the payouts.

Unless they change the winning combinations, the hit rate is what it is.

" 9-10% is a reasonable middle ground, and many side bets are in the acceptable 7% to 14% range."

Percentage of people who regularly play side bets and know the He ? 1-2% on the high side.

Quote: buzzpaff

" 9-10% is a reasonable middle ground, and many side bets are in the acceptable 7% to 14% range."

Percentage of people who regularly play side bets and know the He ? 1-2% on the high side.

You don't have to know it to sense it. Without even quantifying it in minutes, you know how long your stack lasts (assuming same base bet) at some games compared to others.

Quote: Paigowdan

This is a tough issue, and understandably a sore point with gamblers, but for high-payout side bets, the house edge has to be very high in comparison to flat bets offered.

Not necessarily. It depends on the whole payout distribution, not just the high end. If you've got a paytable, it's more often the low-end that dictates the desirable house edge as opposed to the high-end because that's where the bulk of the hits are. Consider Lucky Nines, one of the two side bets for Twist'em:

# Nines Payout
4 Nines 50-to-1
3 Nines 5-to-1
2 Nines 2-to-1

Hit Frequency: 28.14%
House Edge: 1.46%
House Edge if top award pays 25-to-1: 4.02%

1.46% is actually lower than the main bet for Twist'em, but I'm not worried about that because that top award only happens once every 975 hands or so. The bulk of the hits, 28%, are just 2x or 5x wins, with a weighted-average win of 2.5x. For comparison, the Fire Bet's weighted-average win is over 73x.

Quote: Mission146

You don't have to know it to sense it. Without even quantifying it in minutes, you know how long your stack lasts (assuming same base bet) at some games compared to others.

And yet there are players who will always remind you that you should have made the pairs plus bet.

Quote: buzzpaff

And yet there are players who will always remind you that you should have made the pairs plus bet.

Right, but if they always make the bet, then their stack lasts about the same theoretical amount of time. I'm just talking in terms of one game + SB vs. a different game + SB.

Quote: buzzpaff

" 9-10% is a reasonable middle ground, and many side bets are in the acceptable 7% to 14% range."

Percentage of people who regularly play side bets and know the He ? 1-2% on the high side.

players do not need to know the house edge, - but WILL notice if the bet plays badly because of it.

Quote: MathExtremist

Not necessarily. It depends on the whole payout distribution, not just the high end. If you've got a paytable, it's more often the low-end that dictates the desirable house edge as opposed to the high-end because that's where the bulk of the hits are.

True, good point. A lot of the side bets I develop have 500:1 and higher top ends, with payouts that walk out the door. Side bets with a few low-ish payouts act more like flat bets, - where the winnings go back into the table.

But you need those occasional big hits to go out the door. Because with the cash goes a story that gets told to all their friends.

Next thing you know, those friends are planning a casino visit.

Quote: DJTeddyBear

But you need those occasional big hits to go out the door. Because with the cash goes a story that gets told to all their friends.

Next thing you know, those friends are planning a casino visit.

Exactly! The best advertisement is for someone to leave a winner and have it be known.
Yet, the house edges on windfall bets have to account for such money lost to the house, so the HE's can be 10% on side bets with 500:1 + payouts, and very large for progressives.

Quote: Paigowdan

9-10% is a reasonable middle ground, and many side bets are in the acceptable 7% to 14% range.
There are many side bets well above this range that are also acceptable and are getting a lot of action.

I've always felt that prop bets like hardways existed in the 19th century. Their house edge was easily calculated without any higher mathematics. But people still played the bet.

I do think that games should post their HE and their hit rate (like lottery tickets). I think it will be a lot less of disaster than companies think. Pretty soon most people will grow immune to HE, and play the games they like.

Quote: DJTeddyBear

But you need those occasional big hits to go out the door. Because with the cash goes a story that gets told to all their friends.

Next thing you know, those friends are planning a casino visit.

You don't need the win to walk out the door for the story to. Someone who hits a 500x jackpot but loses 400x back still gets to tell their friends they hit the jackpot. I've never hit a royal flush, so when I hit my first one I'll probably cash out, take pictures, the whole nine yards -- but if I were a regular gambler or AP with dozens of royals under my belt I might just keep playing. Especially if I'm on a +EV game, a royal is just variance.

Quote: MathExtremist

Not necessarily. It depends on the whole payout distribution, not just the high end. If you've got a paytable, it's more often the low-end that dictates the desirable house edge as opposed to the high-end because that's where the bulk of the hits are. Consider Lucky Nines, one of the two side bets for Twist'em:

# Nines Payout
4 Nines 50-to-1
3 Nines 5-to-1
2 Nines 2-to-1

Hit Frequency: 28.14%
House Edge: 1.46%
House Edge if top award pays 25-to-1: 4.02%

1.46% is actually lower than the main bet for Twist'em, but I'm not worried about that because that top award only happens once every 975 hands or so. The bulk of the hits, 28%, are just 2x or 5x wins, with a weighted-average win of 2.5x. For comparison, the Fire Bet's weighted-average win is over 73x.

ME, this weighted average win concept is very interesting and I am trying to figure out its meaning when you compare two pay tables. I wonder if there is some consistency between the weighted average win of successful side bets (like PP on 3CP or Trips on UTH) as compared to their max payouts. For example Lucky Nines weighted average win is 1/20th of the max win on a side bet that hits 28%. Is there some comparison of those statistics to other side bets where you could say "Lucky Nines player experience is going to have a similar feel to X bet" based on the weighted average win ratio and/or hit rate.

I guess what I am trying to say is are you on to something here where as a developer you should really be looking at more than just hit rate/house edge when designing a paytable.

One thing I have tried to do, but I don't know if it matters, is to make the positive EV of the various payouts in a paytable equally contribute to the HE. That is to say if Event #1 has a 10% frequency, and I want to make that payout 2-1 (so EV on that event is 0.10*2 = 0.2) then if the next event has a 5% frequency, I tend to make that payout equal 4-1 (so EV is again 0.2; i.e. 05*4= 0.2).

It just seems that this equal weighting will result in a better player experience. But I really don't know if this is true, it is just how I have designed my pay tables to date. Any thoughts are appreciated particularly as they relate to the weighted average win concept you highlighted.

Quote: Paradigm

It just seems that this equal weighting will result in a better player experience.

Yes - for FELT-based side bets. Examine the return, and keep its ratio close to each payout element hit frequency, (or slightly bottom-heavy) - and the bet "feels" better to the player in play.

And..

No - for progressives - where the paytable should be hugely top heavy, to allure the player with a life-changing or year-changing windfall.

Quote: Paradigm

But I really don't know if this is true, it is just how I have designed my pay tables to date. Any thoughts are appreciated particularly as they relate to the weighted average win concept you highlighted.

Quote: Paigowdan

No - for progressives - where the paytable should be hugely top heavy, to allure the player with a life-changing or year-changing windfall.

So when you say "top heavy" do you mean very little of the overall +EV of hit events is assigned the high payout or that a lot of the +EV is assigned to top payout. I think it is the former.

Quote: Paradigm

So when you say "top heavy" do you mean very little of the overall +EV of hit events is assigned the high payout or that a lot of the +EV is assigned to top payout. I think it is the former.

Well, what I meant is that the lower-end pay table items are basically eliminated from the table, to greatly increase the payouts on the top end, and in a fairly uniform manner.

In Pai Gow poker standard progressives, the progressive table REALLY starts at fairly high level, such as a four-of-a-kind, (albeit with a token 4:1 pay on the full house to ping you to keep playing it), - while the corresponding felt side bet starts at trips/straight - to reward players for very common hands.

By doing this, you create progressive system with a low-hit frequency paytable that pays out Hugely when you hit something big - keeping in the sense of "really big money for really big hands" - which is the optimal design for a windfall progressive system.

The design of a "felt bet plus progressive combo" is as follows:
1. Both a felt and a progressive are offered for the same or similar type of bet;
2. The felt side bet pays out starting at the low end, allowing for up to $25 side bets to return decently on a hot streak, and with a hit frequently and strong enough to be rewarding.
3. the progressive table design is a low $1 bet, or a $1 to $5 bet on DEQ "keypad meter" progressive systems, but pays out ONLY on the high end on the hand spectrum, with the low-end "good hands" chopped off so the high end can make for dramatic payouts - like a lottery ticket that gives a month-changing or even life changing experience if a freak hand is hit, and it hits to great fanfare and notice: somebody just paid off his house or sent his kid to an Ivy-league school, we are talking here. $200,000 on a Pai Gow Poker 7-card straight flush is a life changing amount. People go after that!
4. By allowing a $25 or so limit on the felt side bet, a not-so-rare 40:1 payout of up to a $1000 is not uncommon, often seen on the Panda-8 and Dragon-7 felt bets on EZ Baccarat, or hitting a four of a kind on Pai Gow Poker, or a straight flush or trips in 3CP's Pair Plus.
5. But the Progressive must start seriously at 500 in 1 occurance/frequency type hands and better, but have some small token payouts on middling hands to re-feed the player, and to keep him banging away at the progressive system. (Geez, I really sound like a predatory casino operations guy here, but that's how it works...)

I will say this about Three Card poker's design without a progressive, which I feel a progressive is both poor and unnecessary only for THAT game:
I played Three Card poker tonight at the Orleans, and hit big. Went with my wife, and it was HER idea...I was on a small gambling hiatus, and she says over dinner, "y'know, Dan, I'm in the mood to play some Three Card poker at the Orleans...screw seeing a movie...a $200 buy-in, a few beers....WTF..."

So I said, "Honey - NOW you're talking! Okay - Let's go!" (thinking, "did I marry a GREAT woman or WHAT!!!")
The first 3CP table was full - on a Tuesday night 11PM, dig that, and we almost jumped on a near-empty UTH table, but I asked where another 3CP was, and we found two seats together at 3rd base.
We sit down, are were slowly being attritted, and I decided to jump my bet from $5-10-10 to $5-25-25, to profit from the dealer not qualifying every time I risked playing Q-10-2 offsuit. It worked, got a streak of quarters. Tipped the lady $50. My wife now says, "may you get good Karma for that," instead of saying "That's too MUCH!" so I went up to $5-$25-$25, and then got Jh-10h-9h, made $350 in green, and went to $10-$50-$50 - and then got 6-6-6 while my wife simulateneously got 2-2-2 on her $5-$5-$5 bet! Shit...Out comes the black, and we lock things in. We played until we killed off our nickels, leaving the black and green alone, and left with $925 after tipping the dealer $175. Not bad for a $200 buy-in. This money goes to increasing my deposit on a newly ordered Ford Fusion, because I'd be a damn fool to chase it back into the rack after getting my action and some money.

But anyway, the point I am making here is that certain games do NOT well support a progressive and do not need it - and Three Card poker is one of them, I feel. Also, three card poker is neither improved by the 6-card bet on FELT, - except when playing on Shufflemaster's new I-Deal machine tables with electronic 6-card hands and bad beat. I cannot see anything else but the three elegant bets on Three Card's FELT - with a large progressive or complex bets needing I-Deal to do it without it being awkward.

This is because the extreme top and isolated top hand of AKQ in spades occurs frequently (for a progressive jackpot) of 1:25,000, and so the 3CP progressive meter is always small while having to pay off for other suited min-Royals and SF's and trips. Why seek a long-shot of 2000:1 progressive when playing nickels or dimes on the Pair Plus STILL gets you $1,200 after a straight flush, a three of a kind, and a bunch of straights in a lucky hour's play? Shufflemaster's Hit-and-Run is also suffering from low jackpots, and is getting pulled from some places because of it. A Great session with no progressive is possible on many games. If you can't get a meter to maintain $25,000 plus, that Progressive might not get action. To reiterate, it has got to be great money for great hands on a progressive. This is what I mean by "top heavy:" Huge money for huge hands, or the progressive system is ignored by players if offering puny jackpots; they'll play the felt bonus bets.

Are you getting the Fusion Hybrid and why did you order it? A dealer swap can usually get the car you want in a couple of days if it's not in stock and it's not something exotic.

Quote: 1BB

Are you getting the Fusion Hybrid and why did you order it? A dealer swap can usually get the car you want in a couple of days if it's not in stock and it's not something exotic.

As for that, I'm not getting the hybrid Fusion - I'm getting with 1.6L Turbo - with a 6-speed stick, believe it or not. This is a factory order.

Quote: Paradigm

I guess what I am trying to say is are you on to something here where as a developer you should really be looking at more than just hit rate/house edge when designing a paytable.

One thing I have tried to do, but I don't know if it matters, is to make the positive EV of the various payouts in a paytable equally contribute to the HE. That is to say if Event #1 has a 10% frequency, and I want to make that payout 2-1 (so EV on that event is 0.10*2 = 0.2) then if the next event has a 5% frequency, I tend to make that payout equal 4-1 (so EV is again 0.2; i.e. 05*4= 0.2).

It just seems that this equal weighting will result in a better player experience. But I really don't know if this is true, it is just how I have designed my pay tables to date. Any thoughts are appreciated particularly as they relate to the weighted average win concept you highlighted.

First off, remember that I design slot games for a living, so to me everything is a paytable. The passline is a bet where lots of different outcomes all have the same pay: 2x. (2 for 1 in slot speak is even money on tables).

But no, in designing games, I don't normally equalize RTP contribution across all paying outcomes. Most times that's impossible anyway -- the top award is so infrequent that the award, if one were to equally spread out the money, would be far too large. Also, the experience of playing a slot game is often about a handful of specific events -- the free spin trigger, the bonus round trigger, etc -- and there is usually enough money behind those to be more engaging. The bulk of the low-end of a slot paytable is just there to keep enough money coming out to allow the player to hit that bonus round. If the ride is too hard, players leave. But we're also talking about a 4-second game (slots) vs. a 30-, 60- or 90-second game (tables) so the feel is totally different.

All that said, that's a different issue (in my view) than the question of weighted-average pay and successful bets. The data is all on Mike's site for just about every game and side wager out there; perhaps someone wants to do an analysis? All you do is multiply each winning pay by its probability, add it up, and divide by the hit frequency. That statistic can then be correlated with (a) subjective success in the market as well as (b) top award, (c) overall hit frequency, and (d) house edge.

I've designed hundreds of slot machines, mostly for Internet casinos. As Stacy said, I tend to put more of the return in the lower wins. For example, the smallest win might get 5% of the return, and the jackpot 2% only. I tend to think that based on just the line pays, a standard deviation of about 8 per line is a good target, balancing excitement and time on device.

For table games, I have the same principle, putting more of the return in the lower pays, but enough in the high ones for an occasional shot of adrenalin. There is a certain feel and art to (hopefully) getting it right.

Thanks ME.....that makes sense.

In Lucky Nines, I assume the RTP is not equalized but also assume it isn't as heavily weighted toward the low end pay table as a slot pay table would be.

Sounds like in slots, you build the bulk of the RTP into the low end so there are frequent low amount, high frequency payouts to allow continued play that from a player's perspective, allows time for more time on device to "pursue" the free spin/bonuse round, etc. There is no "base game" in slots like there is in table games which is where a table game player would get the bulk of that kind of frequent win.

I'll see what I can distill from weighted average win on some of the successful side bets out there and report back anything worth noting. Thanks again!

One of the problems that I am running into designing slot games today is that the Las Vegas casinos keep asking for tighter and tighter games. One major casino company is now wanting games below 85%.

It is getting harder and harder to make a game fun because so little of the handle is going back to the player. A recent model I have worked on only pays 50% back in the base game and 34% in the bonus. To meet the players expected win amounts in the bonus I am only able to trigger it every 98 spins. In the old days I would have laughed at someone that presented that game to me, today I can't find any other way. High hold percentages are going to be a problem for all game developers in the short term.