How is a pay table created?

How are the odds and probabilities calculations used to create an accurate/well balanced pay table?

More specifically how would a pay table be calculated for a 5 card stud game (Jacks or Better)?

IE: Royal Flush pays 800 to 1 on a Jacks or Better DRAW POKER. What would it be for STUD poker?
so on and so forth.

Thanks for any help!

If you read any of the articles the Wiz has on his WoO site about any game, you'll see how the odds of getting any particular combination is calculated.

From there, it's just a matter of coming up with a paytable where, when extended out, the payout produces a desired house edge.

Yes I've read the articles on the odds and couldn't find any mathematical correlation to the payouts and the odds. IS there an actual formula for figuring that out or is it just trial and error?

Quote: JoeConard

Yes I've read the articles on the odds and couldn't find any mathematical correlation to the payouts and the odds. IS there an actual formula for figuring that out or is it just trial and error?

No there is no formula. It's not trial and error either. The designer is trying to create a paytable that will intrigue the player with enough payouts to keep him playing for a long time. Often some payouts like '2 times' will have much lower frequency than '10 times'. Because players have little or no interest in the '2x' payouts.

A crucial point that players should understand is that there is not a very strong correlation between probability of getting a combination and the payout. Just because something pays 4 times as much is no way connected to being 4 times as unlikely to happen. Payout frequency is designed for psychological manipulation.

Quote: JoeConard

Yes I've read the articles on the odds and couldn't find any mathematical correlation to the payouts and the odds. IS there an actual formula for figuring that out or is it just trial and error?

Not a game designer here, but most games have multiple payout tables that allow houses to set the long-term payback to what they want. In the design of a game, I imagine it's a combination of trial and error and how the developer wants the game to payback. For instance, there could be a VP game that only pays on quads or better. The payouts would be very high, but the hit frequency would be very low. After testing the game, the developer may decide that the payout should be smaller on the top, but include Full Houses, to keep player interest. That piece of the development would be the trial and error piece.

For instance, Paigowdan's game EZ Pai Gow offers a side bet that pays 50-1 on the Queen High Pai Gow for the dealer... that's it. Any other hand than a Queen High Pai Gow is 0:1. The house edge is 10%. He could have had it be ANY Pai Gow, but he would obviously have to lower the payout elsewhere. I'm sure after trials of the bet, it tested well enough to keep the bet as a one-hand, super high payout.

I'm sure he'll chime in when he reads the post... I'd be interested to hear what he has to say about it.

The EZ Pai Gow game is pretty good for discussion because it has several bonus bets with different pay tables. There is actually a Pai Gow protection bet that pays on any Pai Gow. I'm looking at the description here:

https://wizardofodds.com/games/ez-pai-gow-poker/nevada/

If you look at the pay table for the Pai Gow protection bet, you can see that the return is heavily concentrated on the most likely Pai Gow hands. This ensures the bet pays off highly enough to entice the player to continue making it. You could design a paytable where all the listed hands paid off at close to fair odds. This would create a huge jackpot on the A-5 straight flush (fair odds would be over 35000:1) but to the average gambler that bonus bet would just be like pouring money down a hole, never to be seen again. I would say that nobody would play such a bet but the popularity of state lotteries argues against that statement.

It seems that there is an art to balancing the frequency and size of payouts so the player continues to want to make that bet.

Quote: jml24

If you look at the pay table for the Pai Gow protection bet, you can see that the return is heavily concentrated on the most likely Pai Gow hands. This ensures the bet pays off highly enough to entice the player to continue making it. You could design a paytable where all the listed hands paid off at close to fair odds. This would create a huge jackpot on the A-5 straight flush (fair odds would be over 35000:1) but to the average gambler that bonus bet would just be like pouring money down a hole, never to be seen again. I would say that nobody would play such a bet but the popularity of state lotteries argues against that statement.

It seems that there is an art to balancing the frequency and size of payouts so the player continues to want to make that bet.

There is, and a lot of thought went into its design.
We did make the bet somewhat "bottom-heavily" to provide a good winning feel to it. Perhaps a little too much so: tables with the bet tend to have players win back a lot of money on hands that simply would have lost. We've noticed that the bet reduces table hold (increases player return) considerably, and is very popular. Instead of holding 28% on $50,000 action, it holds 22% on $100,000, for example. Less profit percentage, but much more patronage. We cannot get rid of the bet at many locations without strong player protest.

Quote: JoeConard

Yes I've read the articles on the odds and couldn't find any mathematical correlation to the payouts and the odds. IS there an actual formula for figuring that out or is it just trial and error?

I have created, over the past year or so, it seems like close to 50 different paytables for my Poker For Roulette side bet. So I can give a better answer than what I already stated.

There is no "direct" mathematical correlation. Obviously, the events that occur more often will pay less than those that hit less often. That's as close to a correlation as you're gonna get.


And "trial and error" can take on a variety of meanings.

Since Paco says trial and error isn't involved, maybe I've been doing things wrong.

But I do rely upon trial and error.

I plug the odds into Excel, then plug a bunch of payout in, and let Excel calculate the house edge. If it's where I want it, fine. If not, I'll tweak some paylines until the payout IS in my goal area. Isn't that a form of trial and error?


One other factor has affected my process, that probably affects everyone when creating paytables. I like round numbers.

Maybe the math says one of my payouts should be $27, and another should be $63. More likely than not, they're gonna pay $25 and $75. Etc.

Quote: Paigowdan

We've noticed that the bet reduces table hold (increases player return) considerably, and is very popular. Instead of holding 28% on $50,000 action, it holds 22% on $100,000, for example. Less profit percentage, but much more patronage. We cannot get rid of the bet at many locations without strong player protest.

I realize your numbers here are hypothetical, but in that example wouldn't the lower hold percentage be good for the casino due to the increased action($22,000 held vs. $14,000)?

Yes - exactly. So it is effectively "better for the player AND better for the house." A very low volume place cannot support the volitility, but with a steady stream of players, it works out better in general.
The Pai Gow protection bet dumped EZ Pai Gow last night (and they made me deal it instead of craps); one guy kept betting $10 on the protection bet AND kept getting Jack-high and Ten-high Pai Gows ("More black chips for ME? How lovely....great game you got here, Dan...." - while I was thinking, "God...please make the bleeding stop...") His low Pai Gow hands otherwise would have been abject losers, instead he was making bank....Overall, it holds well, not too strong, and gets a ton of action. More asses in seats than a Brazillian porno movie, as they say.
It makes a little more money by returning back a lot of money; gamblers do NOT like getting killed consistently. It only takes in more money for the house IF the players' hands dealt during a session remain in the "one-pair, two-pair" zone, which is seldom the case on a busy table.

We have noticed a STRONG trend to offer Pai Gow without the insurance/protection bet at many locations; if a casino offers the game entirely without the bet on premises, then people must play without it. You will then need to REALLY get a four-of-a-kind or such hand in order to get some money back, - as your ten-high Pai Gow now avails you nothing but a loss....

A lot of People insist on the bet, kind of like saying, "it better have cruise control, or else I won't buy it...." On side-by-side tables, the tables with the bet get heavily favored.

And yes, it IS better to get a LOT more action with a somewhat reduced edge, than a lot LESS action with a killing edge. People insist on the Value meals...

" Payout frequency is designed for psychological manipulation. " Just one reason why penny slots are often
described as the " crack cocaine " of gambling.

Quote: buzzpaff

" Payout frequency is designed for psychological manipulation. "

Of course. In other words, if it feels shitty to play, no one would play the game.

Quote: buzzpaff

Just one reason why penny slots are often
described as the " crack cocaine " of gambling.

What is on one hand described as "desirable, or a value" is often described as "crack-cocaine like." I will say that THIS is the psychological manipulation.

I mean, if you walked into an auto dealership, and a salesman showed you a car with better mileage, better styling, better reliability, AND at a better price, you can also say, "Aha! I cannot resist this offer! I can easily afford this! - How DARE you offer me the crack cocaine of car deals - you BASTARD!! (where do I sign....)"

I imagine a good designer has pay-tables to be easy for the dealer to handle (and remember). Some of the more popular bets seem to have a pay-back of some sort between Evens and 3/1 while keeping a chance of a 25/1 or better payout. Beyond 100/1 and the casinos run scared and don't allow a reasonable bet or the same value as the basic game bet.

The most popular side-bet I see in the UK seems to be the Pair-Plus on 3-card poker (1 4 6 33 35), and the second "Perfect Pairs" (5 12 25 or 5 10 30 or similar) on Blackjack. Note that these both can pay >=25/1 (UK odds).

So my recommendation is to have some action which keeps the player going with regular wins whilst maintaining a long-shot chance that players DO see happen. Also set a reasonable house edge and ensure it is easy to understand. As to jackpot type bets, the problem is that these bets tend to run the player dry and so even with a reasonable run on the main game, results in a loss on the evening.


There was some discussion about house edge - I think the best design has an edge that the player feels is fair. Personally I think 1% is too generous as it might be prone to some kind of counting and over 5% is a rip-off. 1-2% seems very fair, but 2-4% is the norm. WoV advises against playing "Pair-Plus" (that'll teach US casinos to set bad odds), if it had a lower edge then more people would play it and more money be made by the casinos! However as it is reasonable odds (2.7%) in the UK, and easy to play, the bet has proved very popular here.


Why are US casinos so mean compared to UK ones?

Another obvious case is roulette in the UK (with single-zero) which remains the most popular game, whereas in the US (with double-zero) it isn't so popular. I cannot understand why US casinos don't adopt single-zero. Contrarily I have seen a few double-zero wheels appear in the UK and am told, as they also have lower table limits (50p not £1), are very popular on Friday night (presumably with students etc).

" I mean, if you walked into an auto dealership, and a salesman showed you a car with better mileage, better styling, better reliability, AND at a better price, you can also say, "Aha! I cannot resist this offer! I can easily afford this! - How DARE you offer me the crack cocaine of car deals - you BASTARD!! (where do I sign....)" "

Having actually been a used car salesman in my youth, I rememeber salesman fighting to get out the door sometimes. It was when when a guy got out of his car with Moma and the kids. He was there to buy a car, not look. LOL

Quote: charliepatrick

Why are US casinos so mean compared to UK ones?

Another obvious case is roulette in the UK (with single-zero) which remains the most popular game, whereas in the US (with double-zero) it isn't so popular. I cannot understand why US casinos don't adopt single-zero. Contrarily I have seen a few double-zero wheels appear in the UK and am told, as they also have lower table limits (50p not £1), are very popular on Friday night (presumably with students etc).

I suppose you could push a double zero on $5 for single number, $10 on groups of 4, $15 on groups of 6 or 8, $20 on groups of 12, and $25 on groups of 18. It would give the smaller betters some incentive to increase their bet, if they see other people getting pushed.

Quote: charliepatrick

Why are US casinos so mean compared to UK ones?

Another obvious case is roulette in the UK (with single-zero) which remains the most popular game, whereas in the US (with double-zero) it isn't so popular. I cannot understand why US casinos don't adopt single-zero. Contrarily I have seen a few double-zero wheels appear in the UK and am told, as they also have lower table limits (50p not £1), are very popular on Friday night (presumably with students etc).

I suppose you could push a double zero on $5 for single number, $10 on groups of 4, $15 on groups of 6 or 8, $20 on groups of 12, and $25 on groups of 18. It would give the smaller betters some incentive to increase their bet, if they see other people getting pushed.