Pair pays 1.2, math question

I have a program called WinPoker, and it calculates the payback percentage of any given game, no matter how custom the pay table is. Well, the one thing it can't do is decimals. So what I did was I entered in the pay table using only a payout of 1.0 for a pair, and then I entered it in using 2.0 for a pair.

I then took the difference of those games (117.6017% - 95.6105% = 21.9912%), and multiplied it by 20%, since the pair pays 1.2. Then I added it on to the 95.6105% game. I could have equally multiplied the 21.9912% game by 80%, and subtracted that from the 117.6017% game. So I'm wondering, can you do that, or does it not work like that? I'm assuming that you can't do that, because I'm taking the 20% more pay for a pair and added it on to the payback percentage for the entire game. More proof it doesn't work is the product comes out to be 100.00874%, which would only be believable for a promotion, even though it is only ever so slightly over 100%.

Interesting note: 5Dimes has a JOB game that is 100.0000%

If you put in 2 instead of 1.2, strategy could change for the increased payout. If you want to interpolate returns for 1 and 2 payout, you want to do it with the same strategy. Else you overestimate the payout for the 1.2 game.

Quote: MangoJ

If you put in 2 instead of 1.2, strategy could change for the increased payout. If you want to interpolate returns for 1 and 2 payout, you want to do it with the same strategy. Else you overestimate the payout for the 1.2 game.

This software accounts for that. But yes, I forgot about this. I have other software that can give me an advanced strategy based on the pay table I put in, but I bet that software doesn't do decimals either.

Now that I think about it, maybe that 100.00874% payback isn't that far fetched, since nobody will be using the correct strategy for this game. So do you know if you can do math like I did? I still assume not, since I just took the 20% extra pay for a single type of hand, and applied it to the entire game. What a coincidence though that I got within probably 1% of what the game's actual payback is. I guess we'll never know, since it's so unique with that 1.2 for pairs.

LOL, just found a game that pays 4.2 for Straights, 3.2 for Three Of A Kind, 2.2 for Two Pairs, and 1.2 for JOB. I seriously wouldn't be shocked at all if this game were over 100%, since how the hell would you get a strategy for this game?

Oh, and they also have one that is 1600 for the Royal Flush, and then every single other hand pays 2! Ha! Payback for that game is 99.9648%, which is great, however can you say the biggest variance of any casino game ever?

Can you multiply all wagers and payouts by 5?

This would pay:
6 for JOB
11 for Two pair
16 for 3-of-a-kind
21 for Straight

This would also mean that your coin in would have to be 5, instead of 1.

Quote: SilentBob420BMFJ

This software accounts for that. But yes, I forgot about this. I have other software that can give me an advanced strategy based on the pay table I put in, but I bet that software doesn't do decimals either.

As long as you can fix the strategy, you can interpolate between payouts. The reason is: probability of hitting any feature is determined by strategy, not payout.
Hence total return is a linear function of payout. Linear functions can be (linear-)interpolated exactly.

Quote: Dween

Can you multiply all wagers and payouts by 5?

This would pay:
6 for JOB
11 for Two pair
16 for 3-of-a-kind
21 for Straight

This would also mean that your coin in would have to be 5, instead of 1.

Common denominators! Never thought of this. Why would it have to be 5? As long as the ratio between each hand is the same down the line, I don't think it would matter. For instance, take your basic 9/6 JOB game. If, for a 1 coin bet, the Full House paid 90 and the Flush paid 60, it would be the same thing, so long as everything was multiplied by 10.

Quote: SilentBob420BMFJ

Common denominators! Never thought of this. Why would it have to be 5? As long as the ratio between each hand is the same down the line, I don't think it would matter. For instance, take your basic 9/6 JOB game. If, for a 1 coin bet, the Full House paid 90 and the Flush paid 60, it would be the same thing, so long as everything was multiplied by 10.

Crap, I see the problem now. The program is assuming you are betting 1 coin per hand, so if the payout is let's say 6 for JOB, well ya, let's just say the way I did it says the payback percentage is 499%. I guess no way to calculate these decimal games. Now that I understand what you're saying Dween, no I can't just tell it to calculate it for a 5 coin bet, it doesn't work like that. It only works for 1 coin bets, so whatever the pay table is, it's assuming you're betting 1 coin to get that payout.

Edit: Wait, could I just take that result of 499.xx% and divide by 5, since that's what I multiplied all coins by? Ya? I bet that's right.

Edit: I have confirmed that it is indeed what you can do. And since I can now calculate every video poker game they have, I have only come across one that is 100.000%, besides the 100.76% promo. Still pretty sweet though.