Calculating flat envy payout into bet return

I'm in the VERY early stages of creating a variant of an existing game, and i'm trying to nail down the math and return on the bonus bet. I currently have a house edge of 7.49%. I'd like to include a flat envy payout, but im having trouble figuring out how to calculate a flat amount into the math along with the variable regular payouts that are based on how much you bet.


Thank you in advance for any help!

Quote: cestanl

I'm in the VERY early stages of creating a variant of an existing game, and i'm trying to nail down the math and return on the bonus bet. I currently have a house edge of 7.49%. I'd like to include a flat envy payout, but im having trouble figuring out how to calculate a flat amount into the math along with the variable regular payouts that are based on how much you bet.


Thank you in advance for any help!

So, I'm going to take a crack at this, hopefully not wasting your time, but please accept any corrections from the real math guys on here.

I think it makes a big difference whether the table minimum bet on your bet/sidebet qualifies the player for the envy.

But regardless, you start with your fixed bet amount (minimum bet that qualifies for an envy payout) as 1 unit. You'll need that later.

Make a spreadsheet with 5 columns, and as many rows as you have hands that can be envied. This will be a supplemental table to your main HE probability chart.

Then you have a column of hands that generate envy, one per row. Then a column of the fixed amount you will pay for those hands. Then a column of the number of hands possible that will pay that amount. Then a column where you divide each number of possible hands by total hands, to generate the probability of getting that hand. The last column is where you multiply the probability you just generated by the dollar amount you paid for that envy.

At the bottom of that last column, do a summation of all amounts above it: you get a number that represents the total effect of a single envy player (usually a 2nd player, but could be a single player's second hand) to the HE; it will be a positive number that needs to be added to your NEGATIVE number that is your HE. That positive number, in order to reflect the maximum effect, should be multiplied by the maximum amount of players in your game minus 1 (since the player who wins the bet does not also win the envy). That's the maximum exposure of the game to an envy pay, representing a full table with all players qualifying. You're going to want that maximum amount to be under the HE (it needs to stay negative after the addition) or the bet doesn't work (at least the paytable needs adjustment).

Sales-wise, I would make clear that the envy, while it must be considered by the casino, is a variable, and not just lump it into the HE of the game or sidebet that generates it. The HE of a game represents the results for a single player, and someone playing head-to-head never gets an envy pay, and many players don't bet sidebets, so they won't get the envy, and the number of other players who get one often varies, so it would be inaccurate to provide a hard number combining the HE and envy; it would be better to provide a range, or a per-person effect on the bet.

If your players can bet more than the fixed amount that qualifies for the envy, you can also calculate the diminished amount it affects the HE by dividing that positive number by the amount of UNITS (multiples of the minimum qualifier) they can bet. i.e. Minimum bet is $5, so that's 1 unit. Bet $6, that's 1.2 units; $10 is 2 units. The units are your divisor for the one-player envy effect you generated above. But the maximum impact on the HE will be from when all bettors are only betting the minimum required to qualify, so that's the most useful number.