I'm struggling to work out odds on a game that were working on. It's probably best if I write an example as I'm really not a mathematician!
I'm working on a dice game where the player bets 1 coin and rolls 3 dice. If any of the dice are a 6 we payout based on the following.
If 1 dice is a six we pay x If 2 are a six we pay y and if all of them are a 6 we pay z
This seemed simple at first as the odds of rolling 1 six are 1/2, 2 sixes would be 1/14 and 3 sixes would be 1/216 so they would be our odds.
The issue is that in theory would have to roll the dice 216 times to get the jackpot and receive the £216 payout (at £1 per bet). However, if I did do that I would also win 108 times at 2/1, 15 times at 14.4/1 and once at 216/1 (ignoring the luck factor etc).
Therefor for my £216 stake i would win a total of £648.
So what should my payouts be for 1x6, 2x6, and 3x6 (assuming 0% house edge and all that) to be fair to the player?
Thanks for you time.