Righto guys, basically i work in a bookies.. and i'm pretty clued up on the maths, but this one has potentially stumped me out. This problem arised because a customer moaned about the machines not jackpotting in ages, he also mentioned something about a solicitor so i just want some concrete maths to give to his solicitor
The problem is thus;
Jackpot prize is £500
You stake £1 per game
You have a 92% expectation per game (ie you lose 8p per £1 staked)
How much do you need to stake
in order for the jackpot to be paid out?
Please be aware that you can take little wins from the machine too so its not a case of [machine pays out at a ratio of X-8% = 500 where X is total stakes)
Also no smart arse answers with regards to variance 'ooh it could pay out after 1 spin' etc. I want the 'getting dealt AA' value, which is 1 per 220 hands roughly
What i did was to say;
the house edge is 8%. Thus the total stakes must be approx £6800 because 8% of that is £544 and 8% of THAT is approx £44.
Therefore when £6800 is staked, the bookies makes £544 BUT they pay out a £500 lot of that resulting in £44 profit (which is 8% of the paid out amount!)
So the chance of jackpotting is thus 1 in 6800 roughly.