Quote:
Originally Posted by henrix77
Have a question for the collective math/statistics genii...
Assume I am playing a slot machine with an expected aggragate payout percentage of 95%. Each spin costs me $10, and I must wager a grand total of $300,000. I of course realize that my expected loss is $15,000.
However, what are my chances of losing $20,000, $25,000...etc.? Conversely, what are my chances of actually coming out ahead? Is it possible to figure out these expectations without knowing the exact paytable and odds for each winning combination (in other words, is knowing just the overall EV enough)?
I'd be very interested to know what the odds are for falling within certain win/loss ranges, and more importantly, how this is calculated. Thanks to anyone who contributes.
You cannot estimate these without knowing the paytable.
Consider two concrete examples.
1) A spin costs you $10, 1 time in a million you win 9.5 million dollars, all other times you lose your $10. Then your expected loss over 30,000 spins is $15,000, but the most common result after 30,000 spins is to have lost $300,000. The chances of you losing over $25,000 is the same as the chances of you losing over $1 - both occur if you fail to hit the 'jackpot'. This happens (999999/1000000)^30000 = 97% of the time.
2) A spin costs you $10. Every time you get back $9.50. Then your expected lost is still $15,000, and the most common result after 30,000 spins is to have lost $15,000. It is impossible that you lose over $25,000. This game is extremely boring to play
Obviously those were extreme and trivial examples, but the point is to show that the EV of a spin is not enough to answer your questions. You also need to know the variance of a spin, at which point you can use the central limit theorem as the number of spins is so large. It seems to me that to calculate the variance you would need the exact paytable.
If this relates to bonus-whoring then you should choose the machine with the smallest variance to maximize your utility. The machine with the smallest variance will tend to be one that pays out relatively frequently with relatively small prizes, rather than one which has a large jackpot which is rarely hit.