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Probability Discussions of probability theory

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Old 08-05-2010, 09:31 PM   #1
Join Date: Oct 2008
Posts: 156
Slot machine probability...

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

My approach:

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.
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Old 08-05-2010, 10:20 PM   #2
AaronBrown's Avatar
Join Date: May 2005
Location: New York
Posts: 4,240
Re: Slot machine probability...

Your answer mystifies me.

If there were no smaller payouts, then the chance should be 1 in 543. If the smaller payouts added up to EV of 0.92, then the chance should be zero.

The first number below is the total EV of the smaller prizes. The second number is how many spins, on average, between the jackpots. If the EV is zero, the answer is 543 as above. If the EV is 0.5, the answer is 1,170. Your answer of 6,800 corresponds to an EV of the smaller prizes of about 0.862.

Keep in mind that to convince a statistician that there might be a defect in the machine, you'd have to go three times the expected pulls between jackpots.

0.0 543
0.1 610
0.2 694
0.3 806
0.4 962
0.5 1190
0.6 1563
0.7 2273
0.8 4167
0.9 25000
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