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October 2nd, 2018, 11:48 PM   #11
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I suppose you wanna be a millionaire and I can help you there. The trick is not to reinvest the 90 cents return in a new bet but place them in the piggy bank straight away. Repeat the bet 1,111,112 times and then smash your piggy. You'll be flabbergasted by its content!
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October 3rd, 2018, 01:30 PM   #12
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1 + 1 = 2

Now, find a way to prove that 1 + 1 $\neq$ 2.

Am I getting this correct? We're going to need to work with an inconsistent set of axioms and take full advantage of the explosion principle for this one.

In other words, you cannot prove the odds to allow for a 0.90 return on average and then simultaneously prove the same odds to allow for a 1.01 return on average.

There is something you may find interesting though. Consider the St. Petersburg lottery:

"...the expected win for repeated play is an infinite amount of money. Considering nothing but the expected value of the net change in one's monetary wealth, one should therefore play the game at any price if offered the opportunity."

Sooooo, what would you charge someone to play if you were the casino?

Last edited by AplanisTophet; October 3rd, 2018 at 01:33 PM.
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October 4th, 2018, 12:01 AM   #13
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The Saint Petersburg paradox is a serious issue unlike the one in this thread. The practical - and computable - solution to it is to demand that both sides show in advance they can afford to pay out the loss of any unabortable betting round. This is in fact a common customer casino rule for all who cannot identify themselves as Bond - James Bond. When the Petersburg formula is adjusted to match maximum payout with cash reserve then it becomes simple to compute the value of each betting round - something near 2log"max-payout".

Last edited by Arisktotle; October 4th, 2018 at 12:12 AM.
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