Quote from: Bugpowder on May 17, 2013, 12:07:25 AM

Quote from: dooglus on May 16, 2013, 05:29:46 AM

Quote from: organofcorti on May 16, 2013, 03:18:59 AM

The difference is that "quitting while we're ahead" means the first time you're ahead, which will probably happen early on with only a small amount bet gained.

"Quitting while you're behind" in this case means you've lost all you can afford to lose, which won't necessarily be a small amount.

The other difference is that the "ahead" is a state that may never happen for some players, if they lose their first few bets and never recover those losses. On the other hand, given the 1.9% house edge, the "behind" state will happen for all players if they just keep playing long enough. In fact so will the "lost it all" state if they play enough times.

For the purposes of analysis, imagine there's an endless line of players who take on SatoshiDice one at a time, like in a kung-fu movie. Each one starts with 100 BTC and plays until he has lost it all, then quits forever.

We can say that after the Nth player has finished playing, the house profits will be 100*N BTC.

And we can also say that on average each player bets a total of 100 / (1.9/100) = 5263.16 BTC.

I think I've satisfied myself (though probably nobody else) that people's tendencies to quit only when they've lost their bankroll doesn't affect the house's percentage profits, and that the current better-than-expected profits are merely the result of some good house luck earlier this year. Even if that whale was always intending to keep playing until he lost it all, that process could have taken him 10 times longer than it did. The house profits would be the same as they are now, but they would then be less than expected instead of being more than expected as they currently are.

Relevant analogy :

If there is a country where every husband and wife decides to have children until they have a boy, what is the distribution of boys vs. girls in the country?

Exactly the same still. Probability is a continuum regardless of how you go about it.