[MMMMMM]

[ QUOTE ]
He doesn't really compensate for it

[/ QUOTE ] [ QUOTE ]

Yes he does. He knows that eventually he will win 1 unit if he doubles his bet everytime he loses. He has an infinate amount of money so that is no problem, he has an infinate amount of times he is able to make this bet, therefore he is compensating for the times he loses.

[/ QUOTE ]

OK, let's try an example which I believe should show the fallacy of this notion.

Instead of doubling up, and only after losses, let's say the gambler increases his bet by a factor of ten times ON EVERY SINGLE BET. Now, his net result will fluctuate wildly, both in the plus and in the minus columns. In fact, whether he is ahead or behind will be entirely dependent on his last result ONLY.

So, you may argue that whenever he falls behind he is sure to pull ahead in the future--as others have argued in the Martingale example. By the same argument, however, our ever-increasing-ten-times bettor is sure to not only pull ahead at some future point, but also to fall behind at some point. Yet by your logic he is "compensating" for having a negative advantage on every spin, by virtue of sometimes pulling ahead. But this cannot be true, because in this example, you can flip it perfectly upside down and say the same thing from the casino's standpoint. And now it IS the exact same thing (since the bet pattern does not alter based on wins or losses)--except for one little detail: the house edge.

So in the above example your premises and argument are used but the conclusion is clearly false. The bettor is sure to jump ahead AND behind on future spins. That however in no way allows you to take accounting only when he is ahead, or to claim that such a practice compensates for the house advantage.

By this betting pattern, whenever he falls ahead or behind it about is nine times greater than the sum of all his previous results. And he is expected to do so frequently--ON BOTH SIDES.

So merely claiming that because he has to eventually win (or lose) is irrelevant to what his expected value is, or whether he is "compensating" for the house edge. As above, the casino could simply employ the mirror image bookkeeping system. It's purely a fallacy.