Re: Martingale for SNGs
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Sorry; I wasn't trying to address your specific point, but now I will -- you're making a different assumption from the one I started with. You're assuming we'll actually *play* an infinite number of games. I've assumed, as has the original poster, that the gambler facing the -EV gets to choose when to stop. That's all that's necessary to make the original position correct and my statements hold true. So long as one of the two players has a finite amount of money and the other has an infinite amount of money, this contest is over before it begins.
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In essence, this game amounts to a glorified version of "Give me a dollar". The problem as I see it, is that you're still counting one flip as an event when each event is not independent of the others. When you opponent agrees to enter the game with you, he's not agreeing to just flip the coin once. He's agreeing to flip the coin until he loses. A single event here is essentially waiting until your opponent loses, not an individual coin flip. In this sense, each individual event is still -EV for your opponent.
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In short, we're both right. Of course, that's the kind of crazy thing that often happens when you have infinities running around.
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I suppose...
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