送交者: mangolasi 于 2005-5-13, 16:26:06:
回答: the law of small numbers 由 xj 于 2005-5-12, 18:21:33:
wasguru is sharp-eyed. "Sequence" can tell you a lot.
Actually, in the coin tossing assumption, all I look at are:
1) the markovian property of coin tossing, and assume the coin to be fair, thus my choice of T/H would be indifferent.
2)after getting some H in a row, I doubt the fairness of the coin thus Baysien (though I hate the concpet) kicks in and I would bet H.
Hard to see anyone would do the opposite betting T.
And yes, there is fair game (remember the concept "martingale"?). The crux of a glamber's ruin is:
1)the game is fair or less fair (the prob favoring him is <=1/2)
AND
2)his finite resource v.s. a infinite resource rival
AND
3) repeat indefinately or has an infinite stopping criteria (i.e. a more habitus glamber or a more ambitious glamber), that's why Enlighten said the more trials the glamber does, the more likely to lose all money. Thus if the glamber dies before the expected ruin time, the 50-50 game is on average "fair" to him during his play time since it's a martingale. Only if he survive the expected ruin time he is lucky--surviving something he should not in terms of probability. And your sunk cost argument is problematic. A lost is lost forever, but a gain is a gain forever, also.