送交者: Enlighten 于 2005-5-12, 19:40:01:

回答: the law of small numbers 由 xj 于 2005-5-12, 18:21:33:

Although the difference between the observed probability and the expected probablility will get closer to 0 if you have more trials, the difference between the NUMBERS of heads and tails actually tends to increase.

That means a gambler will more likely to lose all his money the more he plays, even if it's a fair coin.

You can prove it mathematically or simply run a simulation very easily.

所有跟贴:

- the difference on the absolute number of heads are sure larger -
**xj**(392 bytes)*2005-5-12, 20:52:00*- In gambling, the random walk has an absorbing barrier -
**wasguru**(42 bytes)*2005-5-12, 21:06:26*- I am not sure about mathematics behind that -
**xj**(417 bytes)*2005-5-12, 22:06:09*- absorbing barrier is when all your money is lost -
**Enlighten**(372 bytes)*2005-5-13, 10:18:08*

- absorbing barrier is when all your money is lost -

- I am not sure about mathematics behind that -

- In gambling, the random walk has an absorbing barrier -