[PairTheBoard]

[ QUOTE ]
kidluckee --

when one says "infinity" what are you really saying? It can't be logically handled because its so abstract that common concepts fail. If some event is truly infinite, then you should think that every possible outcome will eventually be realized simply because it has non-zero probability over an infinite period.

[/ QUOTE ]

It can be handled mathematically. We are not looking at a Fixed event with nonzero probablilty and with infinite trials. If that were the case you would be right in saying the event is bound to happen eventually. But in this case we are looking at a sequence of different events, each one with smaller and smaller probability. We Can handle this situation logically. We have developed mathematics to do so and in some cases of this kind - such as this one - it is Not true that one of the events must eventually occur. In this case the sequence of events is "Going broke before doubling". After each trial where the event does Not happen, the chances of the next event in the sequence are smaller.

It is useful to look at the case of infinity for finding a bound to the probabilty. If we compute the probability of not going broke over infinite time to be say 99.9% then that's a lower bound for the probabilties we're interested in for finite times. For whatever finite time you're really interested in the probabilty for not going broke is therefore greater than 99.9%.

We are in the realm of mathematics here. Vague notions don't carry much weight.

PairTheBoard