In the long run...you'll never win!

[Felipe]

<ul type="square"> I read this article about Gambler's Ruin last night while browsing the web. Where it begins "Coin Flipping" is where I begin.

In short, it says that if there are two players playing a game with even odds(1:1), and they could play an infinite amount of games, one of them would eventually lose all of his money.
[*] "Even with equal odds, the longer one gambles, the greater the chance that the player starting out with the most pennies wins."

The important clause in the article is, I think, that one of the players must have more money than the other. I assume that since they are playing an infinite amount of games, the possibility of one player busting out exists. It is greater than 0.
[*]It follows that the player that starts with fewest pennies is most likely to fail."

But how can this work practically? I mean, does it really matter than the one player with more money will eventually win all the money in the long run? It seems counter-intuitive and wrong, but perhaps it has to do with playing infinite number of games, which is realistically impossible.

What does this really mean? Does this have significance for a player that gets better than even odds many times in a session? Like a good poker player?

But what if we gave both players in equal amounts of money? Does the "gambler's ruin" hold true in this case? Or does it all go to shits?

Frankly, I'm having trouble agreeing with the article. Playing with finite money and finite events, it doesn't seem right (or relevant?) that on even odds (1:1) the player starting with the most money will eventually win it all "in the long run," and the player with the least will lose it all.[/list]