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]

Sounds pretty dumb to me unless someone has a short BR and busts out due to variance. How can a 50/50 gamble mean that anyone is going to eventually lose otherwise???

Since it's a "coin" flip I guess the bet is only the value of the coin? Naturally if the bet size varies it changes everything. I just wanted to make sure.

If player A starts with a very small amount more than B, it seems to me a run of wins by B can change the stack sizes.

As the starting stack sizes become more lop-sided, it seems the larger stack has to have an advantage. Barring extremely long runs by the short stack.

Hell, what do I know about finite problems? I'm still trying to figure out all the simple HE math.

[elitegimp]

think of a simple case -- you and I will each bet $1 on a coin flip. Heads you win, tails I win... but there's a catch. You start with $1, I start with $100. There's a 50% chance you bust out on the first wager!

It would also apply if they started out even. If the game is infinitely long and each bet is the same there is a non-zero probability that one or other player would have a long enough losing streak to bust out.

With uneven stacks it is by no means a certainty that the short stack would bust out first. The probability that the short stack does bust out first is related to the relative size of the starting stacks

interesting thread.

[soko]

Let's just be glad it's impossible to play any game infinity times...

Speaking of time, what a waste of it reading this was.

[soko]

[ QUOTE ]
think of a simple case -- you and I will each bet $1 on a coin flip. Heads you win, tails I win... but there's a catch. You start with $1, I start with $100. There's a 50% chance you bust out on the first wager!

[/ QUOTE ]

Sure, and there is also a 1 in 2^100 (or expanded, a 1 in 1267650600228229401496703205376) chance that the I will win 100 times in a row and you will bust out.

[golfboy7]

Your question is answered by your previous statement.

basically this 'theory' lies on the basis that the larger stack can better absorb variance than the smaller stack.

This is also why we, as poker players, play with large bankrolls.

I have built my roll to 3k and keep it there making frequent withdrawls. Yet I'm still playing 2/4.

Reason? Variance. I don't want to bust out.

[Felipe]

I think I agree with what most people said. There is a good reason why poker players manage their bankrolls, and keep themselves well rolled for a particular stake (limit). I also think that if there are infinite games, then one person will bust, because his/her probability of busting is greater than 0.