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

[Felipe]

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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???

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Did you attempt to read the article?

i'd say for sure... but we aren't playing 50% odds. some of us are higher, some of us are lower.... but playing blackjack where you're playing 49.5% odds if you're good, you will eventually lose all your $$$$$$.

it is true though that this is a good reason to have a 300BB bankroll (5/10 loose passive limit).

i set up some excel spreadsheets with 2BB hour win rate and 12BB/hour variability and it's amazing the different graphs you can get over 100 hours. i have it so i hit F9 and it just updates, but the swings can be frightful or occasionally you get a line that goes straight up. but also occasionally you can get a line that goes almost straight down.

Essentially, looking specifically at this statement

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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.


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This is certainly true (if not obvious), assuming they have finite amount of money.

That is because with infinite # of games (in the long run), there's guaranteed a chance of hitting a long enough bad streak (doesn't have to be infinite) for either player to lose all of their money.

You absolutely don't need an unequal starting amount of money for this to happen.

Btw, your title of "In the long run...you'll never win!" is obviously false, cause if one person loses, the other person obviously wins.

Essentially, it's because of Variance and like what Felipe said
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I also think that if there are infinite games, then one person will bust, because his/her probability of busting is greater than 0.

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Essentially, looking specifically at this statement

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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.


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This is certainly true (if not obvious), assuming they have finite amount of money.



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Ah, I’m pretty sure this isn’t right. This is beyond my limited math knowledge but I had a conversation about a similar problem with a much more knowledgeable friend.

Think about the coin problem this way. Imagine a string of events where that the coin perfectly alternated heads and tails for an infinite number of flips. Well, in this instance, neither player would go broke, ever. Sure it’s ridiculously unlikely, but the key is that it is logically possible and so the event of one of the gamblers going bust is not guaranteed. Does this make sense at all?

There's a way to calcualte this that I don't know; involving a remus(sp?) sum.

[Felipe]

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Ah, I’m pretty sure this isn’t right. This is beyond my limited math knowledge but I had a conversation about a similar problem with a much more knowledgeable friend.

Think about the coin problem this way. Imagine a string of events where that the coin perfectly alternated heads and tails for an infinite number of flips. Well, in this instance, neither player would go broke, ever. Sure it’s ridiculously unlikely, but the key is that it is logically possible and so the event of one of the gamblers going bust is not guaranteed. Does this make sense at all?

There's a way to calcualte this that I don't know; involving a remus(sp?) sum.

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I also think that if there are infinite games, then one person will eventually bust, because his/her probability of busting is greater than 0.


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You say that its rediculously unlikely, but not impossible.

The more I look at it, the more it's making sense to me. An infinite number of games is necessary for the 'theory' to hold, however. Lets say I have a 99.99999999999999999999999999999999999999999999999 99% chance to win a bet. If I play an infinite amount of games I will still lose sometime - guaranteed! I won't lose my whole roll, but I will lose one 'bet'.

edit: Ya. I need to work on that title. Too bad it's too late though.

[wadea]

I think in statistics this is referred to as an "absorbing barriers" problem. If you win 100 times in a row you continue playing to infinity and eventually things will regress to the mean in a 50/50 game. However, the first time you lose 100 in a row you are finished playing and you are the loser. To change this, you need to create an upper absorbing barrier. For example, I think you would be more likely to win than to lose if you played the same game except each time you get to 150, you would start the same game over with 100.

Maybe someone who actually knows statistics can verify this or correct it.

-w.a.

[Exitonly]

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The more I look at it, the more it's making sense to me. An infinite number of games is necessary for the 'theory' to hold, however. Lets say I have a 99.99999999999999999999999999999999999999999999999 99% chance to win a bet. If I play an infinite amount of games I will still lose sometime - guaranteed! I won't lose my whole roll, but I will lose one 'bet'.

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Well if you're only 99.999% then over an infinite amount of games, vs an opponent with a bankroll infinitely larger than yours, you would eventually hit a streak where you would lose your whole bankroll.

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Ah, I’m pretty sure this isn’t right. This is beyond my limited math knowledge but I had a conversation about a similar problem with a much more knowledgeable friend.

Think about the coin problem this way. Imagine a string of events where that the coin perfectly alternated heads and tails for an infinite number of flips. Well, in this instance, neither player would go broke, ever. Sure it’s ridiculously unlikely, but the key is that it is logically possible and so the event of one of the gamblers going bust is not guaranteed. Does this make sense at all?


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I don't think it's correct to think about it this way.

The infinite number of coin flips in this problem produces an infinite random sequence, but you're talking about a specific non-random sequence. Any infinite random sequence must contain every possible finite sequence, this is a fundamental property of infinite random sequences. Hence it follows that the game will eventually end since there will eventually be a run depleting one players stack.

This is especially true if the shorter stack goes all in every time. Say you have two people playing poker one with $100 the other with $5. If delt two randome hands and they both go all in every time the one with $100 is more likely to win, because he covers the $5 bet or the $10 bet or the $20 every time. This to me seems obvious and intuitive in terms of poker, but the part that I think is counter intuitive is the concept of infinity, since it is imaginary. It would be imposible to do it an infinite number of times and for the sake of the exercise you could just say a trillion coin flips. The larger stack just cushions the margine of chance and the shorter stack forces a more volitle situation on the gambler since, in this example, if your broke your done.

i deny it all as a fallacy! if it were true, some sumerian would have all the gold in the world at this very moment. wait, maybe there IS a sumerian with all the gold at this very moment. hmmmm.