Mathematical explanation of having advantage with big stack

[guyincognito210]

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This is not true. Try reading anything on the topic written by Ed Miller on this forum, and I hope you will understand why. I'm not the best person to explain it to you.

But in short, it does not work that way. To stay short-stacked you would have to leave the table and re-buy as a short stack after doubling up. And this is one of the reasons that your argument does not hold up. When you lose, you don't lose everything you have won so far.

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if you cash out of after doubling up then yes you are right. can you cash out and then buy back in for less online in the same game? i thought they would make you buy in for the same you left with on the same table.
i agree with you but if you had a stack differentail like that i think thebig stack is clearly a favorite to win if you play at length.

[Ed Miller]

[ QUOTE ]
[ QUOTE ]
This is not true. Try reading anything on the topic written by Ed Miller on this forum, and I hope you will understand why. I'm not the best person to explain it to you.

But in short, it does not work that way. To stay short-stacked you would have to leave the table and re-buy as a short stack after doubling up. And this is one of the reasons that your argument does not hold up. When you lose, you don't lose everything you have won so far.

[/ QUOTE ]

if you cash out of after doubling up then yes you are right. can you cash out and then buy back in for less online in the same game? i thought they would make you buy in for the same you left with on the same table.
i agree with you but if you had a stack differentail like that i think thebig stack is clearly a favorite to win if you play at length.

[/ QUOTE ]

Say I start with $100 and you start with $12,700. We play a series of even-money games where I am a 4-to-1 favorite.

After one play, there is an 80% chance I have $200.
After two plays, there is a 64% chance I have $400.
After three plays, there is 51% chance I have $800.
After four plays, there is a 41% chance I have $1600.
After five plays, there is a 33% chance I have $3200.
After six plays, there is a 26% chance I have $6400.
After seven plays, there is a 21% chance I have $12,800, and have busted you.

So about one time in five, i'll take my $100 and bust your $12,700. Four times in five, I'll lose my $100. So yes, I am a favorite to lose my $100. But that does NOT mean that the player with $12,700 has the advantage. To see that, assume I have $1,000 in my pocket. If I lose my $100 to you, I go to my pocket for another $100. I'm going to play the double-up game until I've busted you.

There's a 21% chance I'll have busted you on the first $100.
There's a 38% chance I'll have busted you by the second $100.
There's a 51% chance I'll have busted you by the third $100.
There's a 61% chance I'll have busted you by the fourth $100.
There's a 69% chance I'll have busted you by the fifth $100.
There's a 76% chance I'll have busted you by the sixth $100.
There's an 81% chance I'll have busted you by the seventh $100.
There's an 85% chance I'll have busted you by the eighth $100.
There's an 88% chance I'll have busted you by the ninth $100.
There's a 91% chance I'll have busted you by the tenth $100.

So if we take my $1,000, a hundred at a time, against your $12,700, and we play heads-up where I'm routinely the 4-to-1 favorite, I will bust you 91% of the time. And when you bust me, you only win $1,000, whereas when I bust you, I win almost thirteen times that.

[AlanBostick]

There is no mathematical explanation of having advantage with a big stack. There *is* a mathematical explanation of having an advantage of a small stack. To find this explanation, go to http://groups.google.com/ and do an advanced search on the exact phrase "magic glasses" on rec.gambling.*

If you are a good player, the advantage of a big stack is that your implied odds (usually) go up allowing you to play more hands. The more hands you cana play, the less predictable you are.


-It's never a bad beat when the better player wins-

If your aren't that good at playing later streets, then you would might rather have a small stack so you can try to get allin preflop or on the flop and take advantage of the worst players without the better players taking advantage of you on later streets.

Being a middle stack isn't much of a problem in a cash game, but it can often be a problem in tournaments, especially when your stack is between 10-20 big blinds.