Negreanu's tournament theory regarding big pots.

[Che]

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To prove this one need only to ask the probability question "what are the chances that a good player with 20K will double to 40K before going broke".

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Maybe I'm just showing my ignorance here, but I think the size of the blinds also needs to be considered.

If the blinds are negligible, then a good player will certainly double more often than he busts out. But when the blinds are significant (e.g. an orbit costs 1/4 of the stack or more), even a skilled player is probably more likely to bust out than double since opportunities to double up as at least a 51% favorite do not come around every orbit.

I hope someone will elaborate on the flaws in my thinking.

Che

[SossMan]

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I hope someone will elaborate on the flaws in my thinking.


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There aren't any. David is ignoring this important consideration for some reason.

[cferejohn]

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To prove this one need only to ask the probability question "what are the chances that a good player with 20K will double to 40K before going broke".

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Maybe I'm just showing my ignorance here, but I think the size of the blinds also needs to be considered.

If the blinds are negligible, then a good player will certainly double more often than he busts out. But when the blinds are significant (e.g. an orbit costs 1/4 of the stack or more), even a skilled player is probably more likely to bust out than double since opportunities to double up as at least a 51% favorite do not come around every orbit.

I hope someone will elaborate on the flaws in my thinking.

Che

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Well, on average shouldn't you have the best hand *exactly* once every orbit? If there are (say) 7 players, you are going to have the best hand, in the long run, exactly 1 time in 7.

The variation is gigantic, of course, and sometimes you'll be in a situation where it didn't matter which hand you put your money in with, you were destined to lose. Otoh, sometimes you will get good cards and double up twice or more.

The problem is that there is a pretty good chance you will have to put your money in as an underdog sometimes, but remember that you will rarely be *that* big of an underdog, even when you are one.

I can't see where David is going with the idea that the small stack is actually at an *advantage* but if the small stack plays correctly (and in this high blind context playing correctly often involves getting in with marginal hands), they should have a chance of winning equal to their stack size.

Maybe this will halp. Imagine you were heads up and the blinds were so high you were forced all-in every hand. In that case, it is pretty easy to see that your chances of doubling up are identical to your chances of busting.

[aces961]

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a big stack with 40k in chips is going to win a tournament MORE than twice as often as a player with 20k in chips.


LESS, not more, if you are a good player. To prove this one need only to ask the probability question "what are the chances that a good player with 20K will double to 40K before going broke". I'll let others elaborate.

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Lets see if this helps some of you understand why what David says is true. Let 2X be your chance of winning the tourney with a 40k chip stack. Now we ask which happens first to a player with a 20k chip stack, does he double to 40k or go broke, one of these two will eventually happen. Say for a good player his chance of doubling first is 60% and his probability of going broke first is 40%.

Now if he gets to 40k first he will have a 2X chance of winning in this case which happens 60 percent of the time.
If he goes broke first he can't win. .4*0+.6*2X is 1.2X. Thus with a 20k stack this player has a 1.2X chance of winning.

We can see that for the player who will double up before going broke 60 percent of the time he will win less than twice as much with twice as big of a stack since 2 is less than 2.4.

As a side note the case when the 40k in chips gives you twice as high a chance of winning as having 20k chips occurs only if you are equally likely to go broke or double up first when you start with 20k chips.

Also if you will go broke before doubling up from 20k chips over half the time your chances will be higher than twice as much of winning the tourney if you have 40k chips than 20k

[TStoneMBD]

maybe i am incorrect in my assumptions as i am clearly debating with sklansky here, but i think it is far too presumptious to assume that a good player will double up to 40k 60% of the time without concerning many table factors including blind structure. if a player has 20k in chips, is UTG, and the blinds are 5/10k at this point he is not doubling up any more often than a poor player. id like to see a professional double up here more 60% of the time. this is clearly silly to presume this as he will be forced to push with any hand that is greater than the average blind hand. i find it difficult to believe that under these circumstances, a better player with a short stack will win more than half the time as a player of equal skill with a large stack. clearly in this UTG position, if he were to push with say, K4o, he is going to be called by a hand that is at least a 60/40 favorite to his, assuming at least 1 ace was dealt to the table. you are not doubling up 60% of the time here, but 40%, which is why having more chips allows you to survive blinds.

[Bigwig]

I read the article after I read the thread, and don't feel like reading the posts again, so if this has been said, I apoligize.

Daniel is playing limit poker, and therefore, when he calculates his pot odds, he knows that nobody can push in a bet that will cost him the tournament in that particular hand on the river. I don't see how this factor can be ignored when calculating the odds. In no-limit, drawing to the non-nuts, you may still be beaten, and it will cost you more than one extra bet.

[Chaostracize]

Negreanu also makes some weak calls on the turn sometimes... he himself stated "I know I wasn't getting odds, but there's power in that pot!".

A few things: If you're opponent doesn't know you, and sees you showdown a hand the was beaten in the flop and turn, more action in the future. And obviously, if you're drawing to the nuts, and the pot is big which means you've been getting action already, you get paid off when you hit.

[aces961]

First of all the number 60 percent was chosen randomly, as long as it is any number over 50 the result that the good player wins less than twice as much when he has 40k than 20k holds up. Secondly part of being a good player is not letting your stack get to two big blinds. In no limit especially I don't see many good players left with only 2 big blinds unless they have just lost an all in to bring them to that. Even just stealing according to the advanced system chart it would be pretty unlikely to get blinded down to 2 big blinds.
Keep in mind the tourneys that pros play in are usually nothing like the low buy in multitables online that start you off with 100 big blinds if you are lucky.

[Eldog605]

This is a reaction to this entire thread. I would think that if one got double the chips, he'd have much more than double the chances to win the tourney. Of course the downside is that you need to either play a draw with inadequate odds, or call a coin flip to double up and get that edge. Both are risky ventures.

Lets say Player X has a tough choice...he has 20,000 and if he calls a big bet and loses, hes out. Lets say he folds this hand and then gets dealt aces vs an opponent's kings, and NOW he doubles up to 40,000.
But another possibility is that Player X calls the original bet for the 20,000, and he wins and doubles to 40,000. If he then gets dealt aces vs kings on the next hand, he will double up to 80,000. If a player's chips can grow exponentially, and they can, I would think it is pretty clear that doubling up more than double's one's chances at winning a tournament. Just my two cents.

[aces961]

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This is a reaction to this entire thread. I would think that if one got double the chips, he'd have much more than double the chances to win the tourney. Of course the downside is that you need to either play a draw with inadequate odds, or call a coin flip to double up and get that edge. Both are risky ventures.

Lets say Player X has a tough choice...he has 20,000 and if he calls a big bet and loses, hes out. Lets say he folds this hand and then gets dealt aces vs an opponent's kings, and NOW he doubles up to 40,000.
But another possibility is that Player X calls the original bet for the 20,000, and he wins and doubles to 40,000. If he then gets dealt aces vs kings on the next hand, he will double up to 80,000. If a player's chips can grow exponentially, and they can, I would think it is pretty clear that doubling up more than double's one's chances at winning a tournament. Just my two cents.

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I really need to shoot down this arguement immediatly. This arguement never said anything about player skill level so lets assume they are all equally skilled. Say we have 1000 people in a tourney. They each have a 1/1000 chance of winning the tourney at the start, also say they each have 1000 chips. Now say a few hands later 500 people have been knocked out and all 500 people left have exactly 2000 chips. So now we see that the player has a 1/500 chance of winning. Now 1/500 divided by 1/1000 ia 2. So with all players of equal skill the double up in this situation has resulted in a doubling of the chances of the player winning the tourney. So the arguement that doubling up more than doubles one's chances at winning a tourney is false in the situation of equal skill level.

If you look at my previous posts in this thread you will see the only time that doubling up more than doubles ones chances of winning a tourney is when you are a below average player compared to the average player in the tourney.