The concept of "long run" works well in cash games, but is not very applicable in tournaments.
The reason is that ONE loss can be enough to bust you from the tournament.
For example, "in the long run" you are expected to win 4 out of 5 times with AA versus JJ.
However, you cannot know in advance whether you lose the first clash, or the second, or the third, etc.
So, if your "luck" at the bubble was to lose with AA versus JJ, the fact that you could theoretically win the next 4 clashes with AA does not help you if you bust out.
Sure, it does not help you seeing as you are busted at that moment, yet where do you stand in this game if you are not willing to make a bet that you will win 4 out of 5 times?
It's never fun to bubble, and you could very well still reach the FT while folding AA on the bubble.. But even in tournament play I will take this shot without second thought, as even doubling up from 10BB to 20BB is a step in the right direction. And if I happen to bust out, this has happend and will happen again, I'm able to live with it in peace, knowing I made the choice that suits me, and my goal the most.
And just to show the math:
In 4 cases you double up on the bubble and end up with X% of the minimal prize. (X must be >=100)
In 1 case you bust out.
The minimal prize is Y times the buyin.
So:
1st scenario - CALL with AA:
(4 * X% * Y * buyin) - (5 * buyin) = net winnings (averaged for 5 or multiples of 5 cases)
(buyin) * (4 * X% * Y - 5) = net winnings.
2nd scenario - FOLD with AA:
(5 * Y * buyin) - (5 * buyin) = net winnings /you don't earn X% by doubling, but you don't bust 1 time out of 5 either/
(buyin) * (5 * Y - 5) = net winnings.
To compare Scenario 1 with Scenario 2, you must divide by buyin:
4 * X% * Y - 5 ><= 5 * Y - 5
4 * X% * Y ><= 5 * Y
4 * X% ><= 5
X% ><= 1.25
Here is the break-even point !
If doubling up in CHIPS guarantees you minimum 25% bigger prize than the minimal prize, you call.
If you don't win more than 25% than the minimal prize, you fold.
Statistically, the % of the minimal prize is bigger if you have a bigger stack to call with at the bubble !
If you have a very small stack, even doubling up will not guarantee any % over the minimal prize.
Hmmm.. This is all true, doubling up does not necessarily equal to a bigger prize.
But I think that there are a lot of incalculable factors missing..
Going card dead and blinding out after folding AA.
^resulting in a min. payout of 1-2 BI.
Doubling up with AA on the bubble and then losing the very next hand or so..
^Resulting in no payout or again the min. payout.
Having no one call your AA and just swooping the blinds(+antes).
^Could very well result in going absolutely card dead and getting blinded out if you are low enough, but at least gives you another round of hands.
Having multiple people call AA and winning the pot(or split the pot, etc.)
^Best case scenario I guess.
Results can range from busting out to winning a pot that changes your stack (example: half of the average stack) to a stack with a bit more flex in it (example: twice the average stack).
I know I'm pulling something older back up, but I also like a healthy discussion!
Greetz
D V.