One more thing about the folding option: if hero just folds and many people have really small stacks, then the bubble may burst in an estimated for example 10 hands on average. Then hero still has a significant amount of chips (is not totally being blinded out), so the option playing this hand should give that amount plus the average added tournament equity, compensating for the 25% risk of being kicked out in this hand.

After surviving the bubble hero of course immediately starts using normal small stack strategy, all-ins when the cards tell so.

predator, how many hands were played hand for hand on this actual bubble? Just to get a picture of how long they may last. Very important for deciding about folding "good" hands.

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Quote:

so the more chips you have the more $EV you are risking...

The point why a bigger stack can ignore the bubble more is that with a bigger stack this:
means that on average you may win more by playing this hand in absolute money = tournament equity than the 25% of the min cash. With a very small stack the 25% of the min cash is something you may want to try not to lose, for maximizing ev, in this case by folding.

To look at it in extreme: with a really small stack at the bubble your realistic end point for the tournament, if it goes well, is to manage it to the min cash. Excactly when this becomes favorable depends on a row of factors.

I may correct myself a bit, the bigger stacks are better not ignoring the bubble, but should try to cash in on the (rightfully) scared short stacks before the bubble bursts. But they shouldn't be scared themselves, that's of course what I meant.

The quoted example (SNG) you provided above is a totally different situation from the one that OP presented (MTT). Different considerations. Maybe we can discuss them another time, in another thread...

Still makes no sense whatsoever...

Less ignore the added benefit for the short stack by splitting:
Totally hypothetical numbers!!!

small stack:
$EV start/split: 2000$
$EV double: 3000$
$EV lost: 0$

medium stack:
$EV start/split: 6000$
$EV double: 8000$
$EV lost: 0$

(0.5*3000+0.25*2000+0.25*0)-2000=0
(0.5*8000+0.25*6000+0.25*0)-6000=-500

The benefit of doubling as a small stack will always out weight the benefit of
doubling as a mid stack, as long as every additional chip is worth less...
And we don't have some ridiculous scenario involving a really small stacks.

We are talking relative numbers and absolute numbers here, important to keep them apart. When it comes to the min cash, then it's an absolute number, let's say in your example $5000. By playing with the small stack you on average win $1000 by the doubling, but lose .25x$5000= $1250 by busting, that's a net loss of $250. With the medium stack on the other hand you on average win $2000 by the doubling, but still are losing on average $1250 by the busting. But here you can book a net win of on average $750!

I know it's a simplified model, but this is a big flawed assumption. The EV of the medium stack losing is not zero. The big stack can shove, get called by a smaller stack, get scooped, and still have tournament equity. The shortest stack at the table obviously has no such possibility.

There are other simplifying assumptions that might need to be addressed, e.g. a split isn't really the same as folding, but ICM gets really complex fast for split pot games.


And conversely, that's not a good assumption either. A medium stack obviously starts with more equity than a short stack, so it has more to lose by busting out.

It also has more to gain the times it's staying in, during that very hand when it risks to bust. The gamble pays off in the long run.

Remember that a stack potentially can bust at any hand during the whole tournament, if it isn't the biggest at the table. We are only looking at the specifics of the bubble here, what happens during those few hands if a short or middle sized stack gets a good hand near the bubble, with that strange min cash in the horizon.

The bubble is indeed very strange, imo. You go from zero to a substantial amount in just one step. The next steps increase very slowly. In the beginning of the WSOP history the min cashes were lower than the buy in. That would make things smoother, but apparently the psychology of humans don't allow the min cash to be lower than the buy in.

4 pages long lol.

Yeah, looks it's time to move on

No it wasn't flawed, he said that its better to bubble with a medium stack, that
implies at the medium stack always plays for his tournament life (IE shortest
stack at the big stack table). And all my simplifications hurt the equity calc
of the small stack, because he benefits more from splitting. A complete ICM
spot analysis is impossible(not enough data) and unnecessary.

OK, fair enough. Then he's making an unreasonable stipulation. A medium stack usually won't be the shortest stack at the table, and when it shoves UTG+2, it will often be possible for it to get called by a shorter stack. So comparing a short stack shoving, which probably won't cover the calling hand, with a medium stack that might cover, isn't reasonable.

The worst case (get called by a deeper stack, get scooped, gg everyone) is equally bad, $0 EV, but much more likely for a short stack that gets called.

I think if you accept the hand equities in the OP for the actual tournament he was playing in, folding is indeed better than playing the hand.

Let’s do an estimate of his EV in each situation. First, let’s assume that if the OP folds, he makes the money 100% of the time, and he also does so if he splits or scoop when playing the hand (I think reasonable assumptions). I’m also going to ignore the additional equity of the splitting or winning the small blind in the HU pot.

If the OP folds, he wins $2400 100% of the time, plus whatever the additional post-bubble tournament equity he has from a 6000 chip stack. 6000 chips in this tournament is about 0.13% of the chips in play. The tournament has a prize pool of about $1.25 million, of which about $250,000 is immediately awarded on the bubble. So we might estimate that a 6000 chip stack has an additional post-bubble equity of $1,000,000*0.13% = $1300.

So the EV of folding is $2400 + $1300 = $3700

If the OP plays the hand:
- 25% of the time, he busts: EV = $0
- 25% of the time, he splits, which essentially has the same equity as folding: EV = $3700
- 50% of the time he scoops. In this case, he wins $2400 plus the post-bubble equity of a 12k chip stack. We might estimate that this is twice the equity of a 6k stack, or $2600. So EV = $2400 + $2600 = $5000 (This actually slightly overestimates the equity here since chips have diminishing marginal value, but we also aren’t including the small blind, so it probably sort of offsets.)
So the EV of playing the hand is (.25*$0) + (.25*$3700) + (.5*$5000) = $3425

Therefore, folding is slightly the better play here.
The estimate doesn't account for ICM distortions in the post-bubble equity, but if it had, it would lean even more toward folding, since these distortions further enhance the value of your tournament life.
I do think the OP is somewhat underestimating the value of his hand (he certainly doesn’t know the BB has A2KK when he has to make this decision). But if we accept his premise, he was right to fold.

I should also note that if the OP had a medium stack (say, 1% of the chips in play) instead of an extreme short stack, he would be better off playing the hand given the same probabilities of scooping and busting.

In this case, the EV of folding would be $12,400, while the EV of playing would be $14,300.

But will always fold if the bubble hasn't burst, or else we should just play this one.

Not really. Depending on the situation (mostly on the stack size), the pot could be laying us better odds than open-raising with AA2. E.g., suppose we have J98s4 in the BB. The CO opens and it folds to us. If we started with 2bb, we're now getting 3.5:1 to defend. Against a top 15% hand, we have 38.5% equity.

So our chip EV advantage to defending might be greater than our chip EV of open-raising (even bearing in mind that we might take down the blinds without a fight).

However, I agree that if we have more than 1 sb left after folding and there are still a "TON" of shorties left, then it would likely be advantageous not to defend.

In this situation we'll have 4bb left in 2 hands and should fold AA35 as we're getting called nearly 100% to any open, as opposed to opening our 5bb stack and maybe getting a walk 2 hands earlier.

hahahaha

this thread makes me happy

failure ratio (illogical thought : logical thought) is seriously around 99:1

I think it's pretty simple here.

"Pred looks down, sees AA35, oh boy what to do? Thinks about odds and ICM and whatever, then comes to the realization that if he does not bring home a cash, this now part-time player pl08 player, that his wife will have his nutsack for breakfast. Come home empty? Sure you can come to Vegas next year alone. ha ha."

As always, Pred does the smart thing. Hats off to you my friend Sorry I missed you this year.

I don't know about nutsack for breakfast, but a min-cash prob does shade things toward a return trip in the future.

Good point, imo. Thread didn't account for Meta enough.

ppl tryin to cash fold ppl tryin to win get it in simple as that

wat about ppl tryin to maximize ev?

They are over thinking something that in the heat of the moment boils down to what whothedonk said?

In the middle of a hand, it's hard to make this sort of calculation. But when you are hand-for-hand on the bubble, there's a ton of down time. It is really not that difficult to get a rough estimate of what sort of equity you have in a tournament given your stack vs. your equity if you double up, and from there figure out what sort of EV your hand would need to have against a reasonable calling range in order to be playable.

How this EV translates into an actual hand range in NLHE also isn't that hard to estimate. It's a lot less clear in O8. I think the most suspect part of the OP's decision is not that he should fold a hand with 50/25/25 equity, but rather that his actual hand (AA35ds) only has 50/25/25 equity. I ran a pro poker tools simulation of the hand against a top 10% range, and it only gets scooped 17% of time. And this is already assuming that he gets called.

In any case, "I'm playing to win" is a pretty foolish attitude to take any any point in a tournament prior to heads-up. You really need to play with an awareness of the entire prize structure.

Depends on how well rolled you are imo. If you can afford to go for it you should I think.