Analysis (long)
 

My first reaction when I read the question was "push, and it's not close". I thought this was a clear +EV play and don't think that the fact that hero is getting close to being blinded out is very important. Andrew's response that this was a borderline case surprised me, so I decided to do a detailed analysis of the situation.

Assumptions: Typical players with slightly below-average stacks will play tighter than normal in this situation, since they can probably fold their way into the money. However, they will probably not play too tight either since they are risking only 10% of their stack here.

Quick and dirty analysis: Each blind calls with ~45% frequency. For ease of analysis, assume that if SB calls, BB will always fold (obviously this is wrong, we'll get back to this assumption later). You have 40% equity when called.

Results: 30% of the time you win 10,000, the other 70% you get called and have 40% equity but on average you'll only need 42.5% equity to break even so your -EV when you get called is only (-0.025)*(47000)= -1175. Overall EV = +2177.5

So the question remains, what if both blinds call? M.B.E estimated 29% equity in this situation. You only need 31.2% to break even (20000/64000). EV when both blinds call is (-0.022)*(64000)= -1400. This is only slightly lower than the case when one blind calls, and it doesn't account for situations when one blind bets the other one out of the pot.

A more detailed analysis using PokerStove confirms these numbers. I assumed that the BB needs ~40% equity against the button's all-in range to call (35% is break even). I gave the button a raising range of A2o,K2s,K8o,Q6s,Q8o, J7s,J9o,T7s,T9o,96s,98o,86s,76s,65s,45s. This means the BB will call with A2o,K2o,Q8o,Q4s,J9o,J7s,T7s,T9o and 98s. That's about 43% of all hands. Out of laziness, I gave the SB the same calling range, which is quite loose not only because of the reduced pot-odds, but also because SB needs to worry about the BB getting a hand.

Conclusion: EV of pushing is about +1 SB. Folding would be a significant mistake.

Comments?

Re: Tournament Tactics Question
 

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You are really only worried about AA-66 and A8 & A6. Everything else they might reasonably call with is basically a race (mostly 58-42 them).

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What about K8 and thelike?

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Your oppenent has to be pretty dang maniacal to call an all in from Sklansky with K high, weak kicker while on the bubble with a shorter than avg stack.

Not a reasonable call, so I didn't factor it in.

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If they aren't calling with K-high this is an absurdly easy push.
Unfortunately, that assumption is most likely very wrong.

Re: Tournament Tactics Question
 

I can't decide whether to limp, fold or push.

I'm getting called by one of these "typical players" unless their hands are absolutely worthless

14K in the pot.... I'm pushing and hoping to get lucky. I can't see raising to 12K is going to help me much

Re: Tournament Tactics Question
 

Leaving you 5K to not make it through the blinds? If I'd raise, I'd say $12, not $15

Re: Tournament Tactics Question
 

The purpose of raising to 15k is that it forces the small blind to risk more than the value of your stack if he wants to play. Raising to 12k would make the small blinds decision much easier, because it's now possible to reraise to an even 20k. Raising to 12k would be inferior to pushing all-in, but 15k (maybe 16k) is perfect.

Re: Tournament Tactics Question
 

Limping would be horrible. 12k wouldn't be much different from pushing. Something like 15k is optimal.

Re: Tournament Tactics Question
 

Since the blinds have you covered by 130k, I think it's dumb to throw your last chips in since the sb or bb can make a marginal call with a hand that has 86s dominated (not to mention they are getting 2:1 on their call). If the blinds had say 80k, I think it's an easier push. For me, I'd fold and hope to pick up something decent in the next couple hands. If I know I will have my hand called by any two (random) hand, I have 46% pot equity against a random hand. Maybe that's not a bad thing since I would more than double up if one of the blinds folds, but I'm still the underdog to a weighted distribution of all hands. If the players were tight with less chips, I'd push and have no regrets with the outcome.

Re: Tournament Tactics Question
 

These guys are short-stacked so are more likely to not want to take as many chances.
I've seen players fold their blinds for much less equity before without any real cause to do so....thus it isn't THAT unusual.


My point being....a call from the blinds here is NOT automatic. There is slightly more folding equity then some people think imo. Thinking that it's almost a guarantee that you are going to be DEFINITELY called by one of the blinds is ridiculous.

I think that waiting for a better opportunity is kind of reasonable....but you are still behind even with a double-up.
My first instinct is that you need to "Get out of the kiddie-pool and start making some moves!!"



With a hand like 86s the idea here is that you are very likely NOT dominaed if you DO receive a call. You DO have a chance.
The suited-connectedness is NOT irrelevent here (as one poster tried to claim). Every little bit helps.



With a hand like 86s I am going to push here.
With a hand like 86o or 95s I'm going to fold.


Anyway -
I'll estimate a 40% chance that both blinds will fold.

In the other 60% of the times that you get a call (I'll just assume for simplicity that it will ALWAYS be just one call...never both) I think you have roughly a 35% chance of winning the all-in against the general range of hands you are likely to be up against (everything from AA to A8o to KJ to even 33).
So I'll round that off to 21%.


So 40% chance of both blinds folding...plus 21% of a double-up.

My very rough estimates put you at a 61% chance of winning this hand one way or another.

Push-away I think!!!

More conservatively:

If there's only a 33% chance of getting both blinds to fold and if you are only going to win 33% of the time in the situations where one of the other hands calls (the other 67%)....then....

33% + 22% = 55% chance of winning the hand one way or another which doesn't look as promising.



I'm kinda drunk right now but I'm going to continue anyway because I'm just realizing that it's not THAT hard to factor in the difference between just stealing the blinds vs. getting the big double-up.


Lets roughly say that you have a 60% chance of ending up with more chips then you started the hand with.

In 1/3 of those situations you will win the 10k already in the pot plus 17k on average from one of the blinds.

That's 20% of the time you win another 27k
40% of the time you steal the blinds and win 10k
40% of the time you are out of the tournament and end up with zero chips.


When you win it's 1/3 chance that you have 47k at the end of the hand and 2/3 chance that you have 30k.

Combine the two for roughly 35.5k when you do win the hand (and still 0 in the 40% chance that you lose the hand).

60% of 35.5k = 21.3k
If we fold the hand then we will be left with only 19.5k after the ante.


So if I'm not completely crazy and if my estimates are reasonably close (which they probably are not) then it's a call.

I think it's possible that the folding equity might be a little less if the players in the blind actually DO have a clue (not a guarantee) and call with a more appropriate range of hands like they are supposed to.
But I also think it's possible that I greatly understated the chances of a double-up on the range of hands that they will call with (because it's probably inching closer to 40% than I had) so my incorrect estimates may, in fact, balance each other out a bit and STILL warrant a call.

Answering Vince\'s Objection
 

Do not construe the following to mean that I believe you should play the 86s.

If you play about as well as your opponents, a move that will on average double you up half the time and break you half of the time, is a move that neither increases or decreases your chances of winning the tournament. However such a move will decrease your EV especially if you are near the bubble for decent prize money. Reason being that doubling your stack increases your chances of getting into the money but does not double those chances. This is especially true if you have a very large stack, a very tiny stack, or if only one more person must be eliminated.

But none of these things were true in the example given. With a 20K stack size and a few others with 50K, doubling up would in fact almost double the chance of making the money, given four more players had to go busted. Since moving in with the 86s would win the pot around half the time and would on average about double you up, the risk of immediate elimination was almst completely compensated for by the increased chances, if the play was successful, of sneaking into the money. Thus if the play turns out to be warranted if let say, only the final table was paid, it would almost certainly still be warranted under these conditions.

Pushing is the most +$EV play
 

The SB is only getting 28:18, or about 1.5:1 on your push. I don't think he will play a very wide range of hands, and I think he will just call so rarely that the possibility can be ignored. I think he will re-raise to isolate with perhaps AA-66, AKo-A8o, AKs-A7s, KQs-KTs, KQ-KJ, QJs. This comprises 14.6% of hands.

Rounding a bit, he plays 15% and folds 85%.

Let's say that the BB calls anytime SB folds. If BB sometimes folds, this can only improve our ChipEV. So, if the play is +CEV even if SB calls with top 15% and BB calls with any 2 provided that SB folds, it must be +CEV for any other BB calling range.


15% of the time he has one of SB's calling hands.

85% of the time he has one of the other hands in the deck.

So, he calls with one of SB's calling hands 0.85*0.15 = 0.1275, 12.75% of the time; he calls with another hand 0.7225, 72.25% of the time.


On the whole, then,

CASE SB 15% of the time you're facing

AA-66, AKs-A7s, etc.... getting 28000:20000 from the pot


CASE BB1 12.5% of the time you're facing

AA-66, AKs-A7s, etc..... getting 26000:20000 from the pot


CASE BB272.25% of the time you're facing

55-, A6s-, etc..... getting 26000:20000 from the pot


CASE SB:

0.34*28000 - 0.66*20000 = -3680

-3680*0.15 = -552


CASE BB1:

0.34*26000 - 0.66*20000 = -4360

-4360*0.125 = -545


CASE BB2:

0.48*26000 - 0.52*20000 = 2080

2080*0.7225 = 1503


Total CEV: 1503 - 545 - 552 = 406


Thus, given my assumptions, pushing is +CEV. I think my assupmtions are reasonable enough that pushing is almost certainly +CEV. With the big money so far away and the prize structure as top heavy as it is, Chip EV is very close to $EV at this point. If pushing here is +CEV, it is almost certainly +$EV as well.

However...you're 62.4% or so to be dealt a better vs.-random hand than 86s on the very next hand. This seems at first glance to suggest that folding is more +$EV, but I don't think that's actually the case. Your average win-vs.random% will be only 3.8% greater than the 46.2% you have with 86s, you will have one more player to go through, and it is unlikely that the other players will fold to you again. IOW, if you could get a magical re-deal to your button on this hand, you should take it. But since folding loses you both the button and the certainty of being first in the pot, in return for only a small win% improvement, it's no good.

In conclusion, I believe the most +$EV, and thus best, play is to push.