SNG endgame -- how to play 44

[M.B.E.]

NLHE SNG on Stars yesterday, $200+15. Down to last five. I think the correct play is different depending on whether it's a one-table SNG (pays top three, 50-30-20) or two-table (pays top four, 40-30-20-10).

Blinds are 200/400, ante 25. Chip counts are:

small blind: 7255
big blind (me): 3879
UTG: 7280
cutoff: 4216
button: 4370

UTG and cutoff fold; button (a decent player) raises to 1200; SB folds. I have 44 in the big blind. There's 1925 in pot; button has 3145 left; I have 3454 left and it's 800 to call. What's my play?

As you can see by totalling the chips in play, this was a two-table SNG so we were on the bubble. I believe folding is correct, although if the prizes were structured as a one-table SNG, with only the top three getting paid, then raising all-in would be correct.

This problem should be susceptible to a fairly precise mathematical answer (care to give it a try, Bozeman?).

[M.B.E.]

By the way, the blinds were set to rise the very next hand, to 300/600, ante 50. Does that change your answer?

I will post what I did, and the results, later.

[ZManODS]

button (a decent player) raises to 1200

Sounds like you are most likely going to be called here. If you are up against a higher pair you are have 2 outs (not a good spot), at best you are ahead around 55%/45% against 2 overcards. Its a gamble here.

Blinds are coming up quick though and you are in last place so maybe a "gamble" is a good choice, but if you believe you are better than the remaining players i would say fold.

I hate these situations because sometimes you just have to "gamble" and take a shot. If you win you will be a clear favorite to finish in the top 3. But going back to the fact that the top 4 finish, i would say fold in this situation, even if you believe you are at even skill of the remaining players.

Please let me know how you did, and i want to know some other peoples opinions.

[Mike28a]

He who blinds and runs away... or something like that.

[Rushmore]

Although it's not always so simple, in a situation like this (at this point in the tourney, stack sizes, etc.), one of my top pursuits is to be betting and not calling.

Therefore, it's raise or fold, and I think it is pretty likely you're getting called here.

I'd fold here, lose the $400. Hell, you could even do it and decide to raise first in on any two cards over 9 at the next opportunity, which I believe gives you a better chance of finishing in the money.

Been wrong before, but there it is.

[Ignatius]

This problem should be susceptible to a fairly precise mathematical answer
.
I don't think so. The situation is way too close - depending on your specific assumptions on your opponents hand, you should be somewhere between even money and a 4:5 dog, which means that your all-in odds are practically zero EV. If you had, say, a pair of 8s, it would be a clear all-in as you can expect to have him dominated more often than he will dominate you. With 44, against most hands, you are either a small favorite or a big dog.
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Calling is out of the question as it's impossible to play a small pair profitably out of position for 1/3 of your stack, so it's all-in or fold. IMO, the deciding factor in your decision is how often your opponent will fold to an all-in. If you think that he will do so at least 1/4 of the times, then go ahead and raise. Given that he has you covered and is getting 2:1 on the call, this seems very unlikely however, so without any other information, I'd fold in this spot.

[fnurt]

The button could be raising with a very wide variety of hands in this situation, including a pure blind steal. With many of the lesser hands he is unlikely to call an all-in raise, even if the pot is laying him good odds.

I think the chance of getting your opponent to lay it down, coupled with the fact that you are the short stack and thus looking for opportunities to gamble, make this worth a re-raise all-in.

[curmudgeon]

Precise mathematical answer?! /images/graemlins/laugh.gif
Youz pays your money, and youz take your chances.

You are probably a slight favorite here but all-in with 44 is ugly. Don't think I want to take a final stand with 44, but considering the blinds, you may decide its time. Just calling is not profitable, with the flop giving you a set only 10% of the time. So wait for better or not. Its poker, the beauty of it is YOU DECIDE, then take what comes!
Any single all-in showdown is chaos math not newtonian. /images/graemlins/wink.gif
Math won't provide the Answer, just a realm of probable possibles...

[John_Manley]

Fold it. You are right on the money cut-off with the opportunity to get a lot better hands than 44. My hope if I were in your position is to fold, wait for a good hand and hope that two other opponents go all-in against each other. Then you can move into the money without having to take such a risk.

[M.B.E.]

[ QUOTE ]
Math won't provide the Answer, just a realm of probable possibles...

[/ QUOTE ]
I disagree. Mathematically you can calculate my equity in the tournament under the four scenarios:

(1) I fold, leaving me with 3454;
(2) I raise and my opponent folds, leaving me with 5379;
(3) I raise, my opponent calls, and I win, leaving me with 8033; and
(4) I raise, my opponent calls, and I lose, leaving me with 0.

For example, in scenario (1), my probability of taking first-place money is 3454/27000 = 0.128. You can also calculate the probability of 2nd, 3rd, and 4th place money and from there calculate my equity in the tournament.

You can also make a fairly accurate calculation of the probability my opponent will fold if I raise, and the probability I will win the hand if I raise and my opponent does not fold. That's all you need to figure out what my best move is.

Actually, if you could incorporate Bozeman's tournament-place calculator into a spreadsheet, you could calculate my play based on various estimates of my opponent's hand range.

[M.B.E.]

[ QUOTE ]
IMO, the deciding factor in your decision is how often your opponent will fold to an all-in. If you think that he will do so at least 1/4 of the times, then go ahead and raise.

[/ QUOTE ]
Where did you get the 1/4 figure?

[ QUOTE ]
Given that he has you covered and is getting 2:1 on the call, this seems very unlikely however, so without any other information, I'd fold in this spot.

[/ QUOTE ]
Yes, he has me covered, but barely. If he calls and loses his stack will be 491, with the blinds at 300/600. Whereas if he folds he will have 3145, still the short stack but a reasonable shot at getting back into things. (With the 491, he'd need a miracle.)

I think the chance of his folding here is certainly more than 1/4, maybe as high as 1/2.

[M.B.E.]

In the actual hand, I reraised all in. My thinking was that the button could have made this raise with a variety of hands, including any ace and KT/KJ/KQ, maybe others. My stack now was big enough that if I raised him all in, folding would be a reasonable choice. Yes he had me covered, but not by much; if he called my allin and lost, his stack would be less than the big blind on the next hand.

Anyway, he thought a while, let his clock count down a bit, and finally called. He showed AKo. The board didn't help him so I won the hand, which made me the chip leader. I went on to finish second in the tournament. (I got a bad beat on the very last hand, otherwise I would probably have won, but that's another story. Anyway second place paid $1,080 for an $865 profit, nice.)

In retrospect, the fact that his hand was as good as AK made me think that maybe the potential distribution of his hands at the time was narrower than I thought. If that's right, then folding would have been correct because there'd be a greater chance of his having a pocket pair.

Also, the fact that he had to think about calling with AK makes me think I was right that there was a good chance he'd fold a lesser hand to my allin.

As I mentioned, in retrospect I'm happy with the result but I think folding would have been better, since I had enough chips to wait a little while, hoping someone else busts so I get the $360 in fourth-place money. On the other hand, if the prize structure had been 50-30-20 instead of 40-30-20-10, then raising all-in would clearly have been the correct play. But that's just intuitive, I'd love to see a rigorous calculation.

[Ignatius]

> Where did you get the 1/4 figure?
.
Feel free to pick your own number here. Each times he folds two overcards, you earn T1000. Each time he folds an overpair to your 44 (unlikely), you gain T4000. If you assume that he is 4 times more likely to fold overcards than and stick to the original assumtion that your all-EV is zero, then you end up with an EV of 1000*0.2+4000*.05 = 400 which is slightly more than 10% of your stack. For me, this is about the absolute minimum that I would risk my stack for in this situation.
.
> I think the chance of his folding here is certainly more than 1/4, maybe as high as 1/2.
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In that case, your EV should be somewhere between T500 and T1000. Even with the flat payout, moving in should be clearly profitable then. (If the button would have been me, then your chance would have been 0 however, as the only hands I might open-raise less than all-in here are exactly AA and KK.)

[curmudgeon]

Your software is in dire need of reprogramming, and there is a distinct possibility of a bug in your hardware. /images/graemlins/grin.gif

PDOH+PDIH*EOS=IT!
(the probability of me dancing on my opponents head +
the probability of something happening to me IF he does something)
times various estimates of my opponents stupidity = the answer I probably want to hear, but only if I did whatever I did do... on one million almost exactly equal situations. /images/graemlins/confused.gif /images/graemlins/crazy.gif /images/graemlins/wink.gif



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