Odds question

I just played my first live tourney this weekend. I actually did pretty good, bubbling at 9th place out of 67 people. This is the hand that did me in:

4-handed, blinds at 100/200. I'm probably the 3rd largest stack (2nd shortest stack) at the table. There are 5 people on the other table. 9th is bubble, 4-8 get poker chip sets, 1-3 get Best Buy gift cards. I'm playing for a poker chip set.

1st position calls BB, 2nd folds, SB completes, I look down to see :Jh: :Th:. I check.

Flop comes :Ts: :Tc:.

Small blind checks, I check, other guy checks.

Turn is :Ad:.

Small blind checks, I bet 400 (pot is 600). 1st position calls, small blind folds.

River is .

I lead out, betting 400, hoping for a reraise. He reraises me all in. Now I have to think. I'm almost positive he doesn't have AA because of the PF action, he could have 33 or 88, but I'm not counting on that either. Could he have the 4th ten? With a better kicker?

What is the mathematical formula for figuring out what the odds are that he is holding TQ or TK (I'm pretty sure he doesn't have TA).

Results:
I call his allin (He's got me covered) and flip over my TJ. He flips over KT, I bubble out.

Also, how did I play this hand? I realize I'm probably not going to drive the other player off his hand, especially postflop, but was my playing okay?

Thanks,
drdeutsch

Sorry if this should be in the MTT or SNG forum. It started off as an odds question, so please move it if it needs to be.

The only thing that I see is that the next biggest hand to yours is 9T. I would not push AI with 9T or less because it is not a strong set, along with the possibility of a full house.

Tough break though, that's a hard laydown and I don't think you could have played it much differently.

You needed to bet the flop, about 2/3 of the pot. This is a dangerous board. The main thing you're worried about is that flush draw. If you lose to a higher set, meh, that's poker as they say. But checking this flop with the flush draw on board just gave someone a free card, which many people feel is the WORST mistake you can make in poker.

Side note: This advice wouldn't have helped you in this hand, but the point is that it is the right play to make. Tough break though. One other thing, you should've been playing for the biggest Best Buy gift card. Playing for anything other than first is the wrong mindset.

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If you assume he limps UTG with any two (doubtful, but lets work with it)

Then you are beat by:
33 88 AT QT KT T8 T3 AA

The last few hands are not real likely but not impossible that he slowplays AA this way.
Not sure why you rule out AT - this is not uncommon to limp UTG, and why would he bet the flop/raise the turn? Fear of flush draw, maybe - but you didn't bet it either.

There are 52 - 7 = 45 unknown cards, 45x44 = 1980 possible hands for villian

There are 6 x 3 = 18 PP hands (88/33/AA)

There are 4 x 2 = 8 higher sets (KT/QT)

There are 3 x 3 = 9 other boats (AT/T8/T3).

Under our assumptions, there is a 0.4% chance he has exactly a higher set, and overall a 1.7% chance you are beaten.

Now, our assumption is flawed fundamentally in that
a) He is not limping UTG with any 2
b) He is not raising you all in with any 2 most of the time.

So,cannot calculate the exact odds of his holding without more assumptions. Here are some hands that you beat than might make this play:

Nothing: Harrington's rule is 10% bluffs. Let'use that.
Other than the above hands that beat you:
AK/AQ/AJ/A8/A3
less likely
AX (X <= 9, not 2 pair)
KK
QQ

AK/AQ is probably pretty unlikely too, with the UTG limp. Actually, none of these seem real likely, but people can act silly, and for whatever reason, he might have thought your weak river bet was totally weak.

Let's maximize the chances you are good and say he makes this play with ANY ace (probably need a read here).

3 aces X 41 other cards (can't count the T) = 123
add in QQ/KK (played horribly) = 12 x 2 = 24

So we have: 147 hands you can beat
35 hands that beat you

So, you win 0.9 x 0.8 = .72 + .10 (bluff) 82% of the time, if he's a completly loose-agressive nut case.

Realistically - you are probably ahead more than 1/2 the time, so you can probably call.

I'm reminded of a story I heard. Can't remember the source, but basically one player asked another if they would ever fold rockets pre-flop.

The correct answer is that yes - there are times that you should fold even AA pre-flop. When I'm on the bubble or in the money, I always keep the story in mind along with the advice, "Not calling a raise is a SMALL mistake".

First, justification for the folding of AA:
If you are in the money 3 handed:
1st - 20k chips
2nd - 19.5k chips
3rd (you) - 2k chips

1st place takes $50k, 2nd takes $30k and 3rd takes $20k

You are dealt AA in last position and both people go AI before you. By all means, fold your rockets. Even if you win and TRIPLE up, you may have locked in 2nd place but are still hugely short stacked. If you muck the AA, you will either make 2nd by default or be the 2nd chipstack with a 4x advantage over the short stack.

Howard Lederer makes similar points in this article:
http://www.fulltiltpoker.com/proLessons.php?lesson=1
and recommends playing for [generally] the spot just over the bubble. In a sit n go, this is 3rd. Playing for first is the wrong mentality.

My second piece of advice is from [IIRC] Dannenham: "Not calling a raise is a SMALL mistake". If you muck here, I don't know what your stacks look like, but you may be in a great position still. Tourney play is a little different that cash games. In a cash game, calling AA preflop is ALWAYS profitable because you can just buy back in. In a tourney, especially late, being a 60-40 favorite isn't always an automatic AI. If you have a stack to sustain the blinds, you may want to wait until you are a 90-10 favorite before calling someone who has you covered.

Just some thoughts. I'm interested in any criticism of them.

I know that if I ever folded AA in the above situation , the two all-ins would split.

This would cause my skull to split.

I know that if I ever folded AA in the above situation , the two all-ins would split.

This would cause my skull to split.

Lederer's point is actually quite interesting - but I think it assumes that most SNG players play the same on the bubble as they do during the rest of the tournament.

It's clear that if the top 3 pay, it's best to play tight until 4-5 people are left (or you are short stacked! This happens fairly often in a PS Turbo - you can have M=5 with 8 people still in!).

Now - on the bubble should you play for the win or ITM? Coventional FTR wisdom is that you should play to win, but my gut feeling is that you throw away money this way.

I think the proper strategy is to be very aggressive when opening, but very tight when calling (if the call is a significant portion of your stack).

Example, lets say you have something mediocre UTG 4-handed, like QTs or 55 You open raise for 3x. BB (similar stack) Re-raises you to like 5-6x, but is not necessarily pot committed. Now, pushing over is a move... but I'm pretty sure it's not optimal unless you have a read that he will re-steal with junk. I agree, that some (most?) of the time he will not have a hand he can call your all-in with so the push-over is probably +EV. BUT how much are those 9xBB chips worth to you? I guess it's only relevant with pretty deep stacks (20x) - which is very rare on the bubble in an SNG.

What sucks about folding to the re-raise is that you don't defend your raise. Similar to folding a hand like QTs on the BB to a probable steal. What sucks more is bubbling out on a ~3:2 against to double up.

Wow, I think this is a double-highjack in the wrong forum...