Saturday, March 21, 2009

A Little Hand Discussion

In a recent post I implied that Matt made a mistake calling a substantial all in with 44 at the shooting star.

To set the scene there were 29 players left in the Shooting star, the blinds were 2,500/5,000 with a 500 chip ante, Matt was on the button (I've gotten conflicting info about his position, but despite what he said in his comment I think he was on the button based on the sequence he described when we first talked just after the hand) with 85,000 chips or so, Joe Sebok (a bounty) moved all in for 75,000 chips just to Matt's right and Matt called with 44.

Here is what Matt said in his comment: In terms of the call with 4-4, if anyone uses a term other than a "bold call" for that play, then they should refer to it as a "100% correct call." I mention this just in case there were any implications that it could have been the wrong play.

I played with Joe Sebok for a day and a half. For him to move in from the button for 15x the big blind, I can say with absolute certainty that he was raising with any two. With a real hand he would have raised much less. So I'm there with a chip stack that is one-fourth of average, I'm definitely not against a higher pair, and there's even a chance I could have him dominated if he has a card 4 or lower. For those reasons alone, a call was correct because I needed to gamble in order to accumulate chips and get back to having a realistic shot. Now add to the equation the fact that I get $5,000 cash if I win the hand, and not only is it a correct call, it would be a really terrible fold.

Just in case there were "other people" with "other words" to describe the play. :-)



Matt makes a good case for calling, but I still don't totally agree with him. Let's look at this hand in depth.

One of the keys here is what is the range of hands that Sebok could have. Clearly he has a weak hand and doesn't want to be called, but that doesn't mean that the total garbage hands are as likely to as the other weak ones. Despite Matt's assertion that he could have anything, I'd be surprised if anyone no matter how aggressive would just drop the all in bomb with the bottom 25% of hands when they still have 15 big blinds left.

With 44 the only way you're going to be a big favorite is if he has a 2, 3 or 4 in his hand. That's 10 if the 50 unknown cards which if your opponent moved in dark means there is a 36% chance that one of this cards is a 2, 3 or 4. But realistically I think the only hands Sebok would move in with in this spot that have a 2, 3 or 4 in them are 22, 33, 44, A2, A3, A4, K2, K3, K4, and Q2, Q3, Q4 (the last three are a little bit of a stretch in my opinion). There are 24 other hands that contain a 2, 3 or 4 that I think he would have mucked. In my estimation there would only be a 15% chance that his hand would contain a 2, 3, or 4.

We'll assume for this analysis that there is 0% chance that he has a pair bigger than 44. So if there's a 15% chance that he has a 2, 3 or 4 in his hand and 0% chance that he has an overpair there is an 85% chance that he has two overcards. In the best case scenario (vs unsuited, unconnected overcards like J6) 44 will be 55% to win and in the worst case (vs suited and connected overcards) 44 will have a 48% chance to win. So by far the most likely scenario is that you'll end up as a microscopic favorite of 1%-2%.

Let's think about something else - the $5,000 bounty. How much should that come into play in making the decision to call or fold? There was $3,282,480 left in the prize pool and Matt had 1.087% of the chips in play which means his stack was worth $35,680 (if he had 85,000) so even though $5,000 is a lot of money, it's not a major consideration. But it is a minor one and it might be enough to turn this from a fold into a call.

When I decided to write this post I was still thinking this was a fold situation and I was looking to make that point, but after looking at some of the math and taking more time to think about it it's closer to a call than I thought.

With that said - I'd still fold! This hand reminds me of a phenomenon from sit-n-go tournaments. Let's say you're playing a standard 9 handed online SNG with a player that you know as well as you could know an opponent. It's the first hand, you have pocket fives and make a standard raise to 60 chips. Your opponent who is next to act goes all in for 1,500 and everyone folds around to you. Now you know that this could only be AK since you've seen him make this play 1,000 times always with AK and have never seen him make it with another hand. Should you call?

If it were a cash game you'd call in a heart beat. You're 55% to win vs AK off suit and 52% vs AK suited. But in a SNG it's time to muck those fives and the reason is - you can find a better spot to get your money in! In tournaments there are many situations that come up that are positive expectation in term of tournament chips and negative expectation in terms of real world dollars. This is one such situation.

Think about it this way; if the house is taking 10% off the top you need to finish in the top three spots out of nine players 36% of the time (with an equal distribution of 1st, 2nd, and 3rd place finishes) to break even. To show a solid profit you need to make it to the money 40% of the time (I was in the low 40's when I played SNGs for a living).

In the hand outlined above 54% of the time you'll double up and 46% of the time you're broke. That means that the times you double up you need to make the money 67% of the time to break even (that will put your overall in the money percentage at 36%)and 74% to show a solid profit. Guess what? THAT AIN'T GONNA HAPPEN!

Matt's hand has a similar feel to me. While he was in bad shape in terms of what the average stack was he was not on total fumes with 15 big blinds. It just seems like he could have waited for a spot where he was the aggressor or had a better chance of being a substantial favorite.

As a pro it's important to spend time away from the table thinking about these things. I'm sure I'll never be up against Joe Sebok in a $10,000 tournament with 15 big blinds facing an all in and looking down at a small pocket pair. But I will face plenty of situations where I'm thinking of calling an all in with a pocket pair. This discussion and the time I've spent thinking about this hand will make it easier to put it all together and figure out what to do when I only have a matter of seconds to pull the trigger.

I welcome any other comments on this hand.

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