Math and EV: A Scenario

I’ve been doing some poker math lately and calculating expected value (EV), which is whether or not a particular action will win you chips or lose you chips. What I’ve realized is that there are many places in my game where I am offering my opponents too good of a price to call my bets or I’m folding too often when I have the right price to gamble. These calculations can be done mentally as the hands happens, but it can be helpful to reconstruct past hands to conduct this analysis. The process also involves figuring out how your hand performs against your opponent’s possible range of hands.

Here’s an example of a hand I played (I’m not posting the hand to hide identities). I was not the player making the final decision. It’s the final table of a 1,000,000 chip buy-in mtt with 4 of 19 players remaining, and you have 16,000 chips in your stack. The other 3 players have 15,000 each. Only the final 3 get paid, and the winner gets 9,000,000, which is about 20% of your current bankroll. Blinds are 1,200. You are first to act with QT offsuit, and you limp. Two other players limp over to the big blind (ranked around 250, similar to you), who goes all in for 13,800 more to build a pot of 18,600. Do you call?

Let’s assume the big blind is loose-aggressive, the other two limpers won’t call, and that you don’t care about the implications of surviving the bubble (i.e., the value of finishing 3rd vs 4th). The math is: call 13800 to win 18600, which requires slightly more than a 40% chance to win to make calling the correct decision. If you think your opponent definitely has a hand like a weak ace or a weak king, you have a 40-45% chance to win, so calling is marginally correct, and if they have a pocket pair smaller than TT then you are 50%, and if they have even worse hands in their range, it gets even better for you. However, what if they are shoving only big pairs (TT+) or big aces (AJ+)? Suddenly, your hand has only between 38% and 15%, giving you a really bad price to call. If you believe their actual range is a combination of the very strong one and the weaker one, then the decision becomes pretty close to even. This kind of thinking actually changes my perspective on poker because I’ve always thought QTo is far too weak to call, but looking at it mathematically, it is not actually that bad. Of course, the other tournament considerations also come into play. What are your thoughts on going for the gamble on a close decision versus looking for a better situation? The math gets even more complicated with multiple players in the pot because you can get the right price to call even if you only have a small chance to win.

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As played I’d still fold. You’re not too short stacked (13BB). BB could shove virtually any 2 cards against three limpers, SB maybe folds, but the button has still to act if you call. Next hand you’re the button, hopefully a better time to make a move.

Generally, limping first to act 4 handed is weak, if your QTo is too good to fold then raise, at least min raise. Ignoring the bubble situation is wrong; 4 players with the about the same stack should make you put pressure on the others, in fear of being the bubble boy they will fold more often. With a short stack my rule of thumb is to push with 2 cards adding up to 20 in a limped pot or first to act.

Just my 2 €c


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Joe - do you ever use ICMIZER? Here is a link to the result for the hand you described. It looks like a push or fold situation with an EV almost identical either way.

As a disclaimer, I just started using this software and I may be botching the inputs up in a big way. Without software results in front of me, I am not limping this hand here. Depending on the play so far, I will muck it or enter with a 2-3x raise. In this case, I am not calling the shove. I will release the 1BB I have invested and move on.

As a further disclaimer - I am nearly worthless with new software until I get the hang of it so perhaps it would be better to hand this one off to SPG? He seems much more familiar with the ICM and NASH software available than I am. I have a few phone apps for live play and just work off memory online, I do not have as good a selection of tools to address this as someone like SPG does. In fact, SPG - I recall that you posted links to some of your favorite software in another thread but I cannot seem to find it. Any chance you would post some suggestions here for people looking for such things? Thanks.

This is the big issue here. I think you were using the cEV in your example and not the $EV as you should be for tournament calculations. As you know, in cash games, the 2 are the same but in tournaments, especially at the bubble, they are very different. You need to be positive $EV here and the Q10 calling a shove is not in this situation. The + $EV move was the shove. 2nd was the raise and third was the fold. Calling the shove after the limp is pretty significantly - $EV here so the call is to fold from the math standpoint.

You know Joe, I spend more time reading and going over hands than I do playing it seems. Sometimes I wonder if I like the analysis better than the game. In many ways, I think I do.

I agree completely with all of your analysis. I only said to ignore the bubble for the sake of the math. I would never even consider calling in this situation, but the math says it’s not that bad, especially if you think the big blind can be shoving any two cards.

Walock, I haven’t tried to use that software, but I will take a look if it’s free. I’ve never used any real poker software, just my own EV calculation and online equity calculators. Postflop situations are ranges are so complex, I can see how more advanced calculators are helpful. Sometimes I have time to do a little analysis, but not enough time to actually play, so i know what you mean.