Separating the Winners From the Losers
It’s no secret that I find poker theory fascinating. Yesterday I took the Donkey Test and I want to walk through my thought process on one of the questions. I found this question particularly interesting because it really sets apart the winning players from the losing players.
Here is the scenario:
5/10 NL. $1,000 stacks. You raise to $40 from late position. A loose-aggressive player in the big blind (who has been re-raising from the blinds a lot) re-raises to $130 and you call.
Your image is loose aggressive. You and the BB have been in a few big re-raised pots so far, both of you have been bluffing and semi-bluffing relentlessly. Flop is:
He makes a $200 continuation bet. Which hand is best if you plan to raise all-in on this flop?A) 88
B) AK
C) A9
D) QJ
A beginner will look at this question, immediately choose 88 and rationalize this decision by saying “it’s best to have a pair when I move all in.” In this example, 88 is a favorite over any random hand. I don’t know the exact number you would get if you ran a simulation, but 88 would probably win over 80% of the time. The problem is that you are not up against a random hand— you are facing a range of hands.
Hand ranges are all of the possible combinations of hands that your opponent can have at a given time— and they aren’t entirely random. Because we know he is a loose player, meaning he plays a lot of different hands, and has been “bluffing relentlessly,” we are probably looking at 75+ possible different hand combinations. I would assume his range includes {22+, Ax, K9+, Q9,…}. I don’t want to list all of the hands because there are a lot and I think you get the point. Now, if we look at how 88 plays against this specific range, at best we probably have about 50% equity. Equity is essentially our odds of winning the hand + our odds of splitting the pot. From a mathematical standpoint, this is a much closer decision than it seems. If we put AK up against that same range, it is probably a coinflip situation. Again, I haven’t done the math but AK probably has a little bit more equity than 88— if it does, I’m talking about a percentage point or two. QJ and A9 have significantly less equity and should not be considered.
If 88 and AK basically have the same equity, why is AK the right answer? The decision comes down to simple poker theory. If I am shoving this flop— I’m not really looking to get called. By shoving, I am hoping to take the pot down immediately.
Because we have both been playing loose, our ranges are identical. In this situation, I would argue that shoving doesn’t change my hand range. If our ranges are identical, the Villain will call when there is a strong chance he is ahead; a small portion of his range. He will most likely call with 22, 66, any 10, JJ+, and MAYBE a strong ace.
If we have 88 the worst case scenario is a set of 10s. We can only win with a runner-runner straight. A set of 2’s/6’s is identical to 10x (a pair of 10s with one live card). We can improve by drawing to two 8’s or a runner-runner straight. Basically, we are only drawing to two cards in the deck. Our equity would be stronger if we had a lower pair and one live card because we would be drawing to five outs.
AK is much stronger because we are drawing to more outs. Again, if we see a set we aren’t looking good (remember: there are only 1.5 combinations of each set so it is a small part of his range). That scenario leaves runner-runner straight. If he has 10x, JJ, or QQ we can hit either card and improve. Facing KK, we can only improve with an ace.
In short, we are only being called if we are behind. Shoving with AK gives us the greatest chance to improve as opposed to 88.
