Equity calculators like Poker Stove and Pro Poker Tools are great tools for analyzing your play away from the table and after the fact. However, their usefulness is limited if you don’t understand where these numbers come from and what factors influence them. For example, why is your equity versus an overpair so much better with top pair top kicker than with a pocket pair? Why does a big draw lose so much equity on a blank turn?
An equity calculator can tell you how should have played a hand, but if you don’t know how to analyze and learn from it, then it won’t necessarily help you with real-time decision-making at the table or with difficult decisions you may face in the future.
This month, I’m going to discuss a hand sent to me by a student of mine. I found it to be an interesting situation in a multi-way pot where analyzing the ranges of various players and how each of them affects Hero’s equity suggests a better line than what may be the “obvious” play. As you follow along with my analysis, notice that although I use an equity calculator to prove certain points, I always provide logic for my reasoning in a way that can be considered in real-time at the table. The point is that I’m not just armchair quarterbacking here: this is the kind of thinking about equities and ranges that you can and should conduct at the table.
The Hand
This hand occurred at a 6-max no-limit hold ’em table with $2 and $4 blinds. A decent player opened in first position with a pot-sized raise to $14. A better player called next to act, there was one fold, and then Hero called one off the button holding A [heart] T [heart]. The button and small blind folded, and a pretty fishy player in the big blind called.
The four players saw a 7 [heart] 3 [spade] 6 [heart] flop. The big blind, who had only about $200 in front of him, led out with a bet of $28 into a $58 pot. The pre-flop raiser folded, and the third player, who had about $800, called. Hero covered both of his opponents and wanted to know whether I preferred a raise or a call in this situation.
I’ll tell you first that in the actual hand, my student raised. He decided that the big blind almost certainly had a pair and was not going to fold it. Still, the big blind was short-stacked, there was a lot of dead money in the pot, and with two overcards and a flush draw, Hero could have about 50% equity even without a pair. Effectively, a raise would almost certainly force the second, deeper opponent out of the pot and let Hero flip a coin with the big blind with a considerable overlay from the dead money in the pot.
Equity Analysis
While I agree with this reasoning, I don’t think raising is the best way to play the hand if Hero doesn’t expect to have much fold equity against the big blind. Let’s accept my student’s assumptions that big blind has a pair he will not fold, the other Villain will fold to a raise, and Hero has 15 clean outs (9 hearts and 6 non-heart Aces or Tens). When Hero gets all in against 87, a one-pair hand with no significant draws, he has 52.5% equity. Considering that our assumptions are a bit generous to Hero (if Villain has A8 instead of 87, he becomes the slight favorite), I think it’s fair to round Hero’s equity to 50% against the big blind.
That means that when he puts the last $200 in against the big blind, Hero is neither winning nor losing anything. His profit comes from the 50% of the time that he wins the $86 in dead money that is already in the pot ($58 from the pre-flop action plus $28 from the second Villain who ultimately folds on the flop). That money is already in the pot, and we’ve assumed that big blind isn’t folding, so the raise increases Hero’s equity only by folding the third player out of the pot and increasing his own odds of winning.
Thus, we need to consider this third player and how he affects Hero’s equity both now and on future streets. In my view, there are three types of hands this player could have: draws, one-pair hands, and monster hands (two pairs, sets, straights).
If this Villain shows up with a monster, then Hero would of course have a lot to gain from forcing him to fold, but unfortunately he is not going to fold. When he has the monster portion of his range, we would very much prefer just to call here rather than raise and open ourselves up to a re-raise from this player that would force us to fold a good draw to the nuts.
Interestingly, if Villain has a one-pair hand, he barely affects our equity at all. If we assume that the big blind has 87, then letting the middle position player stay in the pot with 65 costs us only about 3.5% equity. This is because unless Villain’s kicker dominates one of Hero’s pair outs (ie, unless Villain has something like T7 or A6 that kills one of our outs), then he will rarely affect the outcome of the hand. Either Hero draws out to a hand that beats both of his opponents, or he does not improve, in which case he would have lost to the big blind whether or not the third player was in the pot.
Granted, equity is equity, and all things being equal we’d prefer the middle position player to fold rather than give him a free card. In light of the risk identified above, though, this small benefit might not be enough to warrant a raise.
This third player affects Hero’s equity most when he has a draw of his own. If we give him 98 for an open-ended straight draw, our equity drops by 7.5%. Given that the pot is already getting large, this is not a trivial cost. However, these draws also offer Hero the best implied odds. If Villain has 98, then a T [heart] or 7 [heart] on the turn will probably result in a huge win for Hero. If Villain has a lower heart draw, there are seven hearts still in the deck that would almost certainly cost him his stack. So while giving a free card to these draws will occasionally cost Hero the pot, it will at least as often set him up to win a much larger pot. I believe that on balance, Hero has more to gain by keeping the third player in the pot than by raising him out.
Another Consideration
I want to address one other possible argument for raising, this one dealing more with the big blind than with the third player. It could be argued that raising makes Hero’s hand easier to play by getting the money in on the flop and ensuring that he will see both the turn and river.
This is one of those situations where easier is not necessarily better. We are assuming these two players are essentially 50/50 to win the pot if all the money goes in on the flop. The question is whether either of them will have the opportunity to outplay the other on a later street if the money does not go in on the flop.
I would argue that in this case, the stars are aligned in Hero’s favor: he is the better player, he has position, and he has the draw. Sure, it would be frustrating if the turn bricks, Villain overbet shoves, and Hero has to fold a draw to the nuts. However, this is still an advantageous situation for Hero relative to getting the money in on the flop. Seeing that the turn will be a brick and having the opportunity to fold is better than getting all in on the flop and then learning that the turn will be a brick.
If Villain bets pot or smaller on the turn, Hero will have the odds to call and see the river, in which case Hero will be able to put the last of the money in on the river when he hits and fold when he misses, which is again far preferable to getting all in on the flop on a coin flip.
Can Villain make similarly good use of information on the turn and river? If he’s disciplined, which he may not be (my student described him as a fish,after all), he may be able to check-fold a heart on the turn. He will not so easily get away on a T or A turn, though. This is the advantage of being the player on the draw: Hero knows which cards are outs for him, while Villain will be in the dark on quite a few turn cards even if he knows that Hero has some sort of draw.
Conclusion
Hero has a very strong hand here, and it is tempting for this reason alone to raise. When we look at where Hero’s substantial equity in this pot comes from, though, we can see that a call is preferable. The important thing to recognize is that a raise will usually result in getting the pot heads up, for a coin flip with substantial overlay, against the player in the big blind.
Thus, the key here is analyzing how the third player in the hand affects Hero’s equity and whether we are better off raising him out on the flop or keeping him in to see the turn. Since Hero is almost always drawing to hands that beat the middle position player’s pairs, and since Hero will lose to big blind if he doesn’t catch any of his outs, then there is very little to gain by folding out this third Villain’s pairs.
When the third Villain has a draw, Hero can count on juicy implied odds by letting him see another card. When Villain has a monster hand, raising is clearly a big mistake. Without even touching an equity calculator or doing any math, we can conclude that calling is better than raising in this spot.
Results
For those of you who like to know such things, I’ll tell you that my student chose to raise to $84. The big blind moved all in, as expected, and the middle position player called again. This was sufficiently suspicious that Hero now chose just to call as well. The turn brought the 2 [diamond], middle position moved all in for about a pot-sized bet, and Hero folded. The river was the 7 [diamond], and middle position showed 43s for a flopped straight to beat the big blind’s 87s.
This article was originally published in Two Plus Two Magazine.