Relative Hand Strength

The “Ranking of Poker Hands” included in every new deck of Bicycle playing cards ought to come with a warning: Rankings valid only at showdown. Quite a few players, knowingly or not, tend to make flop and turn decisions based on these rankings.

This goes hand-in-hand with the tendency to think about a hand as either “drawing” or “made”. It is important to realize that “drawing” and “made” actually have meaning only relative to an opponent’s hand. Whoever has the best hand is “made”, even if his hand is only K-high, and whoever has the worst hand is “drawing”, even if he has trips.

Thinking in these terms can be a costly mistake, as in many cases a draw is actually far more valuable than a made hand. The truly important factor in an early street decision is equity versus an opponent’s range. This article will help you learn to value the relative strength of a hand, based on the equity it has versus an opponent’s range and it’s potential to win money on future streets, rather than its absolute strength, or where it falls on the “Ranking of Poker Hands” chart.

Example One
Consider this example: a tight, predictable player raises from first position at a ten-handed no-limit hold ’em (NLHE) table. You put him on KQs, AJs+, AQo+, 77+. The other players fold, and you call his raise on your big blind. The two of you see a 6 [club] 6 [spade] 8 [spade] flop. You check, and your opponent bets the pot, which you believe he would do with his entire range. You need 33.3% equity to call a pot-sized bet. What do you do if you are holding AK? What about 22?

Many players would either call with both hands, or fold the AK but call with 22. The correct answer is to call with AK and fold 22. (Depending on your opponent, the correct answer could also be to raise, but we’re going to ignore that for the sake of this example.)

This might seem surprising, since 22 is a pair and AK is “still drawing”. Remember, though, that those hand rankings only count at showdown. An equity calculator like Poker Stove quickly reveals that AK has 40% equity vs. your opponent’s range, while 22 has 32%. This is because your 22 is either very slightly ahead of two overcards, which have nine outs, or drawing to only two outs against a better pair. Meanwhile, AK is in great shape against the unpaired portion of our opponent’s range, which is drawing to just 3 outs, and still has 6 outs against the pairs.

Even more important, though more difficult to calculate, is how well each hand will play on future streets. Part of the problem with 22 is that you never know where you stand. Are you calling a bet if a 4 turns? What about if a K turns? Out of position with a hand that has almost no chance of improving, it will be very difficult to outplay your opponent on future streets.

AK will still face some tough decisions, but it also stands to make some money on certain cards. If a K turns, your opponent might try to bluff at it with AQ or AJ. Or, he might check behind with something like 99 and then call a river bet. If an A turns, you’ll win one or two big bets from those same hands, and might induce a bluff from KQ. Your 22, on the other hand, would hate to see any of those cards.

Three Lessons
You won’t always be able to calculate your equity with such precision, but there are three key points to take away from this example that will help you with real-time decision-making. The first is that there is a lot of value in dominating the portion of your opponent’s range that is “drawing”. In this example, AK is actually beating the exact same portion of your opponent’s range that 22 is beating, but AK is beating it by a lot more. Hands like AQ have three outs vs. the AK but nine outs vs. the 22.

The second point is that having outs vs. the “made” portion of your opponent’s range is important. Here, AK has six outs vs. a pair while 22 has only two.

The third point is that, when there’s money behind, you want to have good implied odds on later streets. A hand like 22 will almost never improve, never be able to bet for value, and never know what to do when facing bets on future streets.

Example Two
Let’s take a look at another example that illustrates the first two points more dramatically. You are playing a $5/$10 NLHE game with $2000 in front of you. You open from one off the button with a $40 raise, the Button calls, and the blinds fold. With $95 in the pot, you see a flop of 4 [heart] 7 [heart] T [club]. You make a $95 pot-sized bet, and your opponent raises to $400. You know him to be a tight but tricky player and believe that his range consists of sets, monster draws (ie 5 [heart] 6 [heart] and 8 [heart] 9 [heart]), and about 25% random bluffs. Being out of position, you decide that you will either move all in or fold. Assuming he will fold his bluffs and call with everything else, which hand would you rather have: pocket Aces, a set of 4’s, or A [heart] 2 [heart] for the nut flush draw?

We can rule the Aces out quickly, since they are clearly weaker than the set, right? Well, yes, but in actuality they are almost exactly the same hand. If you calculate your equity vs. Villain’s calling range, you’ll see that 44 has 18% equity and AA has 17% equity.

Yet, if you held 44, your first instinct would probably be to get excited about the the raise. After all, you have the third nuts! Realize, though, that when your all-in bet is called, you lose $806 ((0.82 * -$1865) + (.18 * 4015)) in Expected Value (EV). This happens 75% of the time. The other 25% of the time, your opponent folds and you win about $600. Overall, moving all in here will lose you about $450 in EV, even though you have the third nuts! (Actually, you will win without showdown slightly more often than this, since having 44 in your hand eliminates from your opponent’s range three of the hands that can call your shove, but this is not enough to turn shoving into a winning play).

The nut flush draw actually gives you the best value on your shove, as it has about 31% equity when called. Thus, the EV of moving all in with A [heart] 2 [heart] is .75((.69 * -1865) + (.31 * 4015)) + .25 (590) ~ $116, meaning that shoving with the nut flush draw will win you a little over $100.

Taking It to the Table
Why is this happening? How can you recognize similar situations at the table when you don’t have an equity calculator available to you? The thing to think about is not how strong your hand is in an absolute sense but rather how it fares relative to your opponent’s calling range. In this case, a set of 4’s is either very slightly ahead of a monster draw or way behind a better set. The nut flush draw, on the other hand, is slightly ahead of your opponent’s draws and slightly behind his sets. Even without doing any math, recognizing this much is enough to see that the flush draw will fare better when called than will the set.

Conclusion
It takes some practice to change your mental habits. At first, you may feel silly risking all of your money with “just a draw” in a situation where you would fold a far more highly ranked hand. Less knowledgeable players may even berate you. But disciplining yourself always to think first about equity rather than absolute hand strength will let you get the last laugh while your opponents keep complaining about a “cold deck”.