profitable mistakes

Profitable Mistakes

I want to begin this month by looking at a few hypothetical situations:

1. You are holding a pair of 7’s on a 799 flop and get all your money in against a single opponent. The turn is a 5 and the river is an Ace. Your opponent tables A9 and drags the pot, having rivered a higher full house.

2. Same situation, but this time your opponent shows you 99 for the flopped nuts.

3. You hold 4[spade] 3[spade] on a 9[diamond] 6[spade] 5[spade] flop. Your opponent, a smart and talented player, checks and calls a ¾ pot bet. The turn is the J[club], and he checks and calls another ¾ pot bet. The river is an offsuit Q, and he checks and calls one more ¾ pot bet, turning over A[spade] Q[spade].

4. You hold KT against an extremely loose, passive, and all around bad player. He checks and calls substantial bets on a T95 flop and a 4 turn. The river is a Q, but you put in a value bet anyway, only to be called by AT and realize that you were behind all along.

What do these situations have in common? I would argue that they are all well-played hands where you had an unlucky result.

This may be more obviously the case for the early examples than for the latter ones. In fact, the first two situations are so commonly recognized as stemming from bad luck rather than bad play that they have earned themselves their own vocabulary: the “bad beat” and the “cold deck”.

Most players learn early in their careers not to take a bad beat or a cold deck as indicative of bad play. When trying to improve your game, you focus on the factors that you can control, and there just isn’t anything you can do about a lucky river card or running the second nuts into the nuts.

What is harder to see, and what I want to argue in this article, is that the latter two situations are every bit as unlucky as a bad beat or a cold deck. The results of hands (3) and (4) should not be taken to mean that your river bet was a mistake. If anything, these results suggest that you are bluffing and value betting well on the river.

Remember that neither your bluffs nor your value bets need to succeed 100% of the time to be successful. If they do succeed that often, then you are probably not doing either often enough.

Thinking in Terms of Ranges
Functionally, whenever you play a hand of poker, you are playing your cards against the entire range of hands that your opponent could have in a given situation. The fact that he happens to turn over 99 for quads instead of T9 for trips is inconsequential if you’re sure that he would have played both in exactly the same way. It’s just as far beyond your control and your concern as the Ace that flops to put that AK way ahead of your KK after the money went in pre-flop.

This is more true when playing online than when playing live. When sitting across the felt from real, live poker players you still need to use your poker and logic skills to deduce their hand ranges. However, physical and verbal tells will sometimes help you to narrow their range even further and determine whether they are bluffing this time.

For the most part, though, that information isn’t available online, and even live it is rarely as easy to use as some books make it seem. You have to make the best decisions that you can against your opponent’s entire range and let the cards fall where they may.

The really tricky thing about this is that it makes it very difficult to evaluate your own play. In example (3), did your bluff get called because your opponent rivered top pair? Or was he going to call with his AQ unimproved anyway? Would your bluff have succeeded against the smaller pairs that likely made up the bulk of his range?

Similarly, in example (4), you can’t conclude that you made a bad value bet just because you turned out not to have the best hand. That’s as absurd as concluding that you should have folded your full house in example (1) because your opponent was lucky enough to improve on the river.

So if you don’t have the results to orient you, how do you know whether you are bluffing and value betting well on the river? The truth is that you really can’t know for sure, but just as KK will show a profit against AK all in preflop over time, regardless of the results of any particular trial, so too can you look at trends in your results over time. The occasional picked-off bluff or backfiring value bet isn’t a mistake, it’s actually a hint that you’re bluffing and value betting well. By definition, playing for thin value means you aren’t going to beat the top of your opponent’s range.

Bluffing

Assuming your hand has no showdown value, a river bluff for ¾ of the pot needs to fold out a better hand approximately 43% of the time to show a profit. Of course, it’s impossible to know an opponent’s exact calling range or frequency, but theoretically, if you knew that this bluff would succeed 50% of the time and you didn’t make it, then you would be costing yourself money as surely as if you took it out of your pocket and gave it to your opponent in cash.

If your bluffs are rarely or never called, then you are undoubtedly missing profitable opportunities and leaving money on the table. Strange as it may seem, you want a ¾ pot bluff to be called about 1/3 of the time. Since you can’t know your opponent’s exact calling range, this is the closest you can get to confirmation that you are in fact bluffing at a good frequency.

In the example above, your opponent backed into top pair, top kicker- a much stronger holding than you would expect to see given the passive line that he took. From your perspective, it looked like he had a draw, possibly with a weak pair to go with it. And in fact that is what he had. He just had a few outs that you weren’t counting on. You can imagine how many other hands he could have played similarly but folded on this river: 7-5, 7-6, 9-7, 9-8, 7-7, 8-8, A[spade] 7[spade], A[spade] T[spade], and maybe even A[spade] K[spade]. His lucky river catch notwithstanding, you made a profitable bluff and the river Q is functionally a ‘bad beat’ for you even though you were behind the entire time.

Value Betting

Value betting is an even trickier art than bluffing. Discounting some rare but substantially complicating factors such as the risk of a check-raise bluff, a value bet on the river shows a profit if it is called by a worse hand more often than it is called by a better hand.

That doesn’t mean that you should be losing money on 40-45% of your value bets. Often, when you value bet the river, you will have a hand that is way ahead of your opponent’s calling range and will rarely if ever run into a stronger holding. However, your thinnest value bets should run into better hands with approximately this frequency. If you never make a bet like the one in example (4), where you find yourself betting for value into a hand that is just barely stronger than yours, then you are probably missing a lot of value by checking when your opponent would have called with many slightly weaker hands.

I deliberately chose an example where you were in position and your opponent had already checked. When you are out of position, deciding whether to fire a thin value bet is more complicated, since you must consider the expected value of your bet relative to checking and either calling or folding. But especially when in position against a non-tricky opponent, you can and should bet for value with anything that might be called by worse.

Following from that, your opponent should be calling your river bets very often, frequently with a hand that’s better than yours. As frustrating as it can be to see him table a hand that had you beat all along, you need to realize that this is actually a good sign. As long as this one of the better hands in his range, you should be happy to ship him the pot. Just think of all the times that he calls with JT, J9, or 98 as your compensation for occasionally running into AT. You should accept this result with the same equanimity that you accept that miracle Ace on the river.