When Opponents Don't Play 'Optimally'; or, Hiding from Daniel Negreanu
Andrew Brokos was kind enough to let me grow this article from one of the analogies in his excellent new book, Play Optimal Poker (reviewed here).
So it turns out you owe Daniel Negreanu $100. The origin of the debt is unimportant — what is important is that, at the moment, you are somewhat short of funds and would prefer not to pay it immediately.
You are planning to play poker this evening at either the Bellagio or ARIA. You know that Daniel will be at one of those two properties and, all things being equal, you'd rather not bump into him. Daniel, of course, would like to get your $100 to pay for his beet juice consumption while he's there.
Without going into the details — which are marvelously described in Play Optimal Poker — if you and Daniel each separately flip coins to decide where to go, then you will be at "equilibrium." There is a 50 percent chance you'll bump into each other, and neither of you can do better than that, as long as one of you is flipping a coin.
Suppose, however, you know that Daniel prefers the $200/$400 mixed-game at ARIA to that at Bellagio, and that makes Daniel a 60-40 favorite to go to ARIA. What is your correct play?
Okay, got your answer? Assuming Daniel isn't aware that you know about his mixed-game preference, your correct play is always to go to Bellagio. That will give you a 60 percent chance of avoiding him — better than the 50 percent you'd have if you flipped a coin.
Note that you shouldn't guess where Daniel is going. Your correct play is always to go where he is least likely to show up.
And here's where you say, "But Lee, the good news is that I don't owe Daniel Negreanu any money, so how is this useful to me?" I'm so glad you asked.
Let's consider a situation you probably do face. You are the button in a $1/$3 no-limit hold'em cash game. You are holding two black aces, the board is , the pot is $200, and the villain bets $150. He is representing a hand that beats one pair, even aces, so you now have a bluff catcher.
If you describe this scenario to poker buddies, the conversation will turn toward semi-bluffs that the villain might make, and to what degree your hand contains "blockers" to those bluffs. That is cards which make it harder for your opponent to be making the most likely bluffs.
In this case, your poker buddy might say, "Ah, he might bluff with the nut spade flush draw. But you have the ace of spades, so he's not bluffing with that. This means he's more likely to have a value hand and you should probably fold. If you had two red aces, then he could be bluffing with the nut spade draw and you should seriously consider calling."
This analysis is fine if the villain is bluffing close to optimally. That is if his bluffing frequency is correct, relative to the size of the pot, the size of his bet, his perception of your play, and so on. But this is rarely the case. Few players in low-stakes games bluff at the right frequency. As a pro friend of mine put it, such bets are "stupidly weighted toward value."
And now we return to avoiding Daniel Negreanu. If you know your opponents' late-street bets are "stupidly weighted toward value," then you shouldn't worry about blockers. Like always going to the Bellagio, your correct play is always to fold to such bets.
To carry this analogy further, suppose you learn (again, without Daniel's knowledge) that Daniel's beet juice preference can change his casino choice by up to 5 percent either way. So the true probability of Daniel showing up at ARIA is between 55 and 65 percent. You don't know the exact edge you'll have by always going to Bellagio, but you know for certain that it's the correct strategy.
Similarly, your typical opponent's inclination to make value-heavy bets on late streets is analogous to Daniel's game choice. And the correct response is always to fold one-pair hands to such bets. Only if you believe your opponent is bluffing at optimum frequency should you start looking at secondary considerations such as blockers.
Again, my thanks to Andrew Brokos for the catalyst of this discussion.
Lee Jones can help you avoid Daniel Negreanu and other leaks in your game. Go to leejones.com/coaching and schedule a free coaching consultation. Lee specializes in coaching low-stakes cash game players.