This is the second installment of my weekly poker column in the Economic Times, Range Rover.
‘Math is over-rated in poker,’ said a friend the other day. ‘Poker is about psychology, reads, getting inside your opponent’s heads. Math, shmath, pah.’ This is a popular view among many recreational players – but they couldn’t be more wrong. In my view, maths is the foundation of poker, and everything else feeds into it. If you do not master the numbers game, you cannot master poker.
Consider what a decision at a poker table involves. You’re in a hand against an opponent. From the information available to you, you try to put him on a range of hands, and modify that as the hand progresses. Your actions depend on two things: the equity of your hand against his range; and the likelihood of his folding or calling at any stage. Simply put, pot equity (PE) and fold equity (FE). Once you estimate those, it’s just a matter of crunching the numbers to come up with the mathemetically correct decision.
Now, your reads and psychological insights are not irrelevant. On the contrary, they’re among the tools you use to figure out your opponent’s range, and how likely he is to call or fold. In other words, they help you arrive at both your PE and FE in the hand. But having done that, it boils down to the math. Here’s an example.
Stacks are deep, you open with AJcc on the button. The big blind flats. The flop comes KJ2 with two hearts. BB checks, you bet, BB calls. You now put him on a range that includes any king he calls with preflop, any jack, middle pocket pairs like TT and 99, the open-ender with QT and any flush draw he called with pre. The turn is a brick, an offsuit 5. Both of you check. The river is another offsuit 5. He now bets 75% of pot. What do you do?
You’d expect him to check back here with any jack, TT and 99. Let’s say he value-bets every hand that beats you, most probably top pair. And he bluffs with QT and every plausible missed flush draw. Against this range, we have 33% equity. Since he bet 75% of pot, we’re getting 2.3 to 1 to call here, meaning the call is justified if we have 30% equity. We have 33%, so we call.
But let’s say that you are an astute reader of this particular player, and of the situation. He tends to be passive, this session is almost over, he is about break-even after having been down. In this spot, you estimate he’d bluff with a flush draw or QT just 50% of the time, but would value bet a K every time. The numbers change: against the same range, but with the bluffing layer weighted at 50%, you now have 21% equity. You should fold.
Do you see what happened here? Your psychological insight and player profiling, maybe even a tell of strength you spotted, helped you make the correct play. But it was correct because the numbers said so, and your read merely helped you arrive at the right numbers. At the heart of it was the math.
Another example: A player raises from early position, you flat from the button. The flop is king-high with two hearts. He bets. If you choose to raise, what hands are you raising with here? That depends on both your equity against his range (PE) as well as how often he will fold (FE). If he is a nit who will fold 90% of the time, you can raise with complete air here. If he is a calling machine who doesn’t like folding, your hand needs to be stronger. If your reads help you come up with his folding frequency, math will do the rest.
Normally one puts opponents on ranges, and determines fold equity, based on observation and memory: from their past behaviour, we deduce their present tendencies. Psychology plays a part only at the margins. The great Indian offspinner Erapalli Prasanna once said in a cricketing context: ‘Line is optional. Length is mandatory’. Let me paraphrase that in poker terms: ‘Psychology is optional. Mathematics is mandatory.’
Last week on Range Rover: