Saturday, March 20, 2010

So Ya Think Poker's Easy?

Here’s a question I saw in one of the high limit forums the other day:

“Villain, BB, in this hand is fairly solid. I've maybe played 20-25 hrs with him. Live 30-60 game.

Folded to me (CO) and I open raise AdQd. Folded to BB who calls.

Flop: JsKs5d

Villain checks, I bet, villain calls.

Turn: Jd.

Board is now JsKs5dJd giving me gutshot and nut flush draw.

Villain checks, Hero??”

This is a good question and a close spot for sure. The reaction of most people is “Bet!, you have a flush draw, gut-shot straight draw, and your opponent has shown no strength” All those things are true but if only poker was that easy. It’s not only about what you have, it’s about what you think your opponent has based on his actions to this point in the hand and how you expect him to play this street along with any future streets. And then based on that, what is your best course of action?

So this hand got me thinking, is there any way to answer this question definitively. I don’t think so but if we make some assumptions about what a “solid” player might do and what he might hold, maybe we could come close.

So what would go into answering a question like this?

We need to assign our opponent a range of hands. This alone can get pretty complicated and varies quite a bit from opponent to opponent. First off, it’s beneficial to know whether the villain in this hand calls his premium hands preflop out of the blinds or 3-bets them. In my experience with “solid” players, about half do and half don’t.

So hands like AJ, AQ, AK, KQ, 99, TT, JJ, QQ, KK, and AA might only be half as likely as they would compared with an opponent you know 3-bets which means when we assign our opponent a range, we’d need to divide the total number of hand combos for those premium hands by 2.

Back to assigning our opponent a range. Here’s the information we have:

-He’s solid.

-He called out of the big blind vs. a cutoff raise.

-He called a flop bet on a Ks, Js, 5d board and checked the turn

The most critical piece of information is that he called a Ks, Js, 5d flop. What would a solid player call with? He almost certainly would call with a hand that contains a 5. It’s also possible he has a hand that contains a Jack. Less likely, but also possible, is that he holds a pair of kings or better and is intending to check-raise. It’s possible that he holds an ace high flush draw that he’s playing passively. It’s also possible he has a gutshot straight draw like AQ, AT, Q9, or 9T. I would assume he would nearly always check-raise the flop with QT or a non ace high flush draw so I would exclude those from his range. I would also assume he’s never floating with a random hand given that the board texture so likely hits hero’s cutoff’s open raising range.

So the next question is what is the likelihood of each of the opponent hand groups based on his flop action? This is going to take some more assumptions and here’s what I’d assume from a solid player. I’m not saying this exact player will do these things at these frequencies but that solid players on a whole would come close.

-He’d always call with a one pair hand that contained a 5.

-He’d always call with 66, 77, 88, 99, and TT

-He’d raise about 60% of the time with a hand that contained a jack and call the other 40%

-He’d raise about 90% of the time with a hand that contained a King or a hand better than top pair and call intending to check-raise the other 10%.

-He’d call with an ace high flush draw about 25% of the time and raise the rest.

So what’s the next step? We need to determine the likelihood of him holding each of these hand types. That’s done by the tedious process of counting combos. I’m not going to count them all as the point of this is to show just how much work can go into trying to answer a poker question. But to give you an idea:

The one pair hands that contain a 5 - I’m assuming he calls with all these preflop against a cutoff raise

45s 3 Combos (accounting for 5 that’s already on the board)

56s 3 Combos

57s 3 Combos

85s 3 Combos

K5s 0 Combos (this is a 2 pair hand)

A5s 3 Combos (Ace in hero’s hand and 5 on board)

A5o 6 Combos

So, we have 21 combos of bottom pair hands.

There are 6 ways to make a pocket pair so he has 30 combos of 66-TT that he’s also calling with. But remember we assumed a solid player would 3-bet preflop with 99 and TT half the time so we need to divide the number of combos for these hands by 2 which is actually 6 combos less, So 24 combos in total of pocket pair hands that are calling the flop.

How about one pair hands that contain a Jack?

AJ - 9 Combos (accounting for known ace and jack)

We also assumed a solid player would raise AJ preflop 50% of the time so we’re left with 4.5 combos of AJ

KJ – 0 Combos (It’s a 2 pair hand).

QJ – 12 Combos

JT – 12 Combos

J9 – 12 Combos

J8 – 12 Combos

J7 – 3 Combos (assuming he only calls with J7 suited)

That’s a total of 55.5 combos. But remember again we assumed he’d only call with these hands 40% of the time so we need to multiply 55.5*.4 which leaves 22.2 combos.

I’m not going to count out all the combos for all the different hand types; hopefully you get the picture and see the amount of work involved - it’s worth mentioning there are a few programs that facilitate combo counting like StoxPokerCombo. But let’s assume we did, what’s the next step?

The next step would be to make assumptions about how he would play the various hand types (bottom pair, middle pair, top pair or better, etc.) in his range if we bet the turn or if we check the turn. And when we’re trying to figure out the best course of action we are comparing the value of checking to the value of betting based on the likelihood (see combos) of our opponent holding a certain hand type( like bottom pair, middle pair, etc.), what actions he will take based on our actions, and how each one of the 44 river cards will affect both our actions and our opponent’s actions.

All this sound easy? And this is a relatively simple question in that there are only two streets to play and two players. Imagine there are 3 streets to play, 5 players with different styles, tendencies and hand ranges, and a few thousand turn+river card combinations.


  1. I am grateful that poker is so complicated. If it were easy, anyone could do it.