My approach to poker involves trying to play unexploitably. This style of play is a direct inversion of the classical approach to poker: exploitive play. In exploitive play, the aim is to estimate your opponent's individual hand, range of hands, or overall strategy, then find the play that maximizes your expectation against that.
Unexploitable play operates directly in reverse to this process. First, you estimate the strategy that maximizes your opponent's expectation against your current strategy and then find the strategy that minimizes their expectation against you – given that they are, in turn, always choosing their best counter-strategy to you. The enduring aim is to minimize as much as possible the profit a perfectly exploitive player could earn against you. You're playing perfectly unexploitable poker when this hypothetical loss-rate is driven down to zero.
Both styles can be used to great success, and although my personal opinion is that a profit-maximizing approach to poker is to use both, I sometimes face tricky situations against clever exploitive players that can help me in my aim of playing unexploitably.
I'd like to share a hand with you which really got me to reassess my strategy. My opponent in this hand is also a good friend, and he happens to play an exploitive game as well as anyone else I've played a large number of hands with. This particular spot is an unusual one: with three players left in the hand on the river and with an inside-four-straight board.
$25.00/$50 limit hold 'em – 3 players
Pre Flop: (1.5 SB) Hero is SB with T
Q
BTN raises, Hero 3-bets, BB caps, BTN calls, Hero calls
This is a three-handed online game, where the BTN is the fish, and the BB is my friend. Each player can have a wide range of hands here, with the BTN's being the widest and the BB's the tightest.
Flop: (12 SB) T Q
8 (3 players)
Hero checks, BB bets, BTN calls, Hero raises, BB calls, BTN calls
My check-raise is standard with the preflop aggressor being to my left and with the poor player sandwiched between us. My holding of top two pair is incredibly strong.
Turn: (9 BB) 5 (3 players)
Hero bets, BB calls, BTN calls
Nothing changes here. I'm still far in the lead.
River: (12 BB) J (3 players)
Hero bets, BB raises, BTN calls, Hero folds
The J is ostentatiously bad. However, my holding is still very strong given the wide ranges in play and my opponents' passive play. For this reason, checking seems too timid. I am still ahead of the vast majority of conceivable holdings, with the main exceptions being 9x and AK.
This is limit hold 'em, where in general timidity isn't rewarded, and the cost of getting raised often isn't that great – in stark contrast to no limit hold 'em, where a raise can be for all of your chips.
My bet seems fine. The trouble occurs when my friend raises me.
This is a very unusual situation, and as such my default play probably hasn't been updated as recently as other parts of my strategy. I tend to change my game piece-by-piece. This is often initiated when I see players I respect playing certain situations in a way different to me. I try to find arguments for why their play might be correct and I might be wrong. I also change my strategy if certain situations "feel" wrong or like I'm losing money in certain spots. In either case, repeated exposure to a situation is the most likely catalyst for me to update my strategy, meaning that unusual spots are the most common places for me to make serious mistakes.
In general, bet/folding is the best way to get value from these situations against poor players. It will maximize your winnings against worse hands which will be scared to value bet, and a lot of poor players lack the creativity to bluff-raise multiple opponents. As such, my plan was to fold to a raise from my friend – whatever the third player did.
My friend, being an incredibly strong exploitive player, sensed all this quickly – and bluff-raised in tempo. He was unfortunate that the third player woke up with a large hand; otherwise, his fine play would have won him the hand.
Final Pot: 17 BB
BTN shows A
9 – straight, queen high
BB shows A T – one pair, tens
The key point that I took away from this hand is that I need to be careful about how many hands I bet-fold against strong players in unusual multiway river spots such as this, where the river card creates a lot of possibilities for other hands to have outdrawn me. My default play was to bet/fold a number of hands such as AQ, AA, and KK in addition to that hand I was holding.
But this default play was exploitable. Because the size of the pot is usually large compared to the bets in limit hold 'em, you need to call with the majority of hands that you initially bet for value to be unexploitable. There is in fact an equation which tells you the exact proportion to call with in river spots such as this.1 Compared to all the hands I was bet-folding, I didn't have enough hands which were capable of bet-calling, especially since I'm relatively unlikely to have improved to a straight on this river.
In order to improve my play here I should do two things: check-call with some hands, such as AA, which I bet-folded before and bet-call versus a raise and a fold from the third player with some stronger hands such as my holding of two pair here. These two adjustments would take my bet-folding ratio closer to the optimal figure, therefore reducing the exploitability of my strategy. In fact, if I wanted to counter-exploit an opponent who I thought was bluff-raising too much, then I should actually bet-call more often than the optimal figure suggests. This discussion might seem academic given the hand's actual results, but when I saw the hands at showdown I was genuinely dismayed that my friend had been able to spot such a hole in my game, although in retrospect I was fortunate to see his hand and understand his thinking.
1 Your folding ratio should be the same as the pot odds your opponent is receiving on a bluff-raise succeeding. If the pot is 10 big bets initially, you put one bet in, and your opponent puts two bets in as a raise, then you should fold no more than two hands for every 11 that you call. See Bill Chen and Jerrod Ankenman - The Mathematics of Poker.
