Poker: strategies; taking down the pot
Poker is a game of repeated scenarios (‘spots’). Players only have a few moments to make a decision when the action is on them. They need to rely on heuristics — rules of thumb — to guide their strategies. The chosen strategies will be sound and sophisticated in the hands of a pro but pretty bad for us recreational players.
One would think that the game of poker taps into our basic human understanding of risk and reward, such that we would settle on fairly good heuristics. Against that is that there is so much variance in the game that players can adopt poor strategies without ever being forced to confront the error of their ways. Let’s consider the strategy of ‘taking down the pot’.
Taking down the pot
This refers to the strategy of making a very large bet when our hand is likely best but vulnerable to being outdrawn, with the express goal of winning the pot there and then. For example, the flop comes down 763, and we have 66 for a set, and we bet 2 times the pot to ‘ensure’ that we win the hand.
Note that this is different from making a reasonably sized bet when the board is dynamic, to ensure that the other players are charged to see another card. This is also called ‘betting for protection’ and is solver approved. Also, betting to win the pot when we have a mediocre hand but sense that the opponent is weak is just good poker. But betting when we have >50% equity just to take down the pot is not a ‘thing’; we won’t find Doug Polk advising this ‘take down the pot’ (TDtP) strategy.
But why be greedy?
After we have made some huge bet to take down the pot, after explaining to the table that we just wanted to take down the pot, and after the other players at the table have nodded sagely, we might add that the pot was big enough already and it would be greedy to try for more.
An alternative perspective is that winning a bit extra in those spots might be required just to break even in the long run. We were lucky to flop a set in that situation — picking up pocket pairs and then flopping a set happens less than 1 hand in 100. In the long run, though, every player at the table will flop that set roughly the same number of times. If we win 10 big blinds (BB) on average every time that happens, but all the other players win 25 big blinds, that is a huge leak on the scale of typical edges in poker.
Taking down the pot feels good
The TDtP strategy taps into many of our intuitive tendencies. If we win a pot for 10 BB we naturally feel pleased with the outcome. We conclude we must have played the hand pretty well, rather than pausing to consider that our holding was worth 25 BB of expected value.
Then there is loss aversion. We don’t want to lose a pot because some undeserving opponent, who entered the pot with some absurd 52 holding and now has a gut shot draw on the 763 board, should go on to make a straight and win this pot that was rightfully ours. We remember these outcomes disproportionately. Next time we just want to avoid the tension of playing those later streets; we want to win the pot immediately and move on. A related psychology is that we would like to reduce variance by locking in the win but in poker trying to reduce variance is usually self-defeating. Variance will find you anyway!
Our fast thinking intuition may fall into trap of thinking that the aim of the game is to win the most pots, when our slow thinking analytical brains know that this is not the same as maximising our winnings. In reality, the two goals may not even be positively correlated: one way to win the most pots would just be to enter every pot and call down to the river . .
Some simple maths
Let’s say the flop is 763, we have 66 for middle set, we suspect our opponent has 52 and the pot is 10 BB. In this case we have 85% equity, and we’re in great shape. If no more money goes in the pot we’ll win 8.5 BB on average. Every extra chip that we put into the pot that gets called at these odds earns a 70% return (85% * 100% + 15% * -100%). When we make a bet we want our opponent to call.
However, the bigger our bet is the stronger our opponent’s calling range becomes. If we bet 2BB (20% of pot), then our opponent needs 2/(10+2+2) = 14% pot odds to call. As they have 15% equity they should call, which leads to the curious outcome that it is both profitable for us to bet (we have >50% equity) and also profitable for the opponent to call (they have the required pot odds). The rules of poker create an incentive for multiple players to contest the pot.
If instead we bet 3.3BB (1/3 pot), our opponent will no longer have the required pot odds of 20% to call. (Actually, due to implied odds it may nevertheless by correct to call this modest bet, even if the opponent will often have to fold the turn, but that’s a different topic). If instead we bet 5 BB (1/2 pot) then it’s almost certainly incorrect for the opponent to call, and we can win the full 10 BB in the pot. This is called denying equity. Denying equity is a thing.
The problem with making an even larger bet to take down the pot, is that any opponent willing to call our 100% (or 200%) of pot bet is likely to have better than 52. Sometimes they will already have 54 for the straight (recall, the flop was 763) and we will have put in all that money at less than 50% equity. Fortunately our set vs the straight has some outs; we have about 35% equity. An even worse outcome is if the opponent has 77 for a higher set, and we are (almost) completely crushed with only 5% equity.
Granted, these cooler situations don’t occur that often, but when they do they are expensive and further undermine the TDtP strategy.
A final issue with the TDtP strategy is that the aim of the game is to give our opponent difficult decisions, and taking down the pot doesn’t achieve that. They can just fold when they don’t have it or call us when they have the nuts. And often we play this strategy in an unbalanced way. If we always have a strong but vulnerable hand in this spot then we are effectively playing with our cards face up. One small improvement on the TDtP strategy (call it TDtP+) would therefore be to throw in a 2 times pot bet as a bluff every now and again.
A final comment
It may be that our regular opponents have so many leaks in their game that we don’t strictly need to maximise our winnings in these situations to break even in the long run. We’re just leaving a bit of money on the table. Perhaps some of our opponents have a strategy to call a 200% of pot bet with just a gut-shot. This strategy is even worse than the TDtP strategy — yet it exists in the wild. In that case, by all means, bet two times pot as an exploit.
Generally though, we’re best off betting 33% to 50% of the pot, and hoping they call . .