Poker — bet sizing
I’ve done a previous blog on stack sizes and how they impact poker strategy. I turn now to bet sizing. I can only scratch the surface of this topic, as it is said that poker is a betting game that happens to be played with cards. If I really understood this topic, I’d be playing high stakes poker in Las Vegas instead of sitting here writing this blog!
It’s very easy to bet sub-optimally and never realise it, as the learning feedback loop is very weak. Picture a good player and a bad player, who both win and lose the same number & type of hands, except that the good player wins $10 (when they win the pot) and loses $5 (when they lose). Meanwhile the bad player wins only $5 (when they win) but loses $10 (when they lose the pot). The losing player may well be quite happy with the outcome (look, I won the pot! Ok, I lost that one, but what can you do?) and see no reason to improve.
I discuss three aspects of bet sizing:
1. Psychology of bet sizing
2. Playing like a computer
3. Specific scenario: scary boards
Psychology of bet sizing
Even analytical players fall into various psychological traps when it comes to bet sizing. An important one is that players should be thinking in terms of betting a percentage of the pot but tend to think in $$$ terms. This leads us to play very loose pre-flop and for example be prepared to call $1, even if that is more than 100% of the pot ‘prize’. It’s only $1 after all. Later in the hand, on the river say, players become overly nitty. Calling a bet of $10 into a $20 pot on the river may be a lot more in $$$ terms but is offering us 3 to 1 odds on a call ($10 to potentially win $30).
Given that pot odds are related to the percentage of the pot, suppose we have a monster hand that we want ‘to get stacks in’ with. The theoretical betting structure is to bet x% of the pot on each of the flop, turn and river so that the final bet is ‘all in’. The betting and the pot size grows geometrically. This is, of course, difficult to calculate in live play and multiway pots. In practice, it seems that many players bet smaller on the flop (1/3 of pot, say) and bigger on the turn (2/3 of pot, say).
Returning to the psychology of betting, players tend to regarding any bet between 25% and 50% of pot as ‘small bets’, 50% to 66% as ‘medium bets’, and anything larger as ‘big bets’. They tend to be inelastic within each range: a bet of 26% of pot and 49% of pot get the same percentage of calls/folds.
Interesting psychological things happen around the pot sized bet. Betting pot or more really says that the aggressor means business, so that a bet of 90% of pot may be much more likely to be called than 105% of pot, even though the $$$ difference isn’t that big. All-in bets, regardless of size, are also treated differently (some players are more likely to bluff all-in, others will only go all-in with the nuts).
In online play, there is a button for 50%, 66% or 100% of pot sized bet. A player who takes the trouble to type in a different number may be up to something. Strong or weak? Not sure, but it’s a tell.
More speculatively, it may also be that round bet sizes ($9) somehow look smaller than a bet with lots of digits ($8.56) and that a $10 bet looks a lot bigger than $9 (it’s double digits!). My favourite poker author Andrew Brokus teases players who show up at a new table and ask, ‘what’s the standard bet here?’. Answer: it’s no limit holdem, you can bet whatever you like!
True, and yet there’s a certain social conformity to pre-flop raises. In my online game for a long time 3 big blinds (BB) was the standard opening raise. A 5 BB open would be out of the ordinary and would raise eyebrows. Yet, recently, 5BB has become the standard opening raise. A 3 BB open now looks suspicious.
Live games tend to involve bigger bets. Whole states in the US (i.e. Texas) have bigger bet sizing. Sometimes this is totally rational, depending on the rake structure: the casino may charge by time ($10 per hour, say) or alternatively a percentage of the pot provided it goes to the flop. In the latter case, it makes sense to play tighter but bet bigger. In tournament play, which often includes antes but has no casino rake, play is looser but bet sizing is smaller. But often the different bet sizing is just a matter of social convention.
How much should you bet on the river? Well, to state the obvious, if you’re value betting you need to bet the largest amount that villain’s target holding will call. If you’re bluffing, you need to bet the smallest amount that villain’s target holding will fold (let’s say you’re trying to get him to fold a pair). Easier said than done — it very much depends on the proclivities of the other player! To generalise, many players are size insensitive until they get to pot sized bets. If they have top pair they’ll call a 2/3 pot bet as frequently as 1/3 pot (or more than half as frequently, anyway). You might as well bet the higher amount.
Playing like a computer
Computers won’t fall into the psychological traps described above. That said, computers (viz. GTO solvers) can’t yet solve for the optimal bet size, far as I know. The human user has to set up the allowable bets (33%, 66%, 100% and 200% of pot, say) and the computer will decide for every holding in its range whether to fold/ check/call/raise in a perfectly balanced & unexploitable way for each bet size. The computer may show a clear preference for one or two of the possible bet sizes. It’s very difficult for humans to balance more than one bet size. If we’re trying to play in a balanced way it’s probably best to bet the same amount for our value bets, semi bluffs and pure bluffs.
A lot of players are implicitly betting two bet sizes when they split their range pre-flop by limping with their medium hands and raising their stronger hands. A good player (and computer) would immediately recognise that this is exploitable by attacking the medium strength limps. Medium strength hands are difficult to play in poker. Strong hands are great (obviously) and weak hands are ok (less obviously, but at least they offer the chance to over-achieve their raw equity as we can bluff with them). Medium strength hands, on the other hand, are only good as bluff catchers. Against a computer they have an expected value (EV) of zero.
That’s not to say that having a limping strategy is definitely wrong. A computer would put some strong hands into their limping range to make them less exploitable. It’s just very difficult for a human to achieve this in a balanced way. Some players in my poker group solve this conundrum by limping with everything, even super-premium holdings like pocket queens. But this loses too much EV on these stronger holdings. Although one needs to be really disciplined, adopting a pure raise or fold strategy, never limping, would improve our win rate. The downside is that the number of hands we get to play (the VPIP) goes down.
If our opponents aren’t computers then being totally balanced is less important. If we bet a bit bigger with good hands and smaller with more speculative hands, maybe no one will notice! It’s helpful if we have a 9 ‘full ring’ rather than a smaller number of players around the table, where it’s more difficult to track everyone’s actions.
Specific scenario: scary boards
Let’s consider two specific examples of ‘scary’ boards, namely flops like QQ7 where one of the ranks are paired (paired flops) and flops that are all the same suit (monotone flops). These are scary because our opponent may have trips on the paired board, or a flush on the monotone board. These boards occur infrequently but nevertheless come around a few times every session (paired flops occur 17% of the time, monotone flops 5% of the time.).
The question is: should you bet big or small on scary boards? This is an interesting Rorschach test of a player’s outlook on life! The timid player will worry that the villain has the goods and will fold to aggression. The optimistic player may well view the scary board as an opportunity to pile on the pressure.
Consider monotone flops. Many in my player pool bet big: 2/3s of pot, say. This is not what a computer would do on monotone flops of, for example, 3 hearts. It would bet frequently and small. Anyone not holding a heart should really fold to a small bet; a big bet is not required. On the other hand, anyone holding a heart (or who has flopped a flush) is likely not folding; a big bet is pointless. The key card on this monotone flop is the Ace of hearts. If you have it, other players should (rationally) be scared you have it. If you don’t have it, do you really want to bet big into an opponent who does have it?
Paired flops come in more varieties than monotone flops. Sometimes the pair is higher ranking than the other card (e.g. QQ7); sometimes the unpaired card is higher (e.g. Q77). Sometimes the cards are all high (e.g. AAT) and sometimes low (e.g. 633). These possibilities influence whether the pre-flop raiser has the range or nut advantage, and hence the frequency and size of bet. It gets complicated. Generally speaking though, all the players are less likely to have hit the board (only 2 instead of 3 cards to pair), but when they do they have a strong hand — two pair or trips. This suggests smaller bet sizing in general: your opponent is more likely to have nothing and will fold regardless, or has a strong hand and you’ll be happy to have bet small!
Conclusion
Poker rewards tight aggressive play. When betting we should think in terms of betting a percentage of the pot rather than the $$$ amount, although because we are playing humans there is scope to apply some psychology in bet sizing. It is interesting to see how computers approach bet sizing, though their game theory solutions are highly complex and impossible for a human to emulate. When playing scary boards where your opponent is likely to either have nothing or a very strong hand, leaving you way ahead or way behind, then frequent small bet sizing is generally the way to go.