Bet Sizing In Theory

This tip comes from Joe “TheDefiniteArticle” Towse. Joe is an instructor at the Poker Training site GrinderSchool.com which focuses on providing affordable training targeted at small stakes and microstakes games. Joe has strong background in NLHE Cash Games, with a focus on the quick thought processes required to dominate at 6-max Rush Poker.

When you first thought about bet sizing in no-limit hold’em, you probably heard some vague advice along the lines of ‘bet the most you think they’ll call if you’re value betting, and bet the least you think they’ll fold to if you’re bluffing’, possibly with some confused ideas about ‘betting enough to deny your opponent drawing odds’. This is all well and good if you assume a) that you know precisely what your opponent’s range is and b) that they’re not paying attention (because the biggest amount they’ll call is is clearly not the same as the smallest amount they’ll fold to, though the two are naturally very close). Against competent, observant opponents, you probably want to develop balanced ranges on every street, and if you’re using a strategy of using multiple bet sizes in a particular situation, both of these ranges should be balanced.

But perhaps picking a sizing and deciding on a range is the wrong approach. Let me rephrase that. If you’re using a single sizing, it is the wrong approach; and it is probably the wrong approach if you’re using multiple sizes. Instead, you should decide on a betting range in unison with deciding on a sizing to use. Because if a bettor is betting a balanced range and the caller is calling unexploitably, the bettor has an EV of pot with their betting range (i.e. the portion of their range which they do not bet will almost certainly have an EV of lower than pot), and the caller has an EV of 0 with their range when the bettor bets, the bettor probably wants to bet as much of their range as possible if the caller is calling unexploitably. This assumes perfect polarization which is an imperfect assumption but it is often roughly accurate, and models become vastly more difficult to create, especially on an abstract level, if we don’t make that assumption.

The second useful idea to this is that the bigger the bettor bets relative to the size of the pot, the greater the bluff:value ratio (i.e. the more bluffs they can have relative to the number of value hands they have) they can have. Thus, if you have an infinite number of bluffs (or any number of bluffs which is greater than the number of value hands), and the range which is capable of being value bet stays constant across all sizings, then the optimal bet size is to shove, as this allows the closest possible ratio to 1:1 (the fact that a caller is always getting better than 1:1 on a call means that if we ever have more than 50% bluffs in our range, they can necessarily exploit us by always calling), remembering that in this case, an aggressive range will have an EV of pot and a passive range will have a lower EV (assuming perfect polarization, an EV of 0 as it will necessarily consist of air hands which lose to our opponent’s range).

However, these assumptions are often very far from true. Because in general, good players don’t play strategies such that they reach particular spots with extremely capped ranges, it is very rarely true that ‘the range which is capable of being value bet stays constant across all sizings’ (as the caller has to call much less often against a 2x pot bet than a half-pot bet, their calling range is necessarily much stronger and this affects the hands which can legitimately be value bet). Thus, in deciding what size to bet against good opposition, you ought to consider the size which allows you to bet most often, assuming that your bet/check is the last action in the hand (the model becomes too complex for now if we make alternative assumptions). If your opponent’s range is capped relative to yours and you have a lot of bluffs, it is likely to be an overbet. If your range isn’t particularly strong relative to your opponent’s, it is likely to be a smaller bet. This is something which should mostly be studied away from the tables, but through repeated and extensive hand review, you should be able to get an intuitive sense for it.