Casino News: News: Bet sizing and bluffing

How often should you be bluffing vs value betting when you bet small or big? Dara O’Kearney dispels a myth about bet sizing.

A basic game theory principle is that when we bet we should be balanced between bluffs and value. If we bluff too infrequently or too frequently we become very easy to play against. Opponents can follow a very simple strategy that exploits us: always call if they can beat a bluff versus the over eager bluffer, and always fold if they only beat a bluff against the infrequent bluffer.

So how often should we be bluffing? That depends on our bet sizing. If we bet pot on the river, we should be value betting twice as often as we are bluffing. Why? Because our opponent is getting 2 to 1 on the call so they need to be good a third of the time. If we are bluffing more than a third of the time, they can call with their bluff catchers and make a profit in the long term. If we are bluffing less than a third of the time, they can fold all their bluff catchers and our value bets aren’t getting paid often enough.

If we bet half pot, they only need to be good 25% of the time, so we need to be bluffing 25% (three value bets to every bluff). If we bet a third pot, it’s 20% (four value bets per bluff).

More bluffs for bigger bets

By now you’ll probably have noticed a pattern: the bigger our bet is, the more often we should be bluffing. This is actually the opposite of what a lot of novices think intuitively: they think they can bluff more often when betting small because it costs less so the risk to reward is better on the bluff.

On earlier streets, it’s not quite as clear cut because our bluffs will have some equity (some chance of winning when called). For example, if we are betting pot on river, we need to be bluffing one third of the time (because our hand has no chance of winning when called). But let’s imagine it’s an earlier street and on average our bluffs have 16.66% equity (meaning a one in six chance of winning when called). Now we can be bluffing 40% of the time because our bluffs will win 6.67% of the time when called (one sixth of 40%) so are only losing bluffs 33.33% of the time. The more equity our semi bluffs have the more often we can semi bluff.

Earlier I said the bigger we bet the more often we should bluff. Another way of saying this is the more bluffs we have in a situation the bigger we should bet. Yet another way of saying this is the more value bets we have to hands we want to bluff, the smaller we should bet. Deciding what bet size to use is a complicated matter of determining what works best given the value hands and potential bluffs we have. If our value hands are very strong and our opponents has a lot of good but worse hands that can call, we typically want to bet big to extract maximum value. This also means we get to bluff a lot (in this case we are said to have a polarized range of very strong and very weak hands). On the other hand, if we are betting a lot of weaker hands because our opponent has even weaker hands that can call, we want to use a smaller size so those weaker hands do call. In this case we have a lot less bluffs.

So often we can choose our bet size by considering the strength of our value hands compared to opponent hands that can call, and once we have done that we know how many bluffs we need for balance, and decide what the appropriate hands in our range are to bluff with.

Sometimes though, it’s easier to construct our range working from the other direction: thinking about how many hands we want to bluff with, and comparing that to how many value hands we have, and then choosing the appropriate size. For example, if we decide we have 50 combinations of hands we want to bluff with, and 150 value combos, that means we will be bluffing 25% of the time, so we should bet quarter pot.

A hand example

An example of this where it’s easier to choose the appropriate bet size by looking at the bluffs side of the equation came up when I looked at a hand a student sent me recently in PIO solver.

‘Postflopmalone’ writes:

This hand is from a 2/5 live cash game in Vegas. LoJack opens to 15 and I threebet to 45 with black Kings in the hijack. It folds back to him and he calls. Pot is 105 and I have 480 behind.

The flop came 987 two spades one diamond. He checks. My thinking in game was that while I would check this board at a very high frequency, this is one of the hands I want to bet, both for protection and value. On this very wet board, it benefits strongly from folds so I sized up to two thirds pot.

After my opponent folded however, I thought this bet size might be a mistake, as it strengthens my opponents continuing range too much to hands I’m not in great shape against with my kings. What do you think?

You’re correct that this isn’t a great flop for us so one we need to check behind a lot. Assuming both players are playing GTO ranges our range consists of:

Some sets. We can have all the sets but we would also call 99, 88 and 77 some of the time so actually we don’t have many sets. We have no straights so sets are our strongest hands
We have no two pair but all the overpairs which are strong but vulnerable on this flop
We have no other one pair hands so all that remains are overcards and hands like A5s. With not much Tx and no 6x apart from 66, we don’t have many open ended straight draws. We have some Jx type hands that give us two overs and a gutshot, some flush draws and back door flush draws, plus a lot of hands that have only two overcards

Your opponent on the other hand has:

Made straights (JTs and 65s), all the sets, and some two pairs (98s and 87s)
Not as many overpairs as we have but some pair and a draw hands (T9s, 76s) and more underpairs
A lot less high card only hands

It’s easy to see when we break it down like this that our opponent’s range is stronger. PIO indicates that overall they have a 55/45 equity advantage on this board and because of the nutted advantage an even bigger EV edge (60/45).

This means the opponent can donk a very high frequency on this board having a lot of strong hands that don’t want to let us check behind, and a lot of good bluff candidates that would like us to fold but can improve to winning hands if we call. PIO donks 60% here and checks only 40% as the out of position player. I was interested to see what it wanted to do in position when checked to. As we both expected, it checks a lot (58% of its range). The interesting thing is that when it does bet, it always uses the small sizing of one third pot. I gave it the options to bet half pot, two thirds pot and 1.2x pot but it never uses this size.

This might seem a little counterintuitive at first when we think about just our value range and how much a lot of it wants to “protect” or deny equity to our opponent. However, when we expand our considerations to our opponent’s range (which contains a lot of very strong hands that can call no matter how much we bet) and our own bluffs, it suddenly becomes clear why the solver prefers the smaller size. We struggle to find a lot of good bluffs on this flop, and the bigger we bet the more of them we need to find. Even when we choose the smaller size of third pot, to get up to the required number of bluffs, PIO ends up having to use some hands that don’t seem like great bluffs. For example, a hand like KQs that has no flush draw front or back door is still bluffed almost three quarters of the time.

That combination of factors makes this a spot where even if we think our big hands want to bet big for protection, a better way to play our overall range is to use a smaller sizing of one third pot.

Dara O’Kearney’s new book PKO Poker Strategy is available on kindle or paperback at Amazon right now.