This article is an excerpt from the latest Dimat release, The Math of Hold’em (available from Amazon), by Collin Moshman and Douglas Zare.
In no-limit or pot-limit games, you can choose the size of your bets. Mathematics often helps you to choose one bet size over another. This article looks at bet-sizing when there is the possibility of future betting in the hand.
Example No. 1. It is the first hand of a multi-table tournament.
Effective stack: 1,500
Your hand: Q♥ Q♠
Action: You open raise to 80 in late position and get called by the big blind.
Flop: K♦ Q♣ 2♠
Question: On the flop, should you make a continuation bet of half the pot or closer to the full pot?
Answer: You should bet the full pot. With middle set, you should try to build a big pot against someone with top pair. Right now, the pot is 170, and under most turn and river cards, you want the pot to end up 3,010 (all-in), about a factor of 18 larger. When you bet the pot and get called, the pot increases by a factor of 3. When you bet half-pot and get called, the pot increases by a factor of 2. So, the betting sequence pot-pot-pot would increase the pot by a factor of 3x3x3=27. You would run out of chips, so you can bet a little less than the pot and still get all-in comfortably. The betting sequence 1/2 pot-1/2 pot-1/2 pot multiplies the pot by 2x2x2=8, which would put only half of your stack in. So, to get all-in, you would have to count on getting raised, or you would have to make much larger bets on the turn and river after getting called on the flop, e.g., 1/2 pot-pot-pot.
Another reason to choose the full-pot bet with a K♦ Q♣ 2♠ flop is that many hands will call or raise. These include: A-Q, K-T, Q-J, J-Ts and possibly A-T, etc. If the flop came Q-2-2, you should usually bet less or check. While you clearly still want to play for stacks with this flop, you have the deck monopolized, so that it is less likely for your opponent to like the flop enough to call or raise a pot-sized bet.
When you have a goal of achieving a certain pot size, it is important to look ahead in the hand and bet accordingly. Have a plan for getting the pot the size you realistically want, and that plan usually should not depend on your opponent calling large overbets, bluff-raising your bets, etc.
Final Pot Size Relative to Flop Pot Size as a Function of Bet-Sizing
|Fraction of the Pot Bet
|Resulting Final Pot Size
Relative to Flop Pot Size
|1/2 x Pot||8 x Pflop|
|2/3 x Pot||12.7 x Pflop|
|3/4 x Pot||15.6 x Pflop|
|Pot||27 x Pflop|
|2 x Pot||125 x Pflop|
So while you may worry that larger bets are less likely to be called, it’s important to realize that even slightly increasing the fraction of the pot you bet each street has a dramatic impact on the final pot size.
Let’s look at another example.
Example No. 2. A no-limit hold’em cash game.
Effective stack: $150
Your hand: T♠ 8♠
Action: You raise to $7 on the button. The aggressive big blind calls. The pot is $15.
Flop: Q♠ J♠ 2♥
Action: The big blind checks. The pot is $15.
Question: How much should you bet?
Answer: With your gutshot-straight flush draw, you don’t mind playing a big pot, but you would like to be the one making the final bet so that your opponent could fold. An aggressive opponent will often check/raise you on this flop, as there are many possible made hands and draws. If you bet $15 and he check-raises to $45 or so, you could then shove for $98 (the effective remaining stack at the flop). Unless he is on total air though, it is unlikely he will fold when you’re shoving for just over double his bet amount.
If you bet $10 though, a three-times check-raise would be to $30, and if you shove $98, your bet will have fold equity. Since you currently have T-high, you would rather not have to complete your draw to win the pot. Therefore $10 is a superior bet size here compared with the full-pot $15.
Sometimes you’ll use bet-sizing for the opposite purpose, as in the next example against a similar opponent.
Example No. 3. A no-limit hold’em heads-up sit-and-go.
Effective stack: 1,200
Your hand: K♥ Q♥
Action: You elect to min-raise on the button. The aggressive big blind flat-calls. The pot is 400.
Flop: J♠ T♥ 9♠
Action: The big blind checks.
Question: How much should you bet?
Answer: With your made straight, you would normally want to make a large bet to charge draws, build the pot, and get value from the many worse hands that will like this highly coordinated flop.
Suppose you bet full-pot however. From your opponent’s perspective, you have bet 400 into 400, and if he shoves his remaining 1,000, you will almost certainly call getting 3:1 pot odds. So a perceptive player will tend to fold anything but reasonably strong hands, including most weak to moderate draws.
If you bet 200 though, he can then shove 1,000 into a pot of only 600, making it much more likely that you will fold for another 800. He may therefore shove with many draws and weak made hands that he would otherwise check/fold to a pot-sized bet, such as 6♠ 5♠, T♦ 6♦, a naked queen, or possibly even a naked eight.
In summary, you should always think what you are trying to accomplish through the sizing of your bets. Default bet-sizes, such as two-thirds of the pot at the flop, are fine guidelines. However, you should not rigidly adhere to these default bet-sizes. Underbetting or overbetting the pot will sometimes yield a better result. You should be prepared to modify your bet-sizes for the purpose of getting someone’s stack in by the river with a strong hand, to make sure that you are the one putting in the final raise with a strong draw, to fool an opponent into thinking he has fold equity when you hold a strong made hand, or to accomplish any similar goal.