Poker Basics – The Math of Calling
Poker Basics – The Math of Bluffing
January 11, 2021
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January 16, 2021Today, for newbies, a quick formula to help you decide on whether to call a bet or let your hand go.
If you joined us this week you’ll have seen the simple calculation you can do to determine if a bluff will be profitable. But what about when you think you are being bluffed? What can you do to decide whether you should call or not?
There is a calculation and you might be surprised to learn that it is a similar to the one for bluffing. The calculation is as follows:
Bet/Final Pot = Breakeven %
Whether you are bluffing or calling a bet, it is a similar risk vs reward calculation to determine your breakeven percentage. This time the breakeven percentage is the equity of your hand, rather than the number of times your opponent needs to fold. If you get a breakeven percentage of 40% to call, if your hand usually has 45% equity it is an easy call, if it has 35% equity it’s a minus EV call.
Let’s use a simple example. You are in the Big Blind and it is folded around to the Small Blind, who started the hand with ten big blinds, goes all-in. There was 2.5 big blinds in the pot already (antes are included) and the Small Blind shove is another 9.5 big blinds. It would cost you 9 big blinds to call and the final pot would be 21 big blinds.
9/21 = 42.9%
To profitably call this shove your breakeven percentage is 42.9%, which means that you need 42.9% equity against the Villain’s range to make the call.
In this example, if we assume Villain shoves with the top 49% of hands as a Small Blind probably would in a lot of spots, then this is how each hand might perform. Most Aces, the better broadway hands and pocket pairs above 44 would be a profitable call here.
| A | K | Q | J | T | 9 | 8 | 7 | 6 | 5 | 4 | 3 | 2 | |
| A | 84% | 66% | 64% | 62% | 61% | 58% | 57% | 55% | 53% | 53% | 52% | 51% | 51% |
| K | 64% | 78% | 57% | 56% | 54% | 52% | 50% | 49% | 48% | 47% | 46% | 46% | 45% |
| Q | 62% | 55% | 75% | 53% | 52% | 49% | 47% | 45% | 45% | 44% | 43% | 42% | 42% |
| J | 60% | 53% | 50% | 72% | 50% | 47% | 45% | 43% | 42% | 42% | 41% | 40% | 40% |
| T | 59% | 52% | 49% | 47% | 69% | 46% | 44% | 43% | 41% | 40% | 39% | 39% | 38% |
| 9 | 56% | 49% | 46% | 44% | 43% | 65% | 43% | 42% | 41% | 39% | 38% | 37% | 37% |
| 8 | 55% | 47% | 44% | 42% | 41% | 40% | 62% | 42% | 40% | 39% | 37% | 36% | 35% |
| 7 | 52% | 46% | 42% | 40% | 39% | 39% | 38% | 58% | 40% | 39% | 37% | 36% | 35% |
| 6 | 51% | 45% | 41% | 39% | 38% | 37% | 37% | 37% | 56% | 39% | 38% | 36% | 35% |
| 5 | 50% | 44% | 41% | 38% | 36% | 36% | 35% | 36% | 36% | 53% | 38% | 37% | 35% |
| 4 | 49% | 43% | 40% | 38% | 36% | 34% | 33% | 34% | 34% | 35% | 51% | 36% | 35% |
| 3 | 48% | 42% | 39% | 37% | 35% | 34% | 32% | 32% | 33% | 34% | 33% | 49% | 34% |
| 2 | 48% | 42% | 39% | 36% | 35% | 33% | 31% | 31% | 31% | 31% | 31% | 31% | 47% |
The same calculation can be used to decide if you can call profitably with a draw. Let’s say you have 45 and the flop is 67K. The pot size is 5 big blinds and Villain bets pot. You know you are most likely behind but you can make a flush or a straight. Let’s do the calculation again. It costs 5 big blinds to call and the final pot before going to the turn would be 15.
2.5/10= 33%
Now we have quickly worked out that we are roughly 54% to make a flush or straight by the river in this spot, so it would be a profitable call. There are other factors at play including whether we have clean outs (Villain could have AK for example, removing most of your heart outs) and the prospect of facing future aggression on the turn, but as a rough heuristic it will work most of the time.
Simply having the equity to call does not mean that you should. Factors like ICM, for example, could make a profitable ChipEV call very unprofitable. Then there is playability, a small pair might have very good equity against a range, but has to fold a lot on high card heavy boards. So while we implore you to start using this calculation a lot in your study, know that it is one of many factors in play that need to be considered.
Here are the breakeven percentages for common bet sizes you may find yourself deciding whether to call or not.
| Bet size | Breakeven % |
|---|---|
| 25% Pot | 17% |
| 33% Pot | 20% |
| Half Pot | 25% |
| 2/3rd Pot | 29% |
| Pot | 33% |
| x2 Pot | 40% |
3 Comments
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