To understand bluffing, you need to understand the math in both equity and expected value. Despite some similarities, there is a difference between the two, and they often work together to help you make profitable decisions.
Equity is a percentage (0 to100%). Equity tells you how much of the pot “belongs” to you, or to put it another way, the percentage of the time you expect to win the hand on average from that point onwards…
Expected Value is a monetary value (A negative, up to all your chips, or positive of all the chips in game, (or losing all your chips to winning all the chips in play from everybody) It can be positive or negative.
EV tells you how profitable or unprofitable a certain play, (calling or betting) will be. We work out EV when we are faced with a decision. You need to know your equity to work out your expected value.
Equity is the basic raw material that you need to help you create more effective numbers to work with.
When you combine equity with the chips you could potentially win or lose after making a certain decision, you come up with your expected value.
Making good bluffs in poker is all about the mathematics. It’s all about the EV of your play.
To work out whether a bluff is going to be “a good one”, you need to try and accurately estimate how often your opponent will fold to your bluff.
As you can guess, the more knowledge and experience you have the more accurate your estimate will be.
After you have a percentage in your head, you can go ahead and work out how much you expect to win when they fold and how much you expect to lose when they call. After that you’ll be able to tell if the bluff is going to be a good one or not.
Look at it like this:
Hero (1000): A♦ K♥
Villain (1000): T♠ J♠
Board: A♠ Q♦ 4♠
Your Equity: 56%
You have 56% equity on the flop. This means that you have 56% chance of winning by the river and therefore 56% of the pot currently “belongs” to you.
Villain moves all in on the flop for 1000 (making the pot total 3000) and we have to decide whether or not to call that 1000 bet.
To work out how much we expect to win (or lose) on average every time we call, we need to work out our expected value.
You win 3000 56% of the time. 3000 x 0.56 = 1680
You lose 1000 44% of the time. 1000 x 0.44 = 440
Expected value calculation.
EV is the win, minus loss or 1680 subtract 440 / EV = +1240
Therefore, we expect to win 1240 on average every time we call the 1000 all-in from our opponent in this situation. We couldn’t have known that with just the 56% equity figure on its own.
Let’s say we have a low equity hand, but a high expected value:
Hero (1000): J♦ T♥
Villain (100): A♠ J♠
Board: A♦ Q♠ 4♠
Our Equity: .11%
Our opponent moves all-in for 100 in to the 2000 pot on this flop.
We only have 11% equity here, which is a very, very low equity share indeed. However, if we work out the EV of calling:
•We win 2200 - 11% of the time. 2100 x 0.11 = 231
•We lose 100 - 89% of the time. 100 x 0.89 = 89 EV = 142
Because the bet size is so small compared to how much we can potentially win, it’s a +EV play to call.
In general, to have low equity in a hand but for a call to be +EV, the bet must be small in relation to this size of the pot.
So Equity is a percentage & EV = Expected Value is a monetary value