Calculating the equity of your or an opponent's hand is a fundamental math process and one of the principles in poker math that matters most. Calculating equity is something that you will use all the time when you're playing poker games online, with friends or in a land-based casino. Equity refers to how much of the pot a player can lay claim to — based, of course, on your odds of winning the pot. It may seem counterintuitive, especially for beginners, but you don't need to have the best hand in a poker game to come out the winner. It's the equity you have in your hand — the value of your cards versus what you assess other players may be holding — that'll determine if you win or lose and how well or how badly.
Fold equity is calculating the probability of getting your opponent to fold. If they stubbornly hold out, does this mean they have a strong hand or that they're bluffing? That's another set of odds completely.
Pot odds refer to the size of the bet you have to call on in relation to the size of the total pot as it stands at any given point in the game. This is where the math concept of risk and reward comes into play. Pot odds are expressed as a ratio much like in sports betting, for example, it may be 2:1 (which, in American moneyline format, is -200.) The first number represents the reward and the second represents the risk. This means that in placing a bet with these odds, you risk one unit, say $1, to win $2.
In deciding whether to stay in the game with these odds, you need to calculate your hand equity and weigh all the factors up. The equation for this is risk/risk+reward, i.e. 1/(1+2) so in this case, the magic number is 33%. With a hand equity higher than 33% (-200 in American moneyline,) play on. Lower, and you need to do a few more calculations before you decide how to proceed.
Pot odds ultimately determine whether any call you make will be profitable or not.
Implied odds take the basic pot odds concept one step further. This is a calculation based on what you might expect to win later in the game. It's mostly used to decide whether the risk/reward ratio merits your making a call with a draw. What you need to ask yourself as far as implied odds are concerned is, what the minimum amount you need to win on any betting round is to make a call financially worth your while.
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