Note that I count 10 outs since 10♦ would give you royal flush. Now we can calculate the probability that you hit the flush or straight on the turn. You have 7 outs to hitting a flush (not the J♦ and not counting 10♦), three to a straight (not counting 10♦) and one to royal flush, hence: We can then calculate the winning change by combining the events the following way:įor example, you have K♦Q♦ and your opponent has A♠A♥ with a board A♦5♦J♠ The ‘-’symbol is used as a negative and hence interpreted as -event does not happen. Winning chance is in this case combining the events. If E1, E2 and E3 happen, you win, since you hit something on the river which beats the hit by your opponent. Therefore, if E1 and E3 happen, you lose. When the opponent hits, it beats your hit. To calculate the equity when you know the hand of the opponent, I am going to use the following events: EDIT- The answer where the hand of the opponent is known When you have this probability, you can multiply it with the pot to get your equity. In another answer I explain how you can calculate your probability of winning on the flop or turn. Of course, if you are drawing to a flush but your opponent is drawing to a full house you may have to take this into account, but that is a very hard read to do. When you do not have the best hand, you can just calculate your own chances of hitting your outs. This probability of winning can then be multiplied with the pot, say for example $100,- and you will get your equity. Subtract this probability from 1 and you have your probability of winning. In general: read the hand, approximate his outs and calculate his chance of improving. This is, however, a very loose approximation since he may also hit two outers like two pairs or may also draw to a straight etc.
When you have a solid read, say he is drawing to a flush on the flop, you know that he has a chance of 0.35 to improving and therefore you have a winning chance of 0.75 ( with for example a pair of aces. You can however 'read' his hand based on the board, betting tells, past behaviors, etc. Therefore, calculating equity is cumbersome since you do not know the hand of the opponent. When you already have the best hand, you can only lose if your opponent(s) hit their out, which means they improve to having the best hand. In poker, your equity or expected value can be calculated by taking your chance of winning and multiplying that with the value of the pot. In probability theory, we take the calculated chances as truth in a scenario where the event is repeated infinitely. In general, equity is your expected value when you would run the same hand infinite times.
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