Quick poker math
Frequently at Poker night I will spout off a percentage and people will think I am some kind of weird human calculator. Not true.
Poker math can be very simple.
Preflop there are two cards you have seen, and 50 you haven't. Each card in the deck has a 2% chance to be any given card. Have an AK? That leaves 3 aces and 3 kings in the deck. 6% of a card being any ace plus 6% for any king. That leaves a 60% chance that you will pair at least one of your cards (this is true for any two unpaired cards actually) through the river.
Most of the time though pre flop numbers are two big to matter (your opponent also have a 60% chance to get a pair etc.). Post flop though you can do some pretty quick math if you can add up to 13 and multiply by 2.
You have AK unsuited, Opponent has 55. Flop comes 279 rainbow. There is a 12% chance (2 times number of cards that would improve your hand) chance that your hand will improve on the turn, and that same chance on the river. 24% chance your hand will improve. This is imprecise, but good enough to make an estimate at your odds. (There is actually a 2% chance that your hand will improve, but you still lose, as your opponent gets his 5 along with your ace or king.)
Inside straight draw? 4 cards will improve your hand, 8% chance on the turn, and 8% on the river. Your chance of making an inside straight is 16% after the flop. Double that for an open ended or double belly buster.
Flush draw? 9 cards will make your hand, 18% chance turn, again river. 36% chance to hit a flush after the flop. (3 to the flush at the flop, ~4% chance to hit runner runner, straights have either a .75 or 2% of hitting runner runner).
Pocket pair? 2 cards improve your hand. 4% on the turn, 4% on the river. 8% chance post flop for a pocket pair to improve to trips. (This is why you should fold at this point if you think you are beat)
There is a host of more complicated or precise math. Actually the odds of the turn being any given card are 2.12765%, on the river 2.17391%. Factoring in overlap the 4 flush on the flop is actually ~34.97%, open ended straight is 31.45%. I think most would agree that this system is an awfully close for its relative complexity.
So in conclusion, double the number of cards that could improve your hand, that is the approximate percent chance that you will improve on each card to come.
Poker math can be very simple.
Preflop there are two cards you have seen, and 50 you haven't. Each card in the deck has a 2% chance to be any given card. Have an AK? That leaves 3 aces and 3 kings in the deck. 6% of a card being any ace plus 6% for any king. That leaves a 60% chance that you will pair at least one of your cards (this is true for any two unpaired cards actually) through the river.
Most of the time though pre flop numbers are two big to matter (your opponent also have a 60% chance to get a pair etc.). Post flop though you can do some pretty quick math if you can add up to 13 and multiply by 2.
You have AK unsuited, Opponent has 55. Flop comes 279 rainbow. There is a 12% chance (2 times number of cards that would improve your hand) chance that your hand will improve on the turn, and that same chance on the river. 24% chance your hand will improve. This is imprecise, but good enough to make an estimate at your odds. (There is actually a 2% chance that your hand will improve, but you still lose, as your opponent gets his 5 along with your ace or king.)
Inside straight draw? 4 cards will improve your hand, 8% chance on the turn, and 8% on the river. Your chance of making an inside straight is 16% after the flop. Double that for an open ended or double belly buster.
Flush draw? 9 cards will make your hand, 18% chance turn, again river. 36% chance to hit a flush after the flop. (3 to the flush at the flop, ~4% chance to hit runner runner, straights have either a .75 or 2% of hitting runner runner).
Pocket pair? 2 cards improve your hand. 4% on the turn, 4% on the river. 8% chance post flop for a pocket pair to improve to trips. (This is why you should fold at this point if you think you are beat)
There is a host of more complicated or precise math. Actually the odds of the turn being any given card are 2.12765%, on the river 2.17391%. Factoring in overlap the 4 flush on the flop is actually ~34.97%, open ended straight is 31.45%. I think most would agree that this system is an awfully close for its relative complexity.
So in conclusion, double the number of cards that could improve your hand, that is the approximate percent chance that you will improve on each card to come.