Hand improvement odds
Definition of hand improvement odds
The "hand improvement odds" of a hand is the probability that you will improve your hand. You have a flush draw on the flop and want to know if you can call your opponent's bet. In this situation, you need to know the "hand improvement odds" to know if you can call the bet. To do so, you will need to relate the number of known cards, the hidden cards, the cards to come and the ratio of your opponent's bet to the size of the pot.
Let's go back to our color print above. Let's say the pot is 10 euros. Our opponent bets 10 euros in 10. Simply put, we'll say that we don't have the best hand at this stage and that we need to complete our flush to win the hand. Here we know the 3 cards of the flop plus our two cards, so 5 cards out of 52. We know that 4 spades are already out (for our flush draw). There will thus remain 9 cards out of 47 (the unknown cards) which will be able to help us. So, 1 time out of 5 (47/9 = 5.22 rounded to 5) the turn will give us our suit, i.e. rounded odds of 4:1 (1 time we hit, 4 times we don't hit). Since our opponent bets 10 in 10, we will lose 4 x 10 euros so 40 euros before making 1 x 20 euros so 20 euros. A total loss of 160 -20 or call0 euros in the long run. This is a bad call if we rely on the "hand improvement odds".