Definition of the dimensions of improvement of a hand

Hand improvement odds are 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 improvement odds of a hand to know if you can pay the bet in question. To do this, we need to put together the number of known cards, the hole cards, the upcoming cards and the ratio of our opponent's bet to the size of the pot.

An example

Let's go back to our color draw above. Let's say the pot is 10 Euros. Our opponent bets 10 Euros in 10. To put it simply, we'll say that we don't have the best hand at this stage and 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). This leaves 9 cards out of 47 (the unknown cards) that can help us. So, 1 time out of 5 (47/9 = 5.22 rounded up to 5) the turn will give us our flush, that is to say odds rounded up to 4:1 (1 time we hit, 4 times we don't hit). As 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 140 euros in the long run. This is a bad call according to the odds of improving a hand.