Calculating of Hand Odds
Probability can be calculated easily for a single event, like the flipping of the River card from the Turn. This would simply be: Total Outs / Remaining Cards. For two cards however, like from the Flop to the River, it's a bit trickier. This is calculated by figuring the probability of your cards not hitting twice in a row. This can be calculated as shown below:
Flop to River % = 1 - [ ((47 - Outs) / 47) * ((46 - Outs) / 46) ]
Turn to River % = (47 - Outs) / 46
The number 47 represents the remaining cards left in the deck after the flop - 52 total cards, minus 2 in our hand and 3 on the flop = 47 remaining cards.
Even though there might not technically be 47 cards remaining, we do calculations assuming we are the only players in the game. To illustrate:
Two Over card Draw = 1 - [(47 - 6) / 47 * (46 - 6) / 46] = 1 - [(41/47) * (40/46)] = 1 - [0.87 * 0.87] = 1 - 0.76 = 0.24 = 24% Chance to Draw Over cards from Flop to River.
The formula to change a percent to odds is:
Odds = (1 / Percentage) - 1;
To change the 24% draw we do the following:
Odds = (1 / 24% Two Over card Draw) - 1 = (1 / 0.24) - 1 = 4.17 - 1 = 3.17;