Pair ("one pair"): Only one pair of faces. Ties are broken by the best pair's rank, then the second-best pair's rank, then by the highest remaining cards in order. Ties are broken by those three cards' rank, and then by the highest remaining cards in order. Three of a kind: Three cards with the same face. The highest card in the straight breaks ties. Straight: Five cards in sequential order, but not of one suit. Ties are broken by comparing the two highest cards, then the two second-highest cards, etc. Ties are broken by the triple's rank, then by the pair's rank.įlush: Five cards of the same suit, but with no discernible order. The quadruple-card's rank breaks ties.įull house: One triple and one pair. An ace-high straight flush (i.e., A, K, Q, J, and 10, all of the same suit) is famously called a royal flush and is the best possible hand.įour of a kind: Four cards of the same rank and a remaining card of any rank. Straight flush: Five cards of sequential ranks of the same suit. Aces are usually ranked highest but can form part of low sequences too (acting as a "1" instead) - we'd count both A-2-3-4-5 or 10-J-Q-K-A as straights, but the former is 5-high, and the latter is ace-high. When multiple hands of the highest rank are present, the rank of the individual cards breaks these ties. So, here they are, described and ranked from best to worst below. You'll ideally need a fast hand evaluator, but that should be easy to find online if you don't want to write it yourself.To make sense of our poker probability calculator's outputs and inner workings, we need to know the different hands you might find in poker. So on the turn (pre-river), it's even cheaper to compute the hand equities. Given the flop and turn, there's only 42 possible river cards. Given the flop, there's only choose(43, 2) = 903 boards possible by the end, so the flop probabilities (which you call the pre-turn), it's very cheap to enumerate all the runouts and compute the average equity for the three hands.
This gives you preflop probabilities, and this is the most expensive thing to compute. (Or more accurately, compute the equity for each hand, since sometimes 2 or 3 hands will tie on the river). Enumerate all boards, and count how many times each hand wins on the river.
That means there's choose(46, 5) = 1,370,754 different boards by the river. Given 3 hands (6 cards), there's 46 cards remaining in the deck. For example, if you're considering preflop probabilities, you only care about the entire board by the river, and not the specific flop, turn and river. The trick is to disregard the order the cards come out as much as possible.
The numbers are much smaller than you might expect, so brute-forcing is quite possible.
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