A Rainbow Flop, a Two-Tone Flop, and a Monotone Flop

Players describe a flop in colors before they describe it in ranks. Three cards of one suit are monotone. Three cards of three suits are rainbow. Everything else, in a three-card flop, is two-tone: one suit appears twice, and a second suit appears once. The labels are useful because they change whether a flush is already possible. They are also easy to exaggerate. This page counts them from a full deck and then says what the count is not.

The language of odds versus probability is in Odds and Probability Are Not the Same Number. Nothing here is a reason to put money in a pot. Adults who play can lose that money, and the law depends on the place.

How many flops exist at all

Three cards from a 52-card deck, ignoring order, number 52 times 51 times 50, divided by 6. That is 22,100 flops. This count treats the flop as three cards from a full deck. It is the right picture for the question of how often a random board looks like this. If you already hold two cards, you have removed two cards from the deck, and the chance of a particular monotone flop shifts. The shift is real, and the full-deck figures still tell you which textures are common. They are not a personalized prediction.

Monotone is the rare pattern

A monotone flop is three cards of one suit. A suit has 13 cards, and the ways to choose three of them are 13 times 12 times 11, divided by 6, which is 286. Four suits give 4 times 286, or 1,144 monotone flops. Divide 1,144 by 22,100 and you get about 5.2 percent. About one flop in nineteen is three cards of one suit. On those boards a flush is already finished for anyone holding two cards of that suit, and one card of that suit gives a flush draw. The board itself is not a flush. A flush needs five cards.

Rainbow is common, and it is not half

A rainbow flop uses three different suits. Choose the three suits from four, which can be done in four ways, and then one card from each of those suits: 13 times 13 times 13 is 2,197. Four times 2,197 is 8,788. Divide by 22,100 and you get about 39.8 percent. No suit appears more than once, so the board alone offers nobody a flush draw. People who say rainbow boards are about half are high. The largest share belongs to the next group.

Two-tone is the largest share

Subtract. 22,100 minus 1,144 minus 8,788 is 12,168 two-tone flops, about 55.1 percent. You can build the same number from the other direction. Choose the suit that appears twice: 4 choices, and 13 times 12 divided by 2 is 78 ways to pick those two cards. The singleton comes from one of the other three suits, 39 cards. Four times 78 times 39 is also 12,168. On a two-tone board, a player holding two cards of the doubled suit has a flush, and a player holding one card of that suit has a flush draw. The single suit on the board does not, by itself, offer a one-card flush draw.

What to do with the labels

Use them to read the board, not to invent a debt the deck owes you. A monotone flop is uncommon, so it should surprise you, and then you should still name the five-card possibilities instead of staring at the suits. A two-tone flop is ordinary. Calling it a miracle every time trains you to overreact to a pattern that shows up on most boards. The percentages do not say whether to bet. They do not include ranks, pairs, or straights. They change when the turn arrives, because a fourth card can change the suit counts. If you cannot reproduce 1,144, 8,788, and 12,168, do not quote a tighter figure you heard at the table. The same habit of showing the count is what makes Outs and the Rule of 4 and 2 worth reading slowly.

Frequently asked questions

Does monotone mean three of a kind? No. Monotone means one suit. Three of a kind means one rank. A flop can be one, the other, both, or neither.

Do these percentages include my hole cards? The arithmetic above does not. It counts boards from a full deck. Cards you already hold change the leftovers. Say so if you quote the figures.

Is a two-tone flop a reason to chase a flush? No. The label only says a flush is possible for someone. Price, your actual cards, and your budget are separate, and a flush draw still misses often.