Bridge Odds Calculator

Out of the box the calculator is set to Balanced and 15 to 17 points, and it reports 4.87 percent. Those are the hands that open a strong 1NT, and they turn up roughly once in twenty deals. Change the shape or either end of the point range and the figure updates at once.

Every figure comes from exact counting, with no simulation anywhere. There are 635,013,559,600 different thirteen-card hands. For a given shape and range the calculator counts how many of them qualify and divides by that total.

A shape means the pattern in any suit order, so 5-3-3-2 covers a five-card spade suit exactly as much as a five-card club suit. Balanced adds the three balanced patterns together (4-3-3-3, 4-4-3-2 and 5-3-3-2), and between them they make up 47.60 percent of all hands. Points are the usual 4-3-2-1 count, from 0 to 37. The full tables behind the two controls are on the hand patterns and high-card points pages.

The large figure is the chance that one named hand, yours or partner's, fits the description before the deal. The line underneath turns it into one hand in N, which is easier to picture. Fifteen or more points on any shape comes to 14.18 percent, about one hand in seven, while 20 or more is down at 1.45 percent.

Those frequencies are a fair test of a bidding agreement. Balanced hands turn up on nearly half of all deals, so the methods that describe them get constant use and have to be sound. A bid saved for a 20-count comes up so rarely that most partnerships are happy to let it cost something elsewhere. For the trick-taking side of the same arithmetic, see suit break odds and hand evaluation.

The calculator prices one hand in isolation. Once the auction starts, the other three hands stop being random and the a priori figure is only a starting point.

How many possible bridge hands are there?

There are 635,013,559,600 possible bridge hands, the number of ways to choose 13 cards from a 52-card deck. Every percentage on this page is a count of hands divided by that number.

What are the odds of being dealt a balanced hand?

The odds are 47.60 percent. A balanced hand is 4-3-3-3, 4-4-3-2 or 5-3-3-2, and those three patterns together account for just under half of all deals.

How often is a strong notrump opening dealt?

A balanced hand of 15 to 17 points is dealt 4.87 percent of the time, roughly once in twenty hands. Pick Balanced and the range 15 to 17 in the calculator to see it.

Is the bridge odds calculator a simulation?

No. It counts every qualifying hand exactly, so the figures do not move from one visit to the next and carry no sampling error.