Craps Odds Calculator

Introduction

Craps looks chaotic from the rail, but the underlying math is surprisingly orderly. Every roll of two fair six-sided dice produces one of 36 equally likely combinations, and that fixed sample space is what makes the game analyzable. This calculator is designed to turn that casino math into something practical. Instead of memorizing every probability, you can choose a common bet and instantly see its win probability and expected return. That makes the page useful for beginners who want to understand the game and for experienced players who want a quick numerical check before comparing wagers.

The calculator focuses on five familiar bets: Pass Line, Don't Pass, Field, Place 6, and Place 8. These bets cover several different styles of risk. Some resolve immediately on one roll, while others continue after a point is established. Some pay even money, while others use a fractional payout that reflects the number's true frequency. By putting these side by side, the calculator helps you see an important truth about craps: not all bets are equally expensive in the long run, even when they feel equally exciting in the moment.

At the heart of the game is the distribution of totals from two dice. Because each die has six faces, there are $6\times 6=36$ equally likely outcomes. The totals from 2 through 12 do not occur with equal frequency. A 7 can be rolled in six different ways, while a 2 or 12 appears in only one way each. That uneven distribution is why some bets are stronger than others and why payout tables matter so much.

Understanding Craps Probabilities

The table below summarizes the basic dice distribution used by every calculation on this page. If you are new to craps, this is the best place to start. Once you see how often each total appears, the logic behind Pass Line, Don't Pass, Field, and Place bets becomes much easier to follow.

One useful way to read this table is to compare a target number with 7. In many craps situations, once a point exists, the real contest is whether your number appears before 7. For example, 6 has five combinations and 7 has six, so a race between 6 and 7 is slightly unfavorable to the player. That single comparison explains a large share of the strategy discussion around Place bets and point resolution.

How to Use This Calculator

Using the calculator is simple. First, choose a bet type from the drop-down menu. Then press the Calculate button. The result area will display the estimated win probability and expected return for that wager. If you want to save or share the output, use the Copy Result button. The copied text is plain and compact, which makes it easy to paste into notes, messages, or a betting comparison sheet.

Here is what each input and output means in plain language. The Bet Type menu selects the wager whose math you want to inspect. The Win Probability tells you how often that bet wins under the stated rules, expressed as a percentage. The Payout, when shown, is the amount won relative to a one-unit stake. The Expected Return is the average net result per unit bet over many repetitions. A negative expected return means the casino has the advantage. The more negative the number, the more expensive the bet is over time.

It is important to interpret the result correctly. A bet can have a win probability above 50% and still be unfavorable if the payout is too small, and a bet can win less often than half the time yet still be relatively efficient if the payout is closer to the true odds. In craps, the house edge comes from the gap between fair odds and the actual payout schedule offered by the casino. This calculator helps make that gap visible.

Formula

The general expected value idea used throughout the page is straightforward: multiply each possible outcome by its probability, then add the results. For a simple one-stage bet with a single payout, the net expected return per unit can be written as:

A negative EV corresponds to the house edge. If the expected return is −0.0141 units per unit wagered, the house edge is about 1.41%. That does not mean you lose 1.41% every session. It means that over a very large number of identical bets, the average loss tends to that amount per unit staked.

The Pass Line bet is resolved in two stages. On the come-out roll, 7 or 11 wins immediately, while 2, 3, or 12 loses. Any other total establishes a point. After that, the player wins if the point repeats before a 7 appears. Using conditional probability, the chance of a Pass Line win can be expressed as:

Here $c_p$ is the number of combinations that make point p, and $c7$ equals six. Substituting the values gives a Pass Line win probability of $\frac{244}{495}$, or about 49.293%. The corresponding house edge is $\frac{7}{495}$, about 1.41%.

The Don't Pass bet reverses much of that logic. On the come-out roll, 2 or 3 wins, 7 or 11 loses, and 12 pushes. If a point is established, the bet wins when 7 appears before the point repeats. That produces a win probability of $\frac{251}{495}$ and a house edge of roughly 1.36%, slightly better for the player than Pass Line.

The Field bet is a one-roll wager. It wins on 2, 3, 4, 9, 10, 11, or 12 and loses on 5, 6, 7, or 8. The probability of landing on any field number is $\frac{16}{36}$. Because 2 and 12 often receive bonus payouts, the expected return depends on the exact pay table. This page uses the common version where 2 pays double and 12 pays triple, matching the existing script behavior.

Place 6 and Place 8 are classic examples of a race against 7. Since 6 can be rolled in five ways and 7 in six ways, the probability that 6 appears before 7 is $\frac{5}{11}$. The same is true for 8. Casinos usually pay 7:6 on these bets, which creates a house edge of about 1.52%.

The conditional-probability structure becomes especially clear if you isolate one point. Suppose the point is 6. The chance that 6 appears before 7 is:

Because $c_6=5$ and $c_7=6$, the value is $\frac{5}{11}$. Multiplying by the chance of establishing 6 in the first place, $\frac{5}{36}$, contributes $\frac{25}{396}$ to the full Pass Line win probability.

Worked Odds Table

The following summary table gathers the main values used by the calculator. It is a quick reference rather than a replacement for the explanation above. The expected value column shows the average net gain or loss per unit wagered. Negative values indicate the built-in casino advantage.

One subtle point is worth noting: the explanatory text on craps often discusses house edge in terms of mathematically idealized pay tables, while a calculator script may implement a specific expected-return formula. On this page, the JavaScript behavior has been preserved exactly, so the displayed result for the Field bet follows the script's current logic. That is intentional, because preserving calculator behavior is more important than rewriting the underlying computation in a way that could break consistency with the existing tool.

Example

Suppose you choose Place 6 from the menu and click Calculate. The calculator reports a win probability of about 45.45%, a payout of 1.17:1, and an expected return near −0.0152 units per unit wagered. In ordinary language, that means the bet wins a little less than half the time, but when it wins, it pays more than even money. Even so, the payout is still not quite generous enough to match the true odds, so the casino keeps a small long-run advantage.

As another example, consider the Pass Line. The result is close to a 49.29% win probability with an expected return around −0.0141 units. Many players are surprised that a bet can lose slightly more often than it wins and still be one of the better options on the table. The reason is that the Pass Line is priced relatively fairly compared with many proposition bets found in a live casino. It is not a winning bet in the long run, but it is one of the less costly standard choices.

If you compare that with the Don't Pass result, you will see a slightly better expectation. The difference is small, not dramatic, but it illustrates how tiny rule details matter. The push on 12 changes the arithmetic enough to lower the house edge. Over a few rounds, that difference is invisible. Over thousands of bets, it becomes measurable.

Limitations and Assumptions

This calculator assumes fair dice, independent rolls, and standard casino-style rules for the listed bets. It does not model table-specific variations beyond the payout assumptions already built into the script. In particular, the Field bet can vary from casino to casino, especially in how 2 and 12 are paid. If your table uses a different pay schedule, the real expected return may differ from the displayed result.

The tool also focuses on isolated bets rather than full-session strategy. Real craps play often combines multiple wagers, odds bets behind the line, table minimums, bankroll constraints, and player behavior that changes after wins or losses. None of that is represented here. The result should therefore be read as a clean mathematical snapshot of one bet type, not as a prediction of what will happen in a single casino visit.

Another limitation is psychological rather than mathematical. Probability describes long-run averages, not short-run guarantees. A player can win several unfavorable bets in a row or lose several relatively efficient bets in a row. That does not mean the odds changed. It only means variance is doing what variance does. The law of large numbers tells us that outcomes tend to settle toward their expected values only over many repeated trials.

Finally, this page is educational, not financial or gambling advice. The purpose of the calculator is to clarify risk, payout, and expectation so that the game is easier to understand. If you use it before playing, the healthiest interpretation is simple: lower house edge means slower expected loss, not a path to guaranteed profit. In casino games, the most reliable advantage comes from discipline, not from chasing streaks or assuming that a recent run of rolls has made a certain outcome "due."