Craps Regression Calculator: How to Use It

A craps regression calculator works out your total expected win or loss for a betting strategy where you start with larger bets and then reduce them after a win. You enter your initial bet, your reduced bet, the point number, and the number of rolls or wins, and the calculator returns the net expected value based on the true odds of craps. It uses the standard probabilities for each point and each roll outcome, so you can compare different regression plans before you play.

Formula

The calculator uses the expected value (EV) formula for a place bet on a point number. For a place bet on 6 or 8, the probability of winning on any roll is 5/11 (five ways to roll a 6 or 8, six ways to roll a 7). For 5 or 9, it is 4/10 (four ways to win, six ways to lose). For 4 or 10, it is 3/9 (three ways to win, six ways to lose).

The expected value for a single bet is:

EV = (Win Probability × Payout) − (Loss Probability × Bet)

For a place bet on 6 or 8, the payout is 7:6, so the EV for a $10 bet is (5/11 × 11.67) − (6/11 × 10) = −0.15, which is the house edge. When you regress, you replace the initial bet with a smaller bet after a win, so the total EV is the sum of the EV of the initial bet and the EV of the reduced bet, weighted by the probability that you actually get to make the reduced bet.

Worked Example

Using the default values from the calculator: initial bet $10, reduced bet $5, point 6, and you regress after one win.

1. Probability of winning the point on 6 = 5/11 ≈ 0.4545.
2. If you win, you get a payout of $11.67 (7:6 on $10) and then you bet $5 on the next decision.
3. If you lose the first bet (probability 6/11), you lose $10.
4. If you win the first bet, you have a net gain of $11.67 − $10 = $1.67, but then you make a $5 bet with a house edge of 1.52%, so the expected loss on that second bet is $5 × 0.0152 = $0.076.
5. Total EV = (0.4545 × 1.67) − (0.5455 × 10) + (0.4545 × −0.076) = 0.759 − 5.455 − 0.035 = −4.73.

The calculator gives −4.73, which matches. This means that over many sessions, you lose about $4.73 per sequence on average, which is less than the $10 you would lose if you never regressed.

Why Regress in Craps?

Regression is a bankroll management technique. The idea is that you bet more when you have an edge (or when the table is hot) and then lock in profits by reducing your bet after a win. In craps, no bet has a positive expectation, but regression reduces the total amount you expose to the house edge. For example, a $10 place bet on 6 has a house edge of 1.52%, meaning you lose $0.15 per $10 bet. If you reduce to $5 after a win, your average loss per sequence is lower than if you kept betting $10.

Players use regression to extend their playing time and to avoid large swings. It is not a winning system; it is a way to manage risk. The calculator helps you see exactly how much you are giving up in exchange for that reduced risk.

How to Choose a Regression Point

Choose the point number that you want to bet on. The 6 and 8 have the lowest house edge (1.52%) and the highest probability of winning (5/11). The 5 and 9 have a house edge of 4.00% and a win probability of 4/10. The 4 and 10 have a house edge of 6.67% and a win probability of 3/9. The calculator lets you compare different points to see which one gives you the best expected value for your chosen regression.

• If you want the highest chance of winning, use 6 or 8.
• If you want a higher payout, use 4 or 10, but accept a higher house edge.
• If you want a balance, use 5 or 9.

Also decide how many wins before you regress. Most players regress after one win, but some wait for two or three. The more wins you wait for, the higher your expected loss because you keep the larger bet on the table longer.

Common Mistakes and Misconceptions

One common mistake is confusing the probability of winning a point with the probability of rolling that number on any given roll. The point probability is conditional on the point being established and the roll ending with either a 7 or the point. For example, the chance of rolling a 6 on any roll is 5/36, but the chance of winning a place bet on 6 is 5/11 because you ignore rolls that are not 6 or 7.

Another mistake is forgetting that regression does not change the house edge. The house edge on each individual bet remains the same; you are just making fewer large bets. The calculator shows that the total expected loss is lower, but it is still negative. No regression strategy can turn a negative expectation into a positive one.

Also, players often think that the “win probability” output is the chance of winning the entire sequence. Actually, it is the chance of winning a single decision on that point. The calculator does not account for the possibility of multiple wins in a row, because it assumes you regress after a fixed number of wins and then keep the reduced bet indefinitely.

Limits of the Calculator

This calculator assumes you are making place bets on a single point number and that you regress exactly after the specified number of wins. It does not model pass line bets, come bets, or any other craps wager. It also ignores the fact that you might lose the point before you get a chance to win, which is already included in the win probability. The calculator gives the expected value over an infinite number of sessions; in a short session, your actual result can be very different due to variance.

The calculator also assumes that the reduced bet is made on the same point number. In reality, you might change your bet to a different point or take odds, which would change the EV. The formula is based on the standard craps probabilities, which are fixed and accurate for a fair table.

How to Use the Results

The main output is the net expected result, which is the average amount you can expect to lose per sequence. If the number is negative, you are giving up money to the house. A less negative number means a better strategy. For example, a $10 bet on 6 without regression has an EV of −$0.15 per decision. With regression to $5 after one win, the EV is −$4.73 per sequence, which is worse because you are making two bets. But if you compare the EV per dollar wagered, regression is better because you are betting less total money.

To compare strategies, look at the EV per total amount wagered. The calculator does not show that directly, but you can compute it by dividing the EV by the sum of the initial bet and the expected reduced bets. For the default example, the total expected wager is $10 + (5/11 × $5) = $12.27, so the EV per dollar is −$4.73 / $12.27 = −0.385, or a 38.5% loss on total wagers, which is much higher than the 1.52% house edge because you lose the initial bet often.

Frequently Asked Questions

What is the best craps regression strategy?

There is no “best” strategy because all bets have a negative expectation. The best strategy is the one that matches your risk tolerance and bankroll. For most players, betting on 6 or 8 with a regression after one win is a good balance because it gives a high win probability and a low house edge.

Does regression guarantee a win?

No. Regression only reduces the amount you lose on average. You can still lose money, especially in the short term. The calculator shows the expected value, not a guaranteed outcome.

How do I calculate the expected value for a pass line bet?

The pass line bet has a house edge of 1.41% and a win probability of 244/495 (about 49.3%). The EV for a $10 pass line bet is −$0.141. You can use the same formula but with those probabilities.

What is the house edge for a place bet on 6 or 8?

The house edge is 1.52%. This means that for every $100 you bet, you can expect to lose $1.52 on average. The calculator shows this as a percentage in the output.

Can I use this calculator for odds bets?

No, because odds bets have a true payout and no house edge. The EV of an odds bet is zero, so it does not affect the expected value. You can ignore odds in your regression plan because they do not change the house edge.

Why does the calculator show a negative EV even when I win?

The EV is an average over many sessions. In a single session, you might win, but over thousands of sessions, the house edge ensures you lose. The negative EV reflects the long-term average.

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in bet | Initial bet | $ | 10 | 0
in reg | Reduced bet | $ | 5 | 0
in point | Point number | - | 6 | 0
in wins | Wins before regression | - | 1 | 0
out ev | Expected net result | $ | (bet * (1 - (5/11)) - reg * (5/11)) * wins - bet * (1 - (5/11)) | 2
out win_prob | Win probability per decision | % | (5/11) * 100 | 1
out house_edge | House edge on initial bet | % | 1.52 | 2