How To Calculate The True Odds Of A Craps Pass Line Bet

A pass line wager is one of the most recognised bets on a craps table. It appears simple: the shooter rolls a come-out roll, and the bet either wins immediately, loses immediately, or moves to a point number. The mathematics becomes clearer when each stage is separated.

The dice have 36 equally likely combinations. Seven can be rolled in six ways, while six and eight can each be rolled in five ways. Numbers such as four and ten have three combinations, and five and nine have four. These frequencies determine both the true probability of winning and the casino’s mathematical advantage.

A pass line bet pays even money. A $10 bet returns a $10 profit when it wins, while a losing wager forfeits $10. That payout does not reflect the exact probability of the bet winning, because the chance of success is slightly below 50 percent.

For Australian players comparing table games in AUD, the key figure is the long-term expected loss rather than the result of one roll or one session. A $25 wager can win or lose quickly at a casino in Sydney, Melbourne or Perth, but the underlying edge remains the same.

What Happens On The Come-Out Roll

The first roll is called the come-out roll. A pass line bet wins immediately if the shooter rolls a seven or 11. There are six combinations for seven and two combinations for 11, giving eight winning combinations out of 36.

The bet loses at once when the come-out roll is two, three or 12. Two has one combination, three has two, and 12 has one, so there are four losing combinations. The remaining 24 combinations establish a point: four, five, six, eight, nine or ten.

The initial probabilities are therefore:

• Immediate win: 8/36, or 22.22 percent
• Immediate loss: 4/36, or 11.11 percent
• Point established: 24/36, or 66.67 percent

A point does not mean the bet has won. It creates a second phase in which the point must be rolled again before a seven appears.

Calculating The Point-Phase Probability

Once a point is established, the relevant comparison is between the point number and seven. The point wins if it is repeated before seven, while a seven ends the wager as a loss.

For a point of four or ten, there are three combinations for the point and six combinations for seven. The chance of making the point before seven is therefore 3 divided by 3 plus 6, or one-third. For five or nine, the calculation is 4 divided by 4 plus 6, producing four-tenths. For six or eight, it is 5 divided by 5 plus 6, or five-elevenths.

This is a useful example of why dice combinations matter. A six may look close to seven numerically, but six has five combinations and seven has six, giving it a stronger chance than four or ten. The same probability principles apply when house edge is calculated for other casino wagers.

Combining Every Stage Of The Bet

The full win probability combines immediate wins with point-phase wins. Immediate wins contribute 8/36. For each possible point, multiply the probability of establishing that point by the probability of making it before seven.

The calculation can be written as:

• Immediate win: 8/36
• Point four or ten: 6/36 × 1/3, counted twice
• Point five or nine: 8/36 × 2/5, counted twice
• Point six or eight: 10/36 × 5/11, counted twice

Using the exact fractions gives a total pass line win probability of 244/495, or approximately 49.2929 percent. The loss probability is 251/495, approximately 50.7071 percent. The two figures add to 100 percent, as they should.

The difference between losses and wins is seven outcomes per 495 equivalent trials. That small gap is the source of the standard pass line house edge of 7/495, or about 1.414 percent. This is the true mathematical disadvantage before considering any optional side wager.

Expected Value And Even-Money Payouts

Expected value translates the probabilities into an average result. For a $1 pass line bet, a win produces a $1 profit and a loss produces a $1 loss. The calculation is:

EV = (244/495 × $1) − (251/495 × $1)

The result is −7/495 of a dollar, or approximately −$0.01414 per $1 wagered. On average, that corresponds to a loss of about 14 cents for every $10 bet, assuming a very large number of bets and no other wagers.

This does not predict an individual session. A player can win several consecutive pass line bets, lose repeatedly, or finish ahead after a short visit. Expected value describes the average result over an extensive sequence, not a guaranteed charge applied to each roll.

The term “true odds” can also refer to the fair odds implied by the probability. Since the pass line pays even money while its chance of winning is 244/251 relative to its chance of losing, the payout is slightly less generous than a perfectly fair wager would require.

Why The House Edge Stays Relatively Low

The pass line bet has a lower house edge than many proposition bets in craps because it uses the natural frequencies of the dice and pays a standard even-money return. Its disadvantage is created mainly by the come-out rules: seven and 11 win, while two, three and 12 lose, and the later point phase gives seven a recurring advantage.

Players sometimes compare the pass line with the don’t pass bet. The don’t pass wager generally has a slightly lower house edge, although it involves a push when a 12 appears under standard rules. It also has a different betting perspective, since the wager usually wins when the shooter fails to make the point.

Australian casino settings can make craps feel less familiar than roulette, blackjack or electronic gaming machines. Pokies remain far more visible in the local market, while traditional craps tables are concentrated in selected licensed venues, including major-city casinos. Rules, minimum bets and available table games can differ between properties, so the probability calculation should be kept separate from venue-specific conditions.

Online casino reporting from overseas markets, such as New Jersey revenue trends, should not be treated as evidence that an equivalent online craps product is lawful or available in Australia. Australian gambling law and state-based venue rules create a different environment.

Practical Checks For Reading The Odds

A disciplined calculation is easier when each assumption is kept visible. The following checks help distinguish the pass line’s base probability from unrelated features such as odds bets, bonus bets or proposition wagers:

• Count dice combinations out of 36 rather than treating numbers as equally likely.
• Separate the immediate come-out result from the point phase.
• Use the probability of the point appearing before seven.
• Compare the final win and loss probabilities with the actual payout.
• Express the house edge as a percentage of the amount wagered.
• Keep optional odds and side bets outside the base pass line calculation.
• Use Australian dollars only to scale the result, not to change the probability.

A genuine odds bet behind the pass line is different from the original wager. It is commonly paid at true odds and can reduce the combined house edge, but it increases the amount exposed to variance. The pass line itself still has the 1.414 percent house edge, regardless of whether extra funds are placed behind it.

For a neutral reference on casino mathematics, the casino reference site can be used alongside the direct dice calculation. The essential result remains straightforward: 244 winning outcomes against 251 losing outcomes in the equivalent combined model, producing a 49.2929 percent win chance and a 1.414 percent house edge. For practical budgeting, multiply the total amount wagered by 0.01414 to estimate the long-run theoretical loss, and treat that figure as a mathematical average rather than a forecast for one visit.