A bet with no edge, with a catch
Craps is a game of chance with a built-in house edge, and no bet, system or timing makes it favorable to the player over time. Most players lose money over time, and nobody should gamble money they cannot afford to lose. The odds bet is the one wager in the casino that carries no house edge by itself, which can sound like a loophole. It is not, and the reason is worth understanding.
An odds bet (often called free odds because the casino takes no edge on it) is an extra wager placed behind a Pass Line, Don’t Pass, come or Don’t Come bet once a point exists. It pays at the true odds of the point being repeated before a 7 appears.
Where the true odds come from
After a point is set, only the point number and the 7 matter. The odds depend on how many ways each can be made with two dice:
| Point | Ways to make the point | Ways to make a 7 | Odds of point before 7 | Odds bet pays |
|---|---|---|---|---|
| 4 or 10 | 3 | 6 | 1 to 2 | 2 to 1 |
| 5 or 9 | 4 | 6 | 2 to 3 | 3 to 2 |
| 6 or 8 | 5 | 6 | 5 to 6 | 6 to 5 |
The payout is simply the reverse of the chance. If the point wins 1 time in 3 on average, a fair payout is 2 for every 1 risked. These are payout ratios that exactly match the real odds, so the expected value of the bet is zero.
A worked example
This is a hypothetical illustration. Suppose a player has a $10 Pass Line bet and the point is 4. They add a $10 odds bet.
- The point wins with probability 3/9 = 1/3 and pays $20 on the odds bet.
- The 7 wins for the house with probability 6/9 = 2/3 and takes the $10.
- Expected result on the odds bet: (1/3 × $20) − (2/3 × $10) = $6.67 − $6.67 = $0.
The odds bet breaks even on average. That is the full extent of the “free” in free odds: no edge is added. Nothing is subtracted either.
For a point of 6, a $10 odds bet pays $12 on a win, while 5 and 9 pay $15 on a $10 bet. Amounts that do not divide evenly into the ratio, such as $7 on a 6 (which would pay $8.40), are often rounded down, which costs the player a small amount.
Why the game is not fixed
The odds bet cannot be made on its own. It requires a line bet first, and that line bet carries an edge of roughly 1.4%. The odds do not change the line bet. They only add more money to the same event.
Here is the effect with a hypothetical $10 Pass Line bet. The expected loss on the line bet is about 14 cents (10 × 0.0141). Adding $20 odds on top leaves that expected loss unchanged at about 14 cents, because the odds portion adds $0. But now $30 is exposed instead of $10 when a point is set, so the loss measured as a share of the total amount at risk is lower. The cost relative to what is wagered falls; the cost in dollars stays the same.
Two points follow:
- Higher odds multiples dilute the percentage edge but never eliminate it. The edge on the combined wager approaches zero only if the multiple grows without limit.
- Because more money is exposed, the swing in results grows. A single losing 7 now costs three times as much as the line bet alone. Short-term fluctuation rises even though the expected cost does not. That is a real consideration for anyone with a fixed budget.
Limits on the odds
Casinos cap how much odds can be taken, usually as a multiple of the line bet. A table might allow odds of several times the original bet, and the multiple may differ by point number. Table limits like these are posted, and the details vary by venue, so a player should check the rules at the specific table.
The Don’t Pass side can also take odds, called laying the odds. Because the 7 is the favorite after a point is set, the player must risk more than they win. Laying odds on a 4 requires risking $20 to win $10, the mirror image of the payout above, and again the expected value of the odds portion is zero.
What odds bets do and do not do
- They pay true odds, so the odds portion has no house edge.
- They require an initial line bet, which has an edge.
- They lower the edge as a percentage of total money wagered, not in dollars.
- They increase the size of swings, so they can also speed up losses.
- They do not change the chance of any roll. Each roll is one of 36 equally likely combinations, and rolling a point does not make a 7 more or less likely next.
Odds bets are a good example of why a “zero-edge” label is not the same as “safe.” Anyone who plays craps should decide on a spare-money limit in advance, accept that outcomes are uncertain, and stop when the limit is reached. A local support service can help anyone who feels their gambling is getting out of control.