Strategy description
A Pass Line strategy with an odds multiplier. Bet the pass line for $10. When a point is set, put odds behind it for the following multipliers:
- 1x odds
- 2x odds
- 345x odds (3x odds of 6/8, 4x odds on 5/9, 5x odds on 4/10)
- 10x odds
For a detailed explanation of the pass line bet, see All Bets Are Off: Re-learning the Pass Line Bet in Craps. The 345x odds is a common maximum odds for many casinos, but some offer up to 10x (or even 100x), so that strategy is also shown.
Simulated outcomes
To understand how the strategy could perform on any given day, we simulate 1,000,000 sessions for each of three session types: one shooter, 10 shooters, and one hour (144 rolls, letting active bets finish). The results are given in each tab below. For more information on how to read each chart, table, or statistic, see How to interpret statistics from The Craps Analyst.
Unlike most other strategy pages, the tables and plots show variations of the strategy depending on how much odds are taken behind. This allows for easy comparison and hopefully can help you select the right amount of odds for your bankroll. Note that the plots do not show the 10x odds multiplier because the range is huge and it makes things challenging to compare.
Analysis
One important aspect of the odds bet is that is the only bet in the casino that carries 0% house edge. The casino pays out true odds depending on what the point is—so if the point was 6, the odds of winning are 5:6 and the casino pays out 6:5. What’s the catch? You can only bet odds with a pass line bet down, which has a 1.41% house edge (or don’t pass, but that’s another page). Note that the simulated average winnings is nearly identical to that of the Pass Line bet alone (-$0.36 per shooter, -$3.56 per 10 shooters, -$6.18 per hour), as we would expect. There is some slight differences which are due to simulating only one million sessions instead of an infinite number, especially for large odds multiples which increases the variability. In theoretical terms, the average winnings is the same no matter how much odds you take.
The unsurprising difference when taking higher odds is that the variability increases. This can be seen from the strategy metrics on any session type and in the plots. Variance is typically a good thing in the casino, as long as your bankroll can sustain the losses. (With no variance and a –EV bet you’re guaranteed to lose). Note that even 2x odds on a $10 table, with no other bets, could see swings from -$136 to $120 in the middle 50% of sessions and a whopping -$434 to $444 in the middle 99% of sessions. If you happen to be at a $25 minimum table, those swings would be 2.5x that. The swings can work with a large bankroll, but not with a small bankroll because your win chance increases slightly if you can last for 10-30 shooters (note, this is slightly counterintuitive, but can be seen here with a ~40% win chance on one shooter and a ~45% win chance on ten shooters; the full trend is shown in One Surprising Feature of Dark Side Betting).
Given these insights, I take some issue with message I often hear that “adding odds lowers your house edge.” The argument goes something like this: adding an odds bet (0% edge) to the pass line (1.41% edge) makes the average edge lower than 1.41%. But in real dollar terms, this only means that a $10 pass line with $10 in odds has lower edge than a $20 pass line bet. It does not mean that a $10 pass line with $10 in odds has lower edge than a $10 pass line bet alone—their theoretical loss (theo in casino-speak) is identical. Unfortunately, we can’t just average house edge percentages together because the bet amounts and bet timing matters. And you can’t win or lose percentages at a casino, you can only win or lose dollars. End of rant.
Instead, I like to view the odds bet as “free variance” in the casino. Adding odds doesn’t change your average winnings, but it will increase variability. It’s a great way to tune your strategy to match your own risk preferences, without needing to add other bets that would otherwise decrease your average winnings.
- Per shooter
- Per 10 shooters
- Per hour
Per shooter
Strategy metrics
| Odds Multiple | Average Winnings | Win Chance | Variability |
|---|---|---|---|
| 1x | −$0.37 | 39.2% | $29.86 |
| 2x | −$0.38 | 38.7% | $45.19 |
| 345x | −$0.43 | 39.7% | $77.87 |
| 10x | −$0.49 | 40.4% | $171.59 |
Session quantiles
| Odds Multiple | Worst 1% | Worst 25% | Mid 50% | Best 25% | Best 1% |
|---|---|---|---|---|---|
| 1x | −$30.00 | −$20.00 | −$10.00 | $10.00 | $109.00 |
| 2x | −$40.00 | −$30.00 | −$20.00 | $14.00 | $166.00 |
| 345x | −$70.00 | −$50.00 | −$40.00 | $30.00 | $290.00 |
| 10x | −$120.00 | −$110.00 | −$100.00 | $50.00 | $640.00 |
Resulting winnings after each simulated session
Sample of 10 sessions
Per 10 shooters
Strategy metrics
| Odds Multiple | Average Winnings | Win Chance | Variability |
|---|---|---|---|
| 1x | −$3.53 | 44.1% | $94.37 |
| 2x | −$3.50 | 44.5% | $142.85 |
| 345x | −$3.42 | 45.0% | $246.18 |
| 10x | −$3.27 | 45.0% | $542.42 |
Session quantiles
| Odds Multiple | Worst 1% | Worst 25% | Mid 50% | Best 25% | Best 1% |
|---|---|---|---|---|---|
| 1x | −$176.00 | −$71.00 | −$14.00 | $53.00 | $260.00 |
| 2x | −$260.00 | −$106.00 | −$20.00 | $82.00 | $398.00 |
| 345x | −$450.00 | −$180.00 | −$30.00 | $140.00 | $690.00 |
| 10x | −$960.00 | −$400.00 | −$70.00 | $320.00 | $1,520.00 |
Resulting winnings after each simulated session
Sample of 10 sessions
Per hour
Strategy metrics
| Odds Multiple | Average Winnings | Win Chance | Variability |
|---|---|---|---|
| 1x | −$6.01 | 47.6% | $124.60 |
| 2x | −$6.05 | 48.2% | $189.27 |
| 345x | −$5.96 | 48.8% | $325.65 |
| 10x | −$5.37 | 49.1% | $712.04 |
Session quantiles
| Odds Multiple | Worst 1% | Worst 25% | Mid 50% | Best 25% | Best 1% |
|---|---|---|---|---|---|
| 1x | −$289.00 | −$91.00 | −$7.00 | $78.00 | $288.00 |
| 2x | −$434.00 | −$136.00 | −$8.00 | $120.00 | $444.00 |
| 345x | −$740.00 | −$230.00 | −$10.00 | $210.00 | $770.00 |
| 10x | −$1,610.00 | −$490.00 | −$20.00 | $470.00 | $1,690.00 |
Resulting winnings after each simulated session
Sample of 10 sessions
Comments
One response to “Pass Line with Odds”
[…] as the Don’t Pass mirrors the Pass Line strategy, the outcomes for this strategy mirror the Pass Line with Odds strategy in many ways. The resulting winnings are nearly inverted, this time favoring small wins […]