The Craps Analyst

Category: Strategies

  • Don’t Pass with Odds

    Strategy description

    A Don’t Pass strategy with odds laid behind. Bet the don’t pass for $10. When the point is set, lay odds behind it for the following amounts:

    • Lay odds to win 1x ($10), which is a $12 lay bet on the 6/8, $15 on the 5/9, or $20 on the 4/10
    • Lay odds to win 2x ($20), which is a $24 lay bet on the 6/8, $30 on the 5/9, or $40 on the 4/10
    • Lay odds to win 345x, which is a $60 lay for each number
    • Lay odds to win 10x ($100), which is a $120 lay bet on the 6/8, $150 on the 5/9, or $200 on the 4/10

    Note that most casinos that offer a maximum of 345x odds on the pass line will allow you to lay $60 odds on the don’t pass to win the equivalent 345x, but fewer will offer the opportunity to win 10x odds.

    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.

    Analysis

    Just 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 per-shooter or per-10-shooter with the possibility of huge losses (when you keep replacing the don’t pass bet every time the shooter hits a point). The only difference is when a 12 rolls on the come-out, in which the don’t pass bet pushes and the pass line bet loses. (Side note: if you take the house edge of 1.41% for pass line and 1.36% for don’t pass, add them up to get 2.77%, which is exactly the chance of rolling a 12, i.e. 1 out of 36).

    Just like with the Pass Line with Odds strategy, 1) the average winnings are nearly identical no matter how much odds you take and 2) the variability increases if you take more odds. Laying odds, a 0% house edge bet by itself, acts as “free variance.” It allows you to tune your strategy to match your own risk preferences, without needing to add other bets that would otherwise decrease your average winnings, which is a very nice feature. Just beware that even a small amount of odds can push your resulting winnings to a very wide distribution, which can be a problem if you have limited bankroll or are playing at tables with higher minimums.

    The interesting piece of this strategy is that if you budget per-shooter, the win chance is above 50%. I discuss this phenomenon at length in One Surprising Feature of Dark Side Betting, but essentially because the don’t pass bet is favored to win once you get past the come-out, and you win on the odds bet which is at least as much as the initial don’t pass amount, you end up with many potential small wins that drive the win chance up. The more shooters you play across, the further this will drop, before it eventually drops below 50% (somewhere about 70-80 shooters). Note that unless you have very large odds multipliers, playing your sessions on a per-time basis still has a win chance below 50%, which is more indicative of a slightly negative average winnings. Ultimately, you can’t escape the house edge if you play long enough.

    If you like to play the dark side and aren’t bothered by a strategy with minimal betting (i.e. you don’t get bored waiting for the point to win or lose), then Don’t Pass with Odds offers some great potential returns with minimal average loss over time.

    • Per shooter
    • Per 10 shooters
    • Per hour

    Per shooter

    Strategy metrics

    Win MultipleAverage WinningsWin ChanceVariability
    1x−$0.3359.9%$30.21
    2x−$0.3260.7%$45.58
    345x−$0.2760.0%$78.29
    10x−$0.2159.5%$172.01

    Session quantiles

    Win MultipleWorst 1%Worst 25%Mid 50%Best 25%Best 1%
    1x−$111.00−$12.00$10.00$20.00$30.00
    2x−$168.00−$20.00$20.00$30.00$40.00
    345x−$290.00−$30.00$40.00$50.00$70.00
    10x−$640.00−$50.00$100.00$110.00$120.00

    Resulting winnings after each simulated session

    Sample of 10 sessions

    Per 10 shooters

    Strategy metrics

    Win MultipleAverage WinningsWin ChanceVariability
    1x−$3.4853.0%$95.48
    2x−$3.5153.6%$144.08
    345x−$3.6053.9%$247.49
    10x−$3.7454.5%$543.78

    Session quantiles

    Win MultipleWorst 1%Worst 25%Mid 50%Best 25%Best 1%
    1x−$270.00−$61.00$7.00$66.00$170.00
    2x−$408.00−$90.00$12.00$102.00$256.00
    345x−$700.00−$150.00$20.00$180.00$440.00
    10x−$1,530.00−$330.00$60.00$390.00$950.00

    Resulting winnings after each simulated session

    Sample of 10 sessions

    Per hour

    Strategy metrics

    Win MultipleAverage WinningsWin ChanceVariability
    1x−$6.0648.5%$124.25
    2x−$6.1649.3%$189.08
    345x−$6.2549.7%$325.57
    10x−$6.6950.2%$711.99

    Session quantiles

    Win MultipleWorst 1%Worst 25%Mid 50%Best 25%Best 1%
    1x−$300.00−$89.00−$5.00$79.00$276.00
    2x−$456.00−$132.00−$4.00$124.00$420.00
    345x−$780.00−$220.00$0.00$220.00$730.00
    10x−$1,700.00−$480.00$0.00$480.00$1,600.00

    Resulting winnings after each simulated session

    Sample of 10 sessions

  • Pass Line with Odds

    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 MultipleAverage WinningsWin ChanceVariability
    1x−$0.3739.2%$29.86
    2x−$0.3838.7%$45.19
    345x−$0.4339.7%$77.87
    10x−$0.4940.4%$171.59

    Session quantiles

    Odds MultipleWorst 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 MultipleAverage WinningsWin ChanceVariability
    1x−$3.5344.1%$94.37
    2x−$3.5044.5%$142.85
    345x−$3.4245.0%$246.18
    10x−$3.2745.0%$542.42

    Session quantiles

    Odds MultipleWorst 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 MultipleAverage WinningsWin ChanceVariability
    1x−$6.0147.6%$124.60
    2x−$6.0548.2%$189.27
    345x−$5.9648.8%$325.65
    10x−$5.3749.1%$712.04

    Session quantiles

    Odds MultipleWorst 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

  • Hammerlock

    Strategy description

    This strategy combines a doey-don’t system, odds on the don’t pass, and place bets that stay up for only a few wins, in what ends up being a heavily hedged approach:

    • $10 pass line bet
    • $10 don’t pass bet,
      • Add (lay) $60 in odds once point is established
    • A phased place bet approach (no matter what the point is):
      • Start with $24 place bet each on 6 and 8
      • If one of these bets wins, shift to $44 inside (place the 5, 6, 8, and 9)
      • If one of the inside bets wins, take all place bets down

    The origins of this strategy is somewhat unknown. From some digging, it may have first appeared on gamblersbookcase.com, but it no longer appears there. Since then, some other sites have picked it up. The strategy description here comes from bestcrapsstrategy.net, which originally inspired this blog post: 5 Systems to Try at the Craps Table. The simulations have been re-worked for this page.

    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.

    Analysis

    There’s a lot going on in this strategy, and before looking at the numbers, it helps to break down some of the strategy aspects:

    • Before a point is set, most rolls will be net $0 for the player because both the pass line and don’t pass are bet. The only exception is on a roll of 12, where the player loses $10 on pass line and pushes on the don’t pass.
    • When the place bets are active (either 6/8 or 5/6/8/9), the total outlay for them is either $48 or $44. The don’t pass odds can win either $30 (on 4/10), $45 (on 5/9), or $50 (on 6/8). So a seven-out in this case is heavily hedged, and will typically be a very small win or loss.
    • The best situation is that two place bets win ($28 win on the 6/8, then a $14 win on the 5/6/8/9, for a total of $42 win), and then the shooter sevens-out for a win on the don’t pass odds.
    • The worst situation is that the shooter hits a lot of point numbers, which will lose $60 per point. Some losses are offset by early place bet wins (especially if the point is one of those place numbers), but once two bets win on the shooter, we no longer make the place bets and will net lose $60 per point.

    These situations show up when looking at the results per-shooter. The best win is $92, but wins in the $80-$92 range happen about 15% of the time. The most common outcome is a small win or loss (-$20 to $40). While less common overall, the bigger losses can be huge, with the worst 1% being a $208 loss. As with most dark-side strategies, the win chance for one shooter is above 50%, at 56.8%.

    In longer sessions (per-10-shooter or per-hour), the outcomes become more “normal” or bell-shaped. The negative skew still appears on a per-10-shooter basis, but the win chance decreases to 49.6%.

    Hedging will result in (1) increased house edge and (2) lower variability than making the bets separately. To point (1), the average loss per-10-shooter here is $15.15 or 4.4x that of the Don’t Pass strategy. Yet the variability of $181.42 is less than the total variability we would get when using the pass line, don’t pass, and some place bets combined.

    Overall, the strategy is interesting but carries a high house edge and the potential for big losses. The best case scenario are medium-length rolls that end in a seven-out. But the player may have to weather a hot table where most of the other players are winning big while they continue to lose their $60 odds bets.

    • Per shooter
    • Per 10 shooters
    • Per hour

    Per shooter

    Strategy metrics

    Average WinningsWin ChanceVariability
    −$1.4856.8%$57.36

    Session quantiles

    Worst 1%Worst 25%Mid 50%Best 25%Best 1%
    −$208.00−$18.00$2.00$24.00$92.00

    Resulting winnings after each simulated session

    Sample of 10 sessions

    Per 10 shooters

    Strategy metrics

    Average WinningsWin ChanceVariability
    −$15.1549.6%$181.42

    Session quantiles

    Worst 1%Worst 25%Mid 50%Best 25%Best 1%
    −$508.00−$126.00−$4.00$110.00$362.00

    Resulting winnings after each simulated session

    Sample of 10 sessions

    Per hour

    Strategy metrics

    Average WinningsWin ChanceVariability
    −$26.3946.2%$236.96

    Session quantiles

    Worst 1%Worst 25%Mid 50%Best 25%Best 1%
    −$596.00−$184.00−$22.00$136.00$508.00

    Resulting winnings after each simulated session

    Sample of 10 sessions

  • Iron Cross

    Strategy description

    A strategy designed to win on any roll that’s not a seven, once a point is established:

    • Bet the pass line for $10
    • Add 2x odds when the point is on
    • Place the 5 for $20 (two units)
    • Place the 6 and 8 for $24 each (two units)
    • If the point is 5, 6, or 8, skip the place bet on that number
    • Bet the field for $10 (when the point is on)

    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.

    Analysis

    The Iron Cross is designed to win on any number that isn’t a seven (when the point is on), and we can see this behavior in the per-shooter example session lines—the bankroll increases each roll until a seven-out, at which point the player loses the full outlay (up to $108 with a $10 unit). The amount won on non-seven rolls will vary (and depends on the point set), for example a 3 or 11 rolled only wins $10 on the field, but hitting a point of 4 would win $60 ($10 pass line, $40 odds, $10 field).

    Because there is a lot of betting, the average loss is very high at $5.91 per shooter, $58.42 per 10 shooters, and $101.51 per hour. For per-10-shooter sessions, this average loss is over 16x a Pass Line strategy with the same betting unit. For the same reason, there is a lot of variability compared to other strategies with only one bet.

    When budgeting per-shooter, the quantiles and histogram indicate that the strategy can very likely result in moderate losses but also carry potential for huge wins. The losses are capped, but one seven wipes out the entire outlay; players are hoping for a long roll to build up the winnings before that happens. It’s also worth noting that the middle 50% of winnings (thought of as an average session in some sense) has losses much worse than the average winnings (-$36 vs -$5.91 for one shooter; -$92 vs -$58.42 for ten shooters). This typically means your average session is going to feel worse than the edge from the combined bets dictates, and overall you’re hoping for a huge win in the top 10-20% of luck or better.

    • Per shooter
    • Per 10 shooters
    • Per hour

    Per shooter

    Strategy metrics

    Average WinningsWin ChanceVariability
    −$5.9134.4%$100.31

    Session quantiles

    Worst 1%Worst 25%Mid 50%Best 25%Best 1%
    −$108.00−$74.00−$36.00$32.00$358.00

    Resulting winnings after each simulated session

    Sample of 10 sessions

    Per 10 shooters

    Strategy metrics

    Average WinningsWin ChanceVariability
    −$58.4238.7%$316.90

    Session quantiles

    Worst 1%Worst 25%Mid 50%Best 25%Best 1%
    −$646.00−$286.00−$92.00$132.00$824.00

    Resulting winnings after each simulated session

    Sample of 10 sessions

    Per hour

    Strategy metrics

    Average WinningsWin ChanceVariability
    −$101.5141.1%$436.12

    Session quantiles

    Worst 1%Worst 25%Mid 50%Best 25%Best 1%
    −$1,130.00−$394.00−$98.00$196.00$892.00

    Resulting winnings after each simulated session

    Sample of 10 sessions

  • Place Inside

    Strategy description

    Bet all of the inside place numbers (5, 6, 8, 9), with $10 on the 5/9, and $12 on the 6/8. The bets are kept active only when the point is on, and no bets are active during the come-out rolls. Total outlay is $44 per shooter. Note that each place number rolled will win $14.

    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.

    Analysis

    Looking at sample sessions per-shooter gives a good sense for how the strategy flows: the worst outcomes are when a quick point then seven-out happens, and the entire $44 dollar outlay is wiped out; however, when the shooter goes on a long roll, the winnings will start to offset the betting costs, and could be upwards of $166 (in the luckiest 1% of sessions). This trend continues for 10 shooter sessions, but starts to average out where the luckiest 1% of sessions would win $400 and the unluckiest 1% of sessions would lose $300—a proportionally less wide of a gap. Win chance is relatively low for one shooter (31.6%), but increases for 10 shooters (40.5%), showing a similar trend.

    The strategy consists of some low house edge bets (placing 6/8, 1.52% per bet) and some medium house edge bets (placing 5/9, 4.00% per bet). All together, the average loss is about $19.79 per 10 shooters or $34.36 per hour. For reference, that’s over 5.7 times the average loss of a Pass Line strategy, and the bet’s aren’t even active for all rolls in the session.

    A couple of other interesting points:

    • For one shooter, the chance of a seven-out before winning any bets is 25% (six ways to roll a 7, eighteen ways to roll 5, 6, 8, or 9, so the odds are 1:3, and the probability is 1 out of 4). You can see this in the histogram, where the relative chance of winnings between -$50 and -$40 is 25%, consisting only of the $44 loss when no place bets hit.
    • From there, the height of the bars in the histogram follow a nice descending pattern, representing a geometric distribution, i.e. the number of winning place bets before a seven-out. We can see this pattern because the place bet win ($14) is larger than the width of the bars ($10).
    • The restricted winning amount ($14) and fixed outlay ($44) also causes the strange bumps in the per-10-shooter and per-hour histograms—if we were to have the bar width at $1, the pattern would look much smoother.
    • Per shooter
    • Per 10 shooters
    • Per hour

    Per shooter

    Strategy metrics

    Average WinningsWin ChanceVariability
    −$2.0431.6%$48.51

    Session quantiles

    Worst 1%Worst 25%Mid 50%Best 25%Best 1%
    −$44.00−$44.00−$16.00$12.00$166.00

    Resulting winnings after each simulated session

    Sample of 10 sessions

    Per 10 shooters

    Strategy metrics

    Average WinningsWin ChanceVariability
    −$19.7940.5%$153.37

    Session quantiles

    Worst 1%Worst 25%Mid 50%Best 25%Best 1%
    −$300.00−$132.00−$34.00$78.00$400.00

    Resulting winnings after each simulated session

    Sample of 10 sessions

    Per hour

    Strategy metrics

    Average WinningsWin ChanceVariability
    −$34.3643.5%$208.26

    Session quantiles

    Worst 1%Worst 25%Mid 50%Best 25%Best 1%
    −$524.00−$176.00−$34.00$108.00$442.00

    Resulting winnings after each simulated session

    Sample of 10 sessions

  • Don’t Pass

    Strategy description

    The fundamental dark side strategy, sans odds. Bet the Don’t Pass line for $10 and replace it any time the bet is resolved. The Don’t Pass bet will win on 2 or 3, lose on 7 or 11, and push on 12 before a point is set. Any other number rolled sets the point, and the bet wins on a 7 happening before that point number rolling again. No odds are included in this page.

    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.

    Analysis

    As the don’t pass bet has one of the lowest house edges, the strategy has a reasonable average loss of $0.34 per $10 unit per shooter, or about a $6.05 loss per $10 unit per hour. The average loss is one of the best for any strategy that has continuous betting, but most craps plays don’t want to play just one bet at a time.

    In many ways, the Don’t Pass operates in the opposite way as the Pass Line strategy. When sessions are measured per shooter, the win rate is above 50%—it’s 61.1% per shooter or 51.3% per 10 shooters. This seems strange at first, because the don’t pass bet is not a winning bet by itself; however, the “win rate” includes half of the ties (which account for 23.8% of the per-shooter results and 8.0% of the per-10-shooter results). This phenomenon is discussed in more detail in One Surprising Feature of Dark Side Betting. However, on a per hour basis, the win rate is more reflective of the underlying house edge of the don’t pass bet, at 46.9%.

    To balance out the higher win chance (consisting of smaller wins), Don’t Pass offers has potentially high downside (large losses). Budgeting for 10 shooters, the worst 1% of sessions is a $140 loss, but the best 1% is only a $90 win. As seen in the sample sessions, the big wins tend to be quicker (fast seven-outs) while the big losses are when several shooters go on long runs of hitting points, which require replacing the don’t pass bet. If instead you play on a time-at-the-table basis, the winnings distribution is much closer to a normal distribution with more balanced high and low sessions (Worst 25% = $50 loss, Best 25% = $40 win).

    In terms of variability, the per-shooter variability is about 1.5x that of a $10 coin-flip, which is not surprising given that several $10 bets could happen on one shooter.

    • Per shooter
    • Per 10 shooters
    • Per hour

    Per shooter

    Strategy metrics

    Average WinningsWin ChanceVariability
    −$0.3461.1%$15.90

    Session quantiles

    Worst 1%Worst 25%Mid 50%Best 25%Best 1%
    −$60.00−$10.00$0.00$10.00$20.00

    Resulting winnings after each simulated session

    Sample of 10 sessions

    Per 10 shooters

    Strategy metrics

    Average WinningsWin ChanceVariability
    −$3.4651.3%$50.25

    Session quantiles

    Worst 1%Worst 25%Mid 50%Best 25%Best 1%
    −$140.00−$30.00$0.00$30.00$90.00

    Resulting winnings after each simulated session

    Sample of 10 sessions

    Per hour

    Strategy metrics

    Average WinningsWin ChanceVariability
    −$6.0546.9%$65.45

    Session quantiles

    Worst 1%Worst 25%Mid 50%Best 25%Best 1%
    −$160.00−$50.00−$10.00$40.00$140.00

    Resulting winnings after each simulated session

    Sample of 10 sessions

  • Pass Line

    Strategy description

    The first strategy that most people start with. This one is simple, bet the pass line for $10 and replace it any time the bet is resolved. No odds are included in this page. For a detailed explanation of the pass line bet, see All Bets Are Off: Re-learning the Pass Line Bet in Craps.

    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.

    Analysis

    The low house edge of the pass line bet shows up in this strategy, it’s quite reasonable at an average loss of $0.36 per $10 unit per shooter. If a simple strategy like this can keep you entertained, the cost of entertainment is low compared to many other hobbies (but let’s be realistic, few people play only pass line bets, and minimums are often higher than $10).

    As with many light-side betting strategies in craps, the pass line strategy has a relatively low win chance, just under 40% per shooter or about 43% per 10 shooters. (Side note, it’s counterintuitive that the win chance goes up with more play. Eventually this number does go down, as I’ve explored in this post: One Surprising Feature of Dark Side Betting).

    To balance the slightly low win chance, pass line offers the possibility of big wins with lowered downside. Budgeting for 10 shooters, the worst 1% of sessions is a $100 loss, but the best 1% was a $130 win. Even with only 1 shooter, the best 1% of sessions was a $60 win, though eventually the high likelihood seven-outs will catch up to you.

    If you play on a time-at-the-table basis, the average loss is $6.18 per hour and the winnings distribution is much closer to a normal distribution. Compared with a per-shooter basis, a few quick seven-outs by the shooters won’t completely stop the session, but the potential losses are not as constrained.

    • Per shooter
    • Per 10 shooters
    • Per hour

    Per shooter

    Strategy metrics

    Average WinningsWin ChanceVariability
    −$0.3637.5%$15.68

    Session quantiles

    Worst 1%Worst 25%Mid 50%Best 25%Best 1%
    −$20.00−$10.00−$10.00$10.00$60.00

    Resulting winnings after each simulated session

    Sample of 10 sessions

    Per 10 shooters

    Strategy metrics

    Average WinningsWin ChanceVariability
    −$3.5643.3%$49.55

    Session quantiles

    Worst 1%Worst 25%Mid 50%Best 25%Best 1%
    −$100.00−$40.00−$10.00$30.00$130.00

    Resulting winnings after each simulated session

    Sample of 10 sessions

    Per hour

    Strategy metrics

    Average WinningsWin ChanceVariability
    −$6.1846.0%$65.51

    Session quantiles

    Worst 1%Worst 25%Mid 50%Best 25%Best 1%
    −$160.00−$50.00−$10.00$40.00$150.00

    Resulting winnings after each simulated session

    Sample of 10 sessions