The Craps Analyst

Tag: Light side

  • 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

  • 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

  • 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