Expected loss per hour

Question, gentlemen. I am trying to figure out my expected loss. I have a rough guess as to my expected loss, but I won't out out my guess.

What is my expected loss per hour if I am betting $5 on the pass, with $5 come bets, until there are two come bets up at all times, but never more than two come bets up, and then if a come bet hits, I put up another come bet? No put bets, so if there is as seven out, I just bet pass, and after the point, make a come bet, and then a second come bet (assuming no winner or seven out by the second come bet).

Does anyone know the exact math behind this question? I think that someone has been able to determine the avg number of hands per hour, and the average number of new pass bets per hour, and average number of come bets to put up two come bets at all times. I'm not looking for an eyeball estimate, but a quantitative analysis of my expected loss.

I am asking for a quantitative analysis, so please don't say something like, 'the EV isn't important because it's hard for two numbers to roll, come bets are for suckers', etc.

I just prepped my trip to NM, and my trip to NM, where I expect to have less than $10 in expected loss, would have more costs due to travel and hotel, than if I went to my local Midwest casino, where food and room, for a fact, would be free, but I would play pass with two some bets, so I would have a higher expected loss than going to NM. when I get back from NM, I will itemize all my NM costs.

Depends on whether you are taking odds and how much odds. I've run simulations of this betting style and assuming 110 rolls per hour (a number derived from the Wizard's Craps pages), and taking max 3-4-5 odds, the average loss per hour for 100,000 sessions of play was $4.84. This was with odds not working on the come-out. The simulation also assumed you'd start play with $200 and leave the table under these conditions when a new shooter gets the dice:
- down $150 or more
- up $250 or more
- been at the table for 5 or more hours
- been within $50 of winning the $250 but down from that peak amount by $50 or more

All of these factors can be varied and other simulations run, if you want to provide the criteria.

What program do you use to run the sim? I have a few senerios that I would like to see how they play out on a sim program. I'd love to take a look at whatever program you used.

Thanks cowboy, thats good news. $4.84 an hour sounds lower than I thought. I'm my head, I thought my expected loss was closer to $8-$5 an hour. But $4.84 an hour sounds right.

Quote: cowboy

Depends on whether you are taking odds and how much odds.

No it doesn't -- he's asking about expected loss, and odds bets have no expected loss.

The way to determine the answer is to derive the following:
a) The expected loss per roll of a $5 line bet;
b) The average number of simultaneous line bets (on any given roll) given the stated strategy; and
c) The expected rolls per hour.
Then multiply.

B is the interesting part (because A and C are known). You always have one line bet working, but you can have up to three. You need to find the percentage of the time you'll have 1, 2, and 3 bets up.

For one point, your expected loss is 0.42% of $5 per roll or $0.02 per roll.

The WORST case for n points is 0.02 per roll multiplied by the number of points you will cover.

On average, the number of points covered if you bet the come until you have a certain number of points covered is less than half the max number of points covered.

I have the exact numbers and I went into this in a separate thread.

I also have charts and simulations to help you understand these expected losses. You can just run the sim for 100,000 throws of the dice and look at the slope of the line. There's very little volatility. I can also set the RSR to 6.0 in my random number sim to help see the longer term expectations without having to worry so much about doing so many simulations to get the RSR to hit closer to 6.

details for number of points covered on average for maximum come bets.

If you look at that and take the average number of points covered it might help you understand expected losses for various numbers of come bets.

If your goal is to maximize the average number of free bets, there's a point of diminishing returns that you can see after covering 3 points .. your frequency of being paid (your action) increases, but your average number of working odds bets does not.

On an average speed craps game (I have no idea how to quanitfy 'average'), do you have any idea how many rolls per hour, MExtremist? Im guessing 3 rolls a minute for 180 rolls an hour?

I should state that im trying to figure out my hourly loss.

I will compare all my costs of going to NM vs my costs of playing $5 pass line with two come bets, at a casino that is closer to me. At my local casino, the drive is shorter, and the hotel and food is always comped. So I'm wondering if it's better to just give the house their share of the pass and come bets than it is to go to NM.

Quote: klimate10

Does anyone know the exact math behind this question?

There's no "easy" way to solve this (well, besides with simulations/Monte Carlo methods), as you can get into loops - for example, if your come-out roll is a 4, then you roll a 5, then you roll another 5, you are back in the position you were after your come-out roll (your only bet in play is a point of 4).

Here's an example of what I mean - let P(a) be the result if your only point is a, P(a,b) if you have two separate points (a and b) in play, and P(a,b,c) if you have three (a,b,c) in play, which is the maximum under your conditions.

There are six sets of P(a), fifteen of P(a,b) and twenty of P(a,b,c) that need to be computed, and note that you will come across cases where two sets reference each other.

Here's some results from a sim. I post more about this later and this post was edited for correctness.

Quote: simulator

1 max lines with 0.70 odds bets on average and 1.00 average number of line bets
percentage of n-odds working 29.722% 70.278%
2 max lines with 1.20 odds bets on average and 1.76 average number of line bets
percentage of n-odds working 24.413% 31.541% 44.046%
3 max lines with 1.50 odds bets on average and 2.26 average number of line bets
percentage of n-odds working 23.728% 26.207% 26.771% 23.294%
4 max lines with 1.64 odds bets on average and 2.55 average number of line bets
percentage of n-odds working 23.605% 25.358% 23.883% 17.715% 9.440%
5 max lines with 1.69 odds bets on average and 2.66 average number of line bets
percentage of n-odds working 23.583% 25.221% 23.507% 16.902% 8.297% 2.490%
6 max lines with 1.69 odds bets on average and 2.69 average number of line bets
percentage of n-odds working 23.584% 25.213% 23.479% 16.836% 8.190% 2.392% 0.306%
7 max lines with 1.69 odds bets on average and 2.69 average number of line bets
percentage of n-odds working 23.584% 25.213% 23.479% 16.836% 8.190% 2.392% 0.306%

in reply to ThatDon'tGuy:- which is exactly why the best way you can find this out is to run a simulation. I suppose someone could take a shot at doing it computationally, but as you say, the interwoven possibilities - even for a max of 3 working bets make it extremely difficult - try it for 7 working bets!

Mikey75 the simulation program is something I wrote myself since it was a nice combination of two hobbies of mine - programming and gambling.

I'm not sure about MathExtremist's claim that the odds don't matter. If I run the same simulation with taking single odds ($5-$6-$5) then the hourly loss becomes $5.55 - the difference being that using the boundary conditions i.e. 110 rolls per hour, and:

Quote:

This was with odds not working on the come-out. The simulation also assumed you'd start play with $200 and leave the table under these conditions when a new shooter gets the dice:
- down $150 or more
- up $250 or more
- been at the table for 5 or more hours
- been within $50 of winning the $250 but down from that peak amount by $50 or more

...you'll be at the table much longer. With max odds, the conditions above are met one way or the other on average in 91 rolls but with single odds the conditions are met one way or the other on average in 351 rolls. Now of course that could be due to the fact you play longer and only lose overall on the bets the house has an edge on.

I'll have to alter the simulation to compare the two on the same "playing field", so to speak.

Quote: klimate10

On an average speed craps game (I have no idea how to quanitfy 'average'), do you have any idea how many rolls per hour, MExtremist? Im guessing 3 rolls a minute for 180 rolls an hour?

I derived my figure of 110 rolls per hour from here:

https://wizardofodds.com/ask-the-wizard/136/

I actually used to play this exact way and keep track of how many come bets I made. It was something like 82/hour. This was on a moderately crowded table with okay dealers. So figure an expected loss of $5.78/hour. Really, the difference between playing this way and making a come bet every roll (the way I play now) is very small.

Quote: ThatDonGuy

There's no "easy" way to solve this (well, besides with simulations/Monte Carlo methods),

It's not nearly that complicated.
You'll always have at least one line bet working, but from that you can subtract the percentage of the time you have at least two. When do you have at least two line bets working? If your first bet got past the come-out roll. That's 2/3 of the time, so you have exactly 1 bet up 1/3 of the time. For 2 bets, same idea: you have 2 bets up 2/3 of the time, but from that you subtract the percentage you have 3 bets. There are six possibilities for the first point, so only five for the second -- but only three distinct probabilities. Remember that if you have two points established, you've satisfied the "three bets" criterion. Whether the third bet has traveled yet or not is immaterial to the analysis.

The net result is about 2.13 avg. bets per roll, times about 2.1c/roll per $5 bet, times 100 rolls/hour (est'd) = $4.47 expected loss/hour. The real factor is table speed, which is highly variable based on many factors (e.g., number of players, complexity of their betting patterns, interactions with dealers, etc.), but generally speaking the finding is this:

On average, playing the Three Point Molly costs the player around one bet per hour.

Quote: MathExtremist

The net result is about 2.13 avg. bets per roll, times about 2.1c/roll per $5 bet, times 100 rolls/hour (est'd) = $4.47 expected loss/hour.

Or at 110 rolls per hour, you get 1.1 x $4.47 = $4.92 compared with the $4.84 result from simulation.

Multiplying by the average number of line bets depending on your maximum total come bets to get your total cost for various numbers of maximum pass/come bets of one through seven.

1.0, 1.76, 2.27, 2.55, 2.67, 2.69, and 2.70

You're pretty much limited to 2.7x the cost for a single pass line bet even if you bet the come bet on every single roll, and if you're going to have up to 4 come bets per roll you might as well go all the way in terms of the cost. Those last three come bets only add 5.5% to your average cost per roll compared to stopping with 4 come bets.

The big difference in getting what you "pay" for is making sure you work the odds on the comeout, and the percentage of comeout rolls is almost 30% of all rolls. The whole point of paying the edge on the low volatility of a come bet every roll is to get the variance and chance to win from the free odds. You absolutely have very little chance to win in the long run from betting a come bet every roll because of the low volatility.

1 max lines with 0.70 odds bets on average and 1.00 average number of line bets
percentage of n-odds working 29.597% 70.403%
2 max lines with 1.20 odds bets on average and 1.76 average number of line bets
percentage of n-odds working 24.311% 31.473% 44.216%
3 max lines with 1.50 odds bets on average and 2.27 average number of line bets
percentage of n-odds working 23.607% 26.213% 26.808% 23.372%
4 max lines with 1.64 odds bets on average and 2.55 average number of line bets
percentage of n-odds working 23.492% 25.355% 23.941% 17.720% 9.493%
5 max lines with 1.69 odds bets on average and 2.67 average number of line bets
percentage of n-odds working 23.476% 25.225% 23.511% 16.896% 8.368% 2.524%
6 max lines with 1.70 odds bets on average and 2.69 average number of line bets
percentage of n-odds working 23.474% 25.213% 23.474% 16.822% 8.267% 2.428% 0.322%
7 max lines with 1.70 odds bets on average and 2.70 average number of line bets
percentage of n-odds working 23.474% 25.213% 23.474% 16.822% 8.267% 2.428% 0.322%

Quote: Ahigh

1 max lines with 0.70 odds bets on average and 1.00 average number of line bets
percentage of n-odds working 29.722% 70.278%

Shouldn't that be 33.333% and 66.667%? If you're running simulations, I'd run them for long enough to get your one-bet numbers to match the theoretical. Also, use the Mersenne Twister instead of rand():
http://search.cpan.org/~fangly/Math-Random-MT-1.16/MT.pm

Quote: MathExtremist

Shouldn't that be 33.333% and 66.667%? If you're running simulations, I'd run them for long enough to get your one-bet numbers to match the theoretical. Also, use the Mersenne Twister instead of rand():
http://search.cpan.org/~fangly/Math-Random-MT-1.16/MT.pm

No, I think 29.722% is closer to right than 33.33%. 16.67% of the rolls are right after a seven, and the remaing percentage of comeout rolls are when you have two or more comeout rolls in a row (the naturals winners and losers) and after making your point.

post about what percentage of rolls are comeout rolls

Thanks for the link about the random number generator, but I'm happy with just getting close answers, and I provided the code I wrote to allow someone else to take it further if they wanted to or to fix bugs if they found them.

I think the answer you needed has been put up...

I had a wonderful time last night reading your RT report to Santa Anna in NM. There you won about $19,000 plus all those comps (<envy>).
I guess, why are you changing your betting strategy given your previous experience?

Jeffrey

Im not changing my strategy. Im trying to see if it really is cheaper to play craps in NM, or in my local casino.

Thanks, I appreciate your kind words.

Anyone know of a decent simulator for craps? I have some ideas I'd like to run through one.

This let's you visualize the long-term cost of covering various numbers of points and reflects visually the average number of line bets in action for the various number of points chosen to be covered.



And even more interesting that a crapless table with a single passline bet costs more to play that craps betting the come bet at every opportunity. Then look at crapless with come bet every roll compared to regular craps with come bet every roll.



The "ls" in the chart is an option that puts my simulator into crapless craps mode. "w" means work odds on the comeout, so it has no effect at 0x, just fyi.

Crapless craps is 1.2% per roll instead of 0.42% so it's a little less than 3x as expensive per roll compared to craps, and craps with a come bet every roll is only 2.7x as expensive as just a come bet by itself. So a single unit on crapless is about the same cost as a come bet every roll on regular craps. You can see the white line from 1p on crapless among the 4p,5p,6p lines from craps.

A come bet on every roll in crapless gets pretty expensive, though, as you can see since you can have a whole lot more numbers covered.

Then once you put 10x in there OMG! Hard to see those edge lines as the 10x totally overpowers everything!!!

As a result of this thread, I've spent a bunch of time crunching costs, and I have arrived at the conclusion that working your odds on the comeout is a critical component to getting the best possible edge per roll. Especially if you are rolling a higher RSR. You never want to roll a seven unless you have no working bets. Ideally that's a rare situation.

Anyway, I've learned a lot looking at how turning off your odds bets on the comeout makes it harder to overcome the house edge. This simple fact makes it a huge advantage to only bet a single number as you never have opportunity for odds on the comeout if you never bet the come. So that's a simple approach too if you can handle the boredom.

But I would like to thank the original poster for asking these questions which prompted me to wring out my simulator. I had a couple of bugs in crapless mode that got fixed to match up the work I did in excel to come up with edge per roll at 1.2% on crapless.

But there is a bottom line and that is that if you don't work odds on the comeout, be careful betting 3 or 4 numbers at once as it's easier to lose since you're not having a proper chance to get lucky winning odds on the comeout roll. Much easier to bet one number, and two you can still be alright, but 3, 4, or more come bets and not working the odds on the comeout and/or with not enough odds can be deadly!

Quote: klimate10

Question, gentlemen. I am trying to figure out my expected loss. I have a rough guess as to my expected loss, but I won't out out my guess.

Its simple: Amount Bet multiplied by House Edge.

Quote: klimate10

Does anyone know the exact math behind this question? I think that someone has been able to determine the avg number of hands per hour, and the average number of new pass bets per hour, and average number of come bets to put up two come bets at all times. I'm not looking for an eyeball estimate, but a quantitative analysis of my expected loss.

Such averages are estimates and are often rounded for easy mental math. Its like estimating the number of times a cocktail waitress will appear ... you have lots of figures available but the only one you will ever remember is 38-24-36... and it won't help you a bit, besides: 'the EV isn't important because it's hard for two numbers to roll and come bets are for suckers'.

And as for Rolls Per Minute... on a day boat out of Florida they keep the dice flying, downtown Vegas is fairly slow, The Strip is fairly fast. Local Casinos in Vegas are probably the slowest in Nevada.... but in New Mexico you will probably encounter "the manana effect". They go as slow as they feel like and you can take all your estimates based on Nevada and stuff it!! They will even say that to you ... but will wait to the next day to do so.

If you keep track of the actual rolls per minute you experience, please let us know... I think we will be laughing at the figure.

Good luck.

check out this page nearly all the way to the bottom. For craps it is 'hands'.

https://wizardofodds.com/gambling/house-edge/

I often find this page is what I am looking for too

https://wizardofodds.com/ask-the-wizard/136/

Quote: klimate10

What is my expected loss per hour if I am betting $5 on the pass, with $5 come bets, until there are two come bets up at all times, but never more than two come bets up, and then if a come bet hits, I put up another come bet? No put bets, so if there is as seven out, I just bet pass, and after the point, make a come bet, and then a second come bet (assuming no winner or seven out by the second come bet).

To give the exact equation for your very SPECIFIC question that still remains unanswered.

<average # line/come bets> * <edge per roll for pass line or come bet> * <expected number of rolls per hour> * <length of play in hours> * <bet amount per roll>

or for your specific instance:

1.76 * 0.0042 * <number of rolls> * $5

Here's output for the ratio of line bets to free bets that you can use to come up with a more accurate edge per roll than the Wizard's FAQ for both crapless and craps.

With one pass line bet and no other bets, it's an easy answer as it's just the percentage of rolls that are the comeout roll.

But this gives you the details for every possible "maximum number of line bets" for a strategy that goes from 1 to 7 for craps and 1 to 11 for crapless.

To figure out the combined edge, weight the edge per roll on the line (0.42% for craps and 1.2% for crapless) and the free bets according to the amount of odds. I think the Wizard assumes that you are getting the best deal by not betting any come bets, but the weighted average of free bets even working the comeout goes down as you make more come bets, and this shows the details of that.

CRAPS off on comeout
1 max lines with 0.70 odds bets on average and 1.00 average number of line bets (41.1868/58.8132)
percentage of n-odds working 29.970% 70.030%
2 max lines with 1.13 odds bets on average and 1.75 average number of line bets (39.2188/60.7812)
percentage of n-odds working 30.730% 25.535% 43.735%
3 max lines with 1.39 odds bets on average and 2.26 average number of line bets (38.0679/61.9321)
percentage of n-odds working 31.030% 22.460% 23.360% 23.150%
4 max lines with 1.50 odds bets on average and 2.53 average number of line bets (37.2256/62.7744)
percentage of n-odds working 31.355% 21.905% 21.230% 16.220% 9.290%
5 max lines with 1.54 odds bets on average and 2.65 average number of line bets (36.7695/63.2305)
percentage of n-odds working 31.455% 21.805% 20.915% 15.440% 7.860% 2.525%
6 max lines with 1.55 odds bets on average and 2.68 average number of line bets (36.6097/63.3903)
percentage of n-odds working 31.455% 21.800% 20.865% 15.390% 7.750% 2.400% 0.340%
7 max lines with 1.55 odds bets on average and 2.68 average number of line bets (36.5803/63.4197)
percentage of n-odds working 31.455% 21.800% 20.865% 15.390% 7.750% 2.400% 0.340%


CRAPS working the comeout
1 max lines with 0.70 odds bets on average and 1.00 average number of line bets (41.1868/58.8132)
percentage of n-odds working 29.970% 70.030%
2 max lines with 1.19 odds bets on average and 1.75 average number of line bets (40.4313/59.5687)
percentage of n-odds working 24.865% 31.400% 43.735%
3 max lines with 1.49 odds bets on average and 2.26 average number of line bets (39.7320/60.2680)
percentage of n-odds working 24.060% 26.345% 26.445% 23.150%
4 max lines with 1.63 odds bets on average and 2.53 average number of line bets (39.0924/60.9076)
percentage of n-odds working 23.975% 25.510% 23.795% 17.430% 9.290%
5 max lines with 1.67 odds bets on average and 2.65 average number of line bets (38.7246/61.2754)
percentage of n-odds working 23.920% 25.340% 23.375% 16.690% 8.150% 2.525%
6 max lines with 1.68 odds bets on average and 2.68 average number of line bets (38.5766/61.4234)
percentage of n-odds working 23.920% 25.325% 23.290% 16.605% 8.085% 2.435% 0.340%
7 max lines with 1.68 odds bets on average and 2.68 average number of line bets (38.5466/61.4534)
percentage of n-odds working 23.920% 25.325% 23.290% 16.605% 8.085% 2.435% 0.340%


CRAPLESS off on the comeout
1 max lines with 0.76 odds bets on average and 1.00 average number of line bets (43.1544/56.8456)
percentage of n-odds working 24.085% 75.915%
2 max lines with 1.30 odds bets on average and 1.81 average number of line bets (41.7670/58.2330)
percentage of n-odds working 24.540% 21.415% 54.045%
3 max lines with 1.68 odds bets on average and 2.42 average number of line bets (41.0017/58.9983)
percentage of n-odds working 24.830% 17.825% 21.880% 35.465%
4 max lines with 1.93 odds bets on average and 2.84 average number of line bets (40.4469/59.5531)
percentage of n-odds working 25.070% 17.420% 18.000% 18.510% 21.000%
5 max lines with 2.07 odds bets on average and 3.10 average number of line bets (40.0332/59.9668)
percentage of n-odds working 25.230% 17.365% 17.480% 15.735% 13.320% 10.870%
6 max lines with 2.14 odds bets on average and 3.25 average number of line bets (39.7204/60.2796)
percentage of n-odds working 25.280% 17.345% 17.350% 15.300% 12.130% 8.115% 4.480%
7 max lines with 2.17 odds bets on average and 3.31 average number of line bets (39.5723/60.4277)
percentage of n-odds working 25.275% 17.345% 17.315% 15.205% 11.945% 7.740% 3.710% 1.465%
8 max lines with 2.17 odds bets on average and 3.33 average number of line bets (39.5026/60.4974)
percentage of n-odds working 25.295% 17.345% 17.310% 15.155% 11.890% 7.745% 3.655% 1.260% 0.345%
9 max lines with 2.17 odds bets on average and 3.33 average number of line bets (39.4845/60.5155)
percentage of n-odds working 25.295% 17.345% 17.310% 15.150% 11.880% 7.745% 3.655% 1.245% 0.320% 0.055%
10 max lines with 2.17 odds bets on average and 3.33 average number of line bets (39.4805/60.5195)
percentage of n-odds working 25.295% 17.345% 17.310% 15.150% 11.880% 7.745% 3.655% 1.245% 0.320% 0.055%
11 max lines with 2.17 odds bets on average and 3.33 average number of line bets (39.4805/60.5195)
percentage of n-odds working 25.295% 17.345% 17.310% 15.150% 11.880% 7.745% 3.655% 1.245% 0.320% 0.055%


CRAPLESS working the comeout
1 max lines with 0.76 odds bets on average and 1.00 average number of line bets (43.1544/56.8456)
percentage of n-odds working 24.085% 75.915%
2 max lines with 1.35 odds bets on average and 1.81 average number of line bets (42.7094/57.2906)
percentage of n-odds working 19.440% 26.515% 54.045%
3 max lines with 1.77 odds bets on average and 2.42 average number of line bets (42.2968/57.7032)
percentage of n-odds working 18.865% 20.560% 25.110% 35.465%
4 max lines with 2.05 odds bets on average and 2.84 average number of line bets (41.9254/58.0746)
percentage of n-odds working 18.810% 19.630% 20.215% 20.345% 21.000%
5 max lines with 2.21 odds bets on average and 3.10 average number of line bets (41.6151/58.3849)
percentage of n-odds working 18.800% 19.505% 19.405% 17.165% 14.255% 10.870%
6 max lines with 2.29 odds bets on average and 3.25 average number of line bets (41.3755/58.6245)
percentage of n-odds working 18.780% 19.465% 19.180% 16.545% 12.965% 8.585% 4.480%
7 max lines with 2.32 odds bets on average and 3.31 average number of line bets (41.2479/58.7521)
percentage of n-odds working 18.780% 19.445% 19.140% 16.405% 12.695% 8.200% 3.870% 1.465%
8 max lines with 2.33 odds bets on average and 3.33 average number of line bets (41.1918/58.8082)
percentage of n-odds working 18.780% 19.445% 19.135% 16.350% 12.645% 8.190% 3.805% 1.305% 0.345%
9 max lines with 2.33 odds bets on average and 3.33 average number of line bets (41.1760/58.8240)
percentage of n-odds working 18.780% 19.445% 19.130% 16.345% 12.635% 8.190% 3.800% 1.295% 0.325% 0.055%
10 max lines with 2.33 odds bets on average and 3.33 average number of line bets (41.1720/58.8280)
percentage of n-odds working 18.780% 19.445% 19.130% 16.345% 12.635% 8.190% 3.800% 1.295% 0.325% 0.055%
11 max lines with 2.33 odds bets on average and 3.33 average number of line bets (41.1720/58.8280)
percentage of n-odds working 18.780% 19.445% 19.130% 16.345% 12.635% 8.190% 3.800% 1.295% 0.325% 0.055%
c w ln
0 0 1 1x 0.2470 2x 0.1750 3x 0.1354 4x 0.1105 5x 0.0933 10x 0.0525 20x 0.0280 100x 0.0059
0 0 2 1x 0.2553 2x 0.1834 3x 0.1431 4x 0.1173 5x 0.0994 10x 0.0564 20x 0.0302 100x 0.0064
0 0 3 1x 0.2601 2x 0.1884 3x 0.1477 4x 0.1214 5x 0.1031 10x 0.0588 20x 0.0316 100x 0.0067
0 0 4 1x 0.2637 2x 0.1921 3x 0.1511 4x 0.1246 5x 0.1059 10x 0.0606 20x 0.0327 100x 0.0070
0 0 5 1x 0.2656 2x 0.1942 3x 0.1530 4x 0.1263 5x 0.1075 10x 0.0616 20x 0.0333 100x 0.0071
0 0 6 1x 0.2662 2x 0.1949 3x 0.1537 4x 0.1269 5x 0.1080 10x 0.0620 20x 0.0335 100x 0.0071
0 0 7 1x 0.2664 2x 0.1950 3x 0.1538 4x 0.1270 5x 0.1081 10x 0.0621 20x 0.0335 100x 0.0072
0 1 1 1x 0.2470 2x 0.1750 3x 0.1354 4x 0.1105 5x 0.0933 10x 0.0525 20x 0.0280 100x 0.0059
0 1 2 1x 0.2502 2x 0.1782 3x 0.1383 4x 0.1131 5x 0.0956 10x 0.0539 20x 0.0288 100x 0.0061
0 1 3 1x 0.2531 2x 0.1812 3x 0.1410 4x 0.1155 5x 0.0978 10x 0.0553 20x 0.0296 100x 0.0063
0 1 4 1x 0.2558 2x 0.1839 3x 0.1436 4x 0.1177 5x 0.0998 10x 0.0566 20x 0.0304 100x 0.0064
0 1 5 1x 0.2574 2x 0.1855 3x 0.1450 4x 0.1191 5x 0.1010 10x 0.0574 20x 0.0308 100x 0.0065
0 1 6 1x 0.2580 2x 0.1862 3x 0.1456 4x 0.1196 5x 0.1014 10x 0.0577 20x 0.0310 100x 0.0066
0 1 7 1x 0.2581 2x 0.1863 3x 0.1457 4x 0.1197 5x 0.1015 10x 0.0578 20x 0.0310 100x 0.0066
1 0 1 1x 0.7352 2x 0.5136 3x 0.3946 4x 0.3204 5x 0.2697 10x 0.1505 20x 0.0799 100x 0.0168
1 0 2 1x 0.7532 2x 0.5313 3x 0.4104 4x 0.3343 5x 0.2820 10x 0.1583 20x 0.0843 100x 0.0178
1 0 3 1x 0.7631 2x 0.5412 3x 0.4193 4x 0.3422 5x 0.2890 10x 0.1627 20x 0.0868 100x 0.0183
1 0 4 1x 0.7703 2x 0.5484 3x 0.4258 4x 0.3480 5x 0.2942 10x 0.1660 20x 0.0887 100x 0.0188
1 0 5 1x 0.7756 2x 0.5539 3x 0.4307 4x 0.3524 5x 0.2982 10x 0.1685 20x 0.0901 100x 0.0191
1 0 6 1x 0.7796 2x 0.5580 3x 0.4345 4x 0.3557 5x 0.3012 10x 0.1704 20x 0.0912 100x 0.0193
1 0 7 1x 0.7816 2x 0.5600 3x 0.4363 4x 0.3573 5x 0.3026 10x 0.1713 20x 0.0917 100x 0.0195
1 0 8 1x 0.7825 2x 0.5609 3x 0.4371 4x 0.3581 5x 0.3033 10x 0.1718 20x 0.0920 100x 0.0195
1 0 9 1x 0.7827 2x 0.5611 3x 0.4373 4x 0.3583 5x 0.3034 10x 0.1719 20x 0.0921 100x 0.0195
1 0 10 1x 0.7828 2x 0.5612 3x 0.4374 4x 0.3583 5x 0.3035 10x 0.1719 20x 0.0921 100x 0.0195
1 0 11 1x 0.7828 2x 0.5612 3x 0.4374 4x 0.3583 5x 0.3035 10x 0.1719 20x 0.0921 100x 0.0195
1 1 1 1x 0.7352 2x 0.5136 3x 0.3946 4x 0.3204 5x 0.2697 10x 0.1505 20x 0.0799 100x 0.0168
1 1 2 1x 0.7410 2x 0.5192 3x 0.3996 4x 0.3248 5x 0.2736 10x 0.1530 20x 0.0813 100x 0.0171
1 1 3 1x 0.7463 2x 0.5245 3x 0.4043 4x 0.3289 5x 0.2773 10x 0.1553 20x 0.0826 100x 0.0174
1 1 4 1x 0.7511 2x 0.5292 3x 0.4086 4x 0.3327 5x 0.2806 10x 0.1574 20x 0.0838 100x 0.0177
1 1 5 1x 0.7551 2x 0.5332 3x 0.4121 4x 0.3359 5x 0.2834 10x 0.1591 20x 0.0848 100x 0.0179
1 1 6 1x 0.7582 2x 0.5363 3x 0.4149 4x 0.3383 5x 0.2856 10x 0.1605 20x 0.0856 100x 0.0181
1 1 7 1x 0.7599 2x 0.5380 3x 0.4164 4x 0.3396 5x 0.2868 10x 0.1613 20x 0.0860 100x 0.0182
1 1 8 1x 0.7606 2x 0.5387 3x 0.4170 4x 0.3402 5x 0.2873 10x 0.1616 20x 0.0862 100x 0.0182
1 1 9 1x 0.7608 2x 0.5389 3x 0.4172 4x 0.3404 5x 0.2874 10x 0.1617 20x 0.0862 100x 0.0182
1 1 10 1x 0.7609 2x 0.5390 3x 0.4173 4x 0.3404 5x 0.2875 10x 0.1617 20x 0.0862 100x 0.0182
1 1 11 1x 0.7609 2x 0.5390 3x 0.4173 4x 0.3404 5x 0.2875 10x 0.1617 20x 0.0862 100x 0.0182

The edge per roll on crapless is 2.85x as much on the pass line compared to regular craps. So in general for crapless to get as good of an edge you need to take double or triple the amount of odds you would normally take on a regular craps table.

I think this is about right. There's not much analysis on crapless, but if you pump up big odds (IE: you have the bankroll for it), the edge is not that bad really.

The other thing that's not so obvious is that the 57.6894% number above if you bet the come bet every roll and turn your odds off on the comeout, you're giving up a good deal!

The other numbers to compare on crapless versus craps is to limit the number of rolls with no odds bets working. You can see that in craps you can get the number of rolls with no odds bets available down to 18.625% where as in craps you can only get it down to 23.482%

That a reduction of 20% of the rolls (234 out of every 1000 down to 186 out of every 10000) where you don't have a chance to have a working come bet in craps. Having working come bets is the method, in general, of getting paid from an edge resulting from rolling fewer sevens with your shot. IE: in regular craps, 24% or more of your rolls that you make have no opportunity to make money because you have no odds bets. You need the odds bets to make money with a lower RSR until your RSR gets ridiculously/unrealistically high.

The other thing to notice is that you get it down that low with just a couple of come bets! You don't have to bet the come every roll on crapless to have at least one come bet working for a much higher percentage of rolls giving you a great chance to win from any non-seven repeater you can muster!

Increasing the frequency of opportunity for working come bets is just as important to exploit a controlled shot as reducing the size of the hurdle to something you can overcome.

Here is my table for the house edge per roll in regular craps. I've never done it for Crapless Craps.

Quote: Wizard

Here is my table for the house edge per roll in regular craps.

Most useful. It assumes sixty rolls which is reasonable in Las Vegas but woefully inadequate on those Florida day boats. As for The Land of Disenchantman (New Mexico) where the original poster in this thread is bound, I've not been there but have heard that everything is too slow down there.

Will be interesting to get the straight dope on it though since my source loathed every minute of his two years in New Mexico.

This is the only really difficult bet to calculate the edge per roll on in craps is the pass line.

I did the work here.

https://wizardofvegas.com/forum/gambling/craps/13414-crapless-craps-revisited/#post228642



Please feel free to update edge per bet and per roll for crapless.

Also, the fact that the pass line lasts longer in crapless makes the edge per roll a smaller multiple (2.85x) than the edge per bet resolved (3.817x).

The edge per roll when buying some bets with commission on the win are lower than any other (non-free) bet on a regular craps table.

EG: buying the aces or boxcars with commission on the win is a $1 vig and a 0.571% edge per bet resolved at the sweet spot of $25. It lasts an average of 5.1428 rolls for an edge per roll of 0.11% (!!!)

I think reviewing this game as purely a sucker game neglects some of the really good bets that can be had here in Vegas at the Plaza and the Las Vegas Club.

I am also telling the stratosphere they should step up to the plate and do commission on the win for $25 and higher buy bets. But I think the Strat is scared to.

Even the Plaza has a special limit of only $500 max bet for buying the two and twelve because of the unusual exposure for a low edge pay on a high multiple.

I'm also just curious if anybody understand from a couple posts ago about the percentage of bets that are odds bets versus line/come bets.

Depending on how many come bets you make and more importantly if you're working the comeout roll, the average edge per roll will be different as the ratio of free bets to line bets changes.

Alright, this is what I ultimately wanted to get to which is a chart of edge per roll in a matrix.
The number 1-7 and 1-11 is the maximum number of passline + come bets on the felt. You always bet the come unless your total number of passline bets + come bets is equal to this number.

This gives you the AVERAGE edge per roll including all the simulated state and percentage of line bets versus working odds bets for both craps and crapless craps.

This is the most complete list of edges per roll for all the smartest ways to bet the pass line with odds on both games. It helps to see how you need to play the game in order to get an average edge below that of a place bet for example. Normalizing all strategies into edge per roll helps you get the best possible math by being able to compare apples to apples.