Posted by odiousgambit
Jan 27, 2013

The 'Brier

Some enjoyable gaming at the 'Brier in WV this week. So my New Year's resolution, to gamble more, is under way.

A change in the BJ being offered, it's no longer S17 but H17. This time lost a minor amount playing BJ for a couple of hours. Only saw one hand where dealer took another card to hit soft 17, and it didnt matter to anyone's hand. In Craps, I'm amazed that merely pushing on '12' sends a darkside player from @ 1.4% PA to @1.4% HE as you get no sense the 12 is playing much of a role. Now at BJ I'll evidently be amazed at the effect of this rule change that matters a lot but [so far] is seldom seen in action.

Good couple of days at the Craps table slugging it out for about 3 hours each day. Apparently will still not be able to hang with the Big Boys at the WoV forum as such stretches are quite enough, thank you. $5 table action was never upped to anything higher, and still 3x4x5x. The second night the table was hot nearly the whole time and I made back all losses in BJ and prior day's Craps. Gave a lot of it back when the table cooled but was up too much to wind up down for the trip. Naturally the table was lots of fun with everybody winning. Tipped pretty heavy and walked out happy to be up just a bit overall. My new way of looking at my bankroll is working great, not playing scared now. The dice seemed to sense it and cooperated! A larger session bankroll was in view and the dice had to bow to such confidence, unable to come after it [indulging that superstition].

As for further gambling opps, out the blue Harrington DE is sending some great coupons my way, including the free Ace for up to $100. A February thing for everybody I'd guess, otherwise somehow my name was retrieved from the Low Roller file where it has been for months. I'd like to think some competitiveness is kicking in.


Doc Jan 29, 2013

I've only been to the Greenbrier once, and I posted a report here about that a few years ago. At the time, the main casino was still under construction, and the only games (no craps) were in their Tavern Casino. Is that small space still operating? I'm glad to hear that they are offering the low minimums -- if you have to spend a small fortune to stay there and gain entry to the casino, at least they aren't gouging you at the tables. Do you know whether they hike the limits on weekends? (I didn't catch which days you were there.)

odiousgambit Jan 29, 2013

It's a bit pricey to stay there alright. Not the place to go "regularly" to gamble.

The tavern casino is no more. The new area is very nice with very friendly dealers. The minimums were lower this time compared to the two other times we've gone. I suspect they go up on the weekend, but I haven't been there on a weekend! They evidently take in plenty with the casino, so weekends must be busier for the gaming.

Doc Jan 30, 2013

I received an email promo yesterday for their Winter Escape special, which is still priced out of my comfort zone. I looked at the web site, and the Tavern Casino is described as available for private events. What a place to hold a private casino night!

Posted by odiousgambit
Jan 09, 2013

1 Year of Craps Crazy Simulation

Was just having Wincraps do 90,000 come-outs and calling it something barely within the bounds of possible to do in a year, assuming some sanity:

3x4x5x $10 table, taking full odds, $10 on pass invariable.

8 hours per day, 5 days a week, at my usual pace of about 45 come-outs per hour; in reality it would have to be less hours and more come betting I think, but those are the numbers. Then 50 weeks, calling that one game. Takes the computer forever to kick out a few games.

In Teddy's blewout-bankroll thread, discussion about possible winners. Coincidentally was crunching this year-long thing. Sure enough, first player wins big for a whole year. Been running for hours and only 752 completions so far.

PS: each player starts at $0 bankroll {plays on credit I guess [g]}


tringlomane Jan 09, 2013

Those next 15 look pretty rough.

7craps Jan 10, 2013

Interesting concept.

I ran your 90k come-outs 10,000 times in a few minutes and here are the results

Bankroll decreased . . = 80.390% of the time

Bankroll increased . . = 19.600% of the time


EV =-$12,727.27

SD = $14,746.90

ev/sd = -0.863047596

0.194055649 prob even or ahead

I also went by 4 hour sessions at 30 bets per hour (something I could do)

30K come-outs 10,000 times

Bankroll decreased . . = 69.540% of the time

Bankroll increased . . = 30.440% of the time


EV =-$-4242.42

SD = $8,514.12

ev/sd = -0.498280762

0.309143083 prob even or ahead

Results look close to expectations

It would take a very large bankroll to make it to the end

ev + 2*SD would get you to a bust rate of about 1 session in 20. Ouch

Yes, unlimited casino credit would work out just fine

odiousgambit Jan 10, 2013

I was wondering what kind of bankroll would be needed. This does not give the answer exactly, but it would seem that a $50k bankroll would probably last the year. Both the high and low for 729 games was slightly higher at about $65k, so $100k to be nearly totally safe. But what about the next year? I think to say for sure you could keep going year after year ,$150k or more is more like it, with some $20k replacement coming in every year.

odiousgambit Jan 10, 2013

umm, I meant 752 games.

Posted by odiousgambit
Dec 12, 2012


The last post gave everybody a headache, I'm sure.

Nonetheless, the subject interests me, if only me.

The only certainty: The session size that is optimal in terms of chances to win, is one bet.
Fairly indisputable: To bet enough that your theoretical loss is in the neighborhood of the value of one standard deviation for the session, is to have crippled the chances for a session win.

Where to be 'in between' is disputable.

One thing that dawned on me after looking at all this myself is that EV as a percentage of SD can be higher in a low HE bet than in a sucker bet like Any 7 and not be as deadly. For the latter, a 12 % figure already knocks winning down to about 30% of sessions, whereas for Craps with odds it is still perhaps acceptable at about 44% of sessions getting the W.

So perhaps there is needed another modifier that re-factors the HE?

Posted by odiousgambit
Dec 11, 2012

Wincraps and Craps sessions

Wincraps and Craps sessions

Sticking with the formulas from the last post, I am now comparing EV divided by Standard Deviation for players who like various amounts of action as a session. A player can look at the consequences of longer sessions, and look at the percentage of games that produced a winner or a loser. It is certainly expected that it should be the less, the better, as it is said that the best chance comes from placing just one bet. My "thing" has been that a player can look at this EV / SD as a percentage.

I start here with a sucker bet, so betting on the line with odds is below this


Illustration: The Any 7 Bet

Purpose: to show that EV rapidly grows as a % of one SD with sucker bets, and the consequences, as session betting increases by number of bets.

Note: Couldnt manage to write an auto-bet file that stopped exactly at 10,000 games. One game = 2 bets or 5 bets as below.

View a session bet progression from 2 bets to 5 bets. Bet $1

Standard deviation for the any 7 bet: 1.86

First: 2 bets per session [yes, within two bets the EV is eating into the SD]
about 10,000 sessions

the math:
SD * $1 * the square root of the number of initial bets made in the session, that is

1.86 * 1 * 1.4142135623731 = 2.630437226013966

EV for 2 bet is 16.67% * $2 = -$0.3334

This theoretical loss divided by one SD is

0.3334 / 2.630437226013966 = 0.126746989703007591006

already at 12% plus
player wins about 30% of these 2 bet sessions


Standard deviation: 1.86
5 bets per session

SD * $1 * the square root of the number of initial bets made in the session

1.86 * 1 * 2.23606797749979 = 4.1590864381496094

EV for 5 bets is 16.67% * $5 = -$0.8335

This theoretical loss divided by one SD is

0.8335 / 4.1590864381496094 = 0.200404587015706931066

very high at 20%
player wins less than 20% of sessions.

PS: just noticed all the ties. What's up with that? Don't know.
PPS: turns out that if you have one win and 4 losses in a 5 bet session of "any 7" that is a break-even. Oddly, it is a common outcome, try it yourself.



I had Wincraps crunch out 10,000 games and log the results. The player would bet $10 on the pass line, and always take full 3x4x5x odds and make no other bets. There would be so many come-outs played per game, a game as defined by Wincraps, essentially a session as defined by me. I ran next an increased number of come-outs, to simulate a player who needs more action and stays at the table longer. As this number of come-outs got larger and larger, the program started to take forever to finish, with the last few looks taking overnight to finish. Bear in mind it would take me years to play the number of come-outs represented by 4 or 5 thousand trials, and surely there are no players who would do it in a day, so it starts to lose its meaning as a session.

The previous blog post established for my satisfaction that 180 come-outs bet in a session is not excessive, that a player still had good chances for getting the W. This kind of action is typical for me in a day.

I realize 10,000 games is not really enough, but see above; hopefully this will have value without producing total faith in the numbers.

All I have been basing this on is gut, not having too much to go on. It does seem to me that it should be clear that as theoretical loss equals the value of one standard deviation, the player has overdone it. This condition is certainly rapidly achieved with certain bets. For that player at that point, he has to be on the lucky side of one standard deviation to expect to break even! So to say one's EV must be less than one SD becomes common sense.

But where do you draw the line for a player playing smarter than that? Somewhat arbitrarily I arrived at the suspicion that theoretical
expectations exceeding the value of 10% of one SD could be a dividing line between smart play and not-so-smart. Since the smartest play is one bet, one can see the unclear nature of this.

Adding ties to the win side, the below shows a progression in win/loss % of approx:










If mentally graphing this, note that the first two are close to the same thing and towards the end I jumped out a bit. Nonetheless it is somewhat wobbly [more than 10,000 games would help?] and seems to be recursive [is that the term?]. I feel though it has probative value.

See first comment for the math for examining EV as a percentage of one SD for the various parameters. A work in progress, will finish later. However, my initial thought that a criterion of 10% means trouble, seems to be holding up. Perhaps it depends on the player. If a player likes bets like the "YO", perhaps also 1500 come-outs in a session is also in his tolerance, as the 45/55 ratio, if it were one bet, would mean an HE of 10% for one bet [if I have that right].

Your thoughts are welcome.


180 come-outs per game, 20k games [exception]

criterion = 3.9% (absolute value of EV divided by one standard deviation for one game i.e. session)

48.5/51.5 win/loss ratio with ties added to wins


500 come-outs per game, 10k games

criterion = 6.4%



1000 come-outs per game, 10k games




1500 come-outs per game, 10k games



2000 come-outs per game, 10k games




2500 come-outs per game, 10k games


3000 come-outs per game, 10k games


4000 come-outs per game, 10k games


5000 come-outs per game, 10k games


odiousgambit Dec 11, 2012


180 come-outs

this was determined in the prior post: EV / one SD = -25.45 / 659.50= -0.03858984078848 or about 3.9%


500 come-outs

using again SD * $10 * the square root of the number of initial bets made in the session

"SD is 4.915632" for the 3x4x5x game [see prior post]

sqrt(500) = 22.3606797749979

so that is,

4.915632 * 10 * 22.3606797749979 = 1099.168730437324771728

EV = 5000 * (-7/495)

EV / SD = -70.70707070707071 / 1099.168730437324771728 = 0.064327767656689600052365

6.4 % approx.


1000 come-outs

SD * $10 * the square root of the number of initial bets made in the session

"SD is 4.915632" for the 3x4x5x game

sqrt(1000) = 31.62277660168379

4.915632 * 10 * 31.62277660168379 = 1554.4593259208809200528

EV = 10000 * (-7/495) = -141.41414141414141

EV / SD = 141.41414141414141 / 1554.4593259208809200528 = 0.0909732014572757795009369

about 9.1%


1500 come-outs

SD * $10 * the square root of the number of initial bets made in the session

"SD is 4.915632" for the 3x4x5x game

sqrt(1500) = 38.72983346207417

4.915632 * 10 * 38.72983346207417 = 1903.8160872084257642544

EV = 15000 * (-7/495) = -212.12121212121212

EV / SD = 212.12121212121212 / 1903.8160872084257642544 = 0.111418961918872333653953

about 11.1%


2000 come-outs

SD * $10 * the square root of the number of initial bets made in the session

"SD is 4.915632" for the 3x4x5x game

sqrt(2000) = 44.72135954999579

4.915632 * 10 * 44.72135954999579 = 2198.3374608746490518928

EV = 20000 * (-7/495) =-282.82828282828283

EV / SD = 282.82828282828283 / 2198.3374608746490518928 = 0.1286555353133792243240909

about 12.9%

7craps Dec 12, 2012

the reason to calculate ev and sd is so you do not have to run lots of simple simulations.

Let the central limit theorem work for you.

Excel can then easily make many tables for the data you are simming.

goatcabin made a few posts about this as well as I.

I do not have links for them at the moment.

345X odds skews the results a bit but the ev/sd values are very close to actual calculations.

Steve Fry has a free craps sim that can run millions of sims way faster the WC. Just google.

It only does basic bets unless you know how to re-do his code and compile it yourself.

ev/sd = z score

that score is looked up or calculated to give a probability of being even or ahead after N trials. (normally 30 minimum)

In Excel one can easily find probabilities for any interval so desired.

more later on

My head cold does not let me go further

Excellent work BTW

odiousgambit Dec 12, 2012

>Excellent work BTW

thank you sir, that means a lot. Your help has been much appreciated.

Posted by odiousgambit
Nov 29, 2012

Revisit of Session Length

I admit the way I look at gambling differs from most gamblers. You might say I look at it like someone who plays a game, a game that has scoring, against better opponents. Maybe it was a loss last time, but when you walk out on the field for the next game the scoreboard says zero to zero. I am trying to win sessions and also get the W for the day, against the odds.

Better opponent? With negative expectation games that is one way to look at it.

If this is not the way you look at gambling, you should skip this post, which is the beauty of blogging.


A look at the proper length of a Craps session, and chances for the W in a day.

Hopefully I have all this right.

"The standard deviation of the final result over n bets is the product of the standard deviation for one bet (see table) and the square root of the number of initial bets made in the session. This assumes that all bets made are of equal size"

from http://wizardofodds.com/gambling/house-edge/

3x4x5x: "The standard deviation per pass line bet is 4.915632."

from http://wizardofodds.com/ask-the-wizard/craps/probability/

My assumption for such a statement is that the original pass line bet has to remain the same amount. Good, that is typical for me.


2 sessions of Craps for myself usually means 4 hours and 180 bets on the line with full odds [with my typical come betting].

3x4x5x and a $10 table; experience has shown this pushes my tolerance for risk, with a feeling of reduced chances for the W.


Edited figures by the correction to the formula:

SD * $10 * the square root of the number of initial bets made in the session

Thanks Pappa Chubby and 7Craps

"SD is 4.915632" 3x4x5x

sqrt (180) = 13.41640786499874

13.41640786499874 * 4.915632 = 65.95012382623948630368

65.95012382623948630368 * $10 = one SD for four hours playing $10 Craps = $659.50

EV = $1800 * (-7/495) = $-25.45

range: up 634.05 or down $-684.95 [this in particular sounds more like it]

Odi Criterion = EV / one SD = -25.45 / 659.50= -0.03858984078848


*To deviate by one SD is a matter of luck itself, it would seem. I guess that makes sense.

*I have come across nothing else to go by. Is no one else interested, or is it too personal from player to player to be a broad application? I dunno, seems to me there is a point at which foolishness enters the picture with session length.

*In any case, the number crunching here seems to correlate with my experience in the following way: as EV approaches 10% of one SD a player starts damaging his chances for getting the W.

*Since this is still [edit: well less!] less than 10% I will accept that the 2 session thing I like to do is not in the realm of foolishness.

a rare case of finding a figure for the SD of Craps with odds btw


Buzzard Nov 29, 2012

Your wife occasionally has Gracie Allen moments. Reading your blog I was reminded of George Burns.

I believe both quotes apply to this blog : I honestly think it is better to be a failure at something you love than to be a success at something you hate.

Everything that goes up must come down. But there comes a time when not everything that's down can come up.

odiousgambit Nov 29, 2012

Buzzard, they do fit.

>a failure at something you love

That's me and Craps alright [g] But that's also EV

RaleighCraps Nov 29, 2012

Hi odiousgambit. That is an interesting and informative way of looking at your session length. Since I only play about 6x a year, I have a hard time playing a 'short' session, even though I know the longer I play, the more likely I come out on the losing end. Even with that, 6 to 8 hours session is not abnormal for me, or 10-12 hours in a 24 hr period. I just love the game, no matter how badly she treats me.

I can also note though, that many of my wins or break even sessions have come at the end of 4+ hour sessions. Had I quit after an hour or two, I would have booked a loss. So a long session can work for you as well as against you.

What I have noticed is almost every session I have ever played has had a good to great roll by someone. The sessions I make money, I am active on that good roll. The sessions I lose money, I am low on chips and am just trying to not go broke, so I don't get much benefit from the roll.

PapaChubby Nov 29, 2012

You didn't calculate your session SD right. Correct method is 4.915632 * sqrt(180) = 65.95

7craps Nov 29, 2012

Yes, more work on your session SD is needed

SD is 4.915632

This is also just for a one unit bet.

You need to multiply this by the bet amount.

Total Bet SD =

SD * $10 * the square root of the number of initial bets made in the session (180) = $659.50

EV = 180 * $10 * (-7/495) or -$25.45

There is your picture

About 5X more likely to be $625 or more ahead after the session (assuming a bankroll large enough)

than falling between $0 and -$50 (EV of $25 +/- $25)

Good luck losing exactly $25 every session as most EV pushers want everyone to believe.

One can expect to bust a EV + 2SD bankroll every 1 in 20 sessions or so on average,

meaning it could happen 2 times in 20 sessions 25% of the time.

I did not check my math

go for it

odiousgambit Nov 30, 2012

preserving incorrect math for comparison

"SD is 4.915632" 3x4x5x

4.915632 * 180 = 884.81376

sqrt (884.81376) = 29.74581920203241

so, $297.46 deviation = one SD for four hours playing $10 Craps

EV = $1800 * 1.41% = $25.38

range: up $272 or down $-322.84

imbalance of range: $50.84 [difference]

Odi Criterion = EV / one SD = 25.38 / 297.46 = 0.08532239628858

odiousgambit Nov 30, 2012

thanks for the help! I trust the look of these numbers better too, not to mention it is obvious I bow to superior knowledge in this [g]

R-craps, yep, know what you mean. In fact it strikes me that there is always only one guy, if there is anyone, who just gets the lucky 5 or 6 or more points made on his hand. It never seems to be we all win by one guy making 2-3 points, next guy same, one guy pso, next guy 2-3 points. It's always just one guy or gal!

odiousgambit Nov 30, 2012

please note that the blog post now contains the corrected math