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

_

Observations

*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

Nov 16, 2012

## My Gambling Problem Raises its Ugly Head Again

My old gambling problem is bugging me again: I just don't gamble enough.That statement of course is my little joke, but actually I take this quite seriously. I suspect many of you are bored by this seriousness [in which case skip this paragraph]; or at least wondering if I have enough bankroll to be a player. When I view that last consideration, I keep thinking to myself that the bankroll I am comfortable with is completely in line with the type of action I seek. So what's the problem? Well, Lately the problem has been exacerbated by being on a losing streak. I am determined not to play to chase losses, rightly one assumes. On the other hand, a player wants to play. Somebody at this site recently quipped "you can't win, but you also can't quit" and I think that is about the size of it. But really my bankroll, till now kind of vague, is fairly intact. What's been giving me pause has been that actual losses can be 30 to 40 times theoretical in a session, and I can't seem to find what to expect in the long run. If it is plausible to lose like that in the long run, then such a rate could ruin a pretty hefty bankroll in short order. Note I do not use the word "possible" as of course, the answer has to be that it is possible; but how about plausible? Although not unbroken, the bad streak started about 18 months ago and I am currently at about 14 times theoretical EV for that period, which is been bad enough. If I adjust EV with the freeplay I got recently, though, it starts to look astronomical. So I guess I just won't figure freeplay in; but 14 times theoretical losses still sucks and is bankroll threatening. I've laid off playing lately. Did I really needed to?

I have become a player that nearly entirely plays Craps only. I wondered if Wincraps could help with the question. I figure I have seen the equivalence of about 1500 rolls of the dice per year lately. Not much! but hey I don't live in Vegas! I figured 25,000 rolls would be at least a serious chunk of a lifetime of Craps for me, even if I pick up the pace, so I ran Wincraps for this 25k rolls, $10 table, 3x4x5x taking full odds, and repeated this 100 times; I like to consider these 100 different players.

The below shows the results. The number for each file is the final status of the player's losses compared to his theoretical final losses, shown as the multiple of this EV, for example the last on the list lost 9.5 times theoretical loss. The first bunch did the best, bearing in mind that a negative times a negative is positive. Although this is nearly half, the idea that I could wind up there I just have to dismiss; for one thing, for current purposes I am carrying that '14 times EV' with me. Checking a few of these, quite a few that wound up just fine at some point were as much as 40 times EV for their early-on losses btw. I'd say about 10% of these players wound up in a zone I would just as soon avoid, the rest I could live with.

Contemplating all this has made me focus on bankroll instead of my old method, which was to look at actual losses compared to an arbitrary amount I had decided I was comfortable losing in a year. By chance this was similar to 0.1% of readily cashable assets and I started using that as a hard figure for "losses not to exceed". I still have an idea of what I like to see in terms of losses per year, but this is a sea-change for me. I am switching to a bankroll method instead of a "losses put on the brakes" method. It just seems now, experimenting, that the fact of the matter is, I havent seen enough rolls of the dice to even know what my play might do to that bankroll. I am going to roll the bones till I have a more sizable portion of 25,000 rolls experienced.

So what bankroll? I guess I am comfortable discussing the amount. At 18 months ago a $10,000 bankroll was fairly much what was in my thoughts it seems. You have to say you would be OK with losing it, it is not just a matter of raising it. The answer to that for me is yes, however, not in a short period of time like 20+ times EV might do.

We will see what happens to that bankroll with the losing streak already taking a small piece of it. I figure a player should grow the bankroll 4% per year on the 10k, to keep the roll from vanishing by definition eventually, doing negative expectation. Note that the worst outcomes are short of 10 times EV, so I am concluding that 20 or more times EV after 25,000 rolls is in the realm of the most unlucky. This as it is represents 2.5 million rolls of the dice! Maybe if I looked at 1000 players some poor guy would hit 20 times EV, but I have to gamble that it won't be me, surely the odds are pretty good for that.

Final matter: my old method was keeping me out of trouble with excessive gambling losses. I just don't want to be that guy who has that problem. So a fair question for me is, am I deluding myself with faulty rationalization so I can get my fix like some dope fiend? One reason I think I can say no to that is because no one else seems to talk much about the utility of some arbitrary loss per year; a bankroll is always what is discussed. However, any comments are welcome, thanks in advance.

### Comments

Every player goes through extreme droughts, so bad as you have it now, it is not atypical. You knew that, but it is still nice to hear. I myself just broke out of a 2 year slump at craps, that had me losing most of my session bankroll that I took on every trip. And I broke out with my biggest craps win ever!

Coincidentally, I had also been advised that I was developing a 'losers' attitude when I headed to a casino, so I was conscious to be upbeat this trip. Did it help? Hell if I know, but it certainly couldn't hurt, and I WON. Power of Positive thinking? Well, I am positive I am going to win the Lottery, but it ain't happened YET. :-)

I tend to save up money for a trip and then take what I can afford to lose. If I bust out that trip, I have no bankroll to speak of until I rebuild it. Not really a good way, but it matches well to my tendency to play above my bankroll limits (I take enough to be a $10 craps player, but will have way more than that in ACTION). I need to compartmentalize it in this fashion. Otherwise, I would just 'borrow' against the bankroll I did not have with me on a given trip, and over bet it.

Your money management system, with the % of bankroll is a much smarter system, IF you stick to it. But if you were to lose $3,000, staying within your % criteria, and then feel like throwing up over it, that is not good. No matter how you look at it, if you later regret losing the money, you should not be playing it. I got to that point in my losing streak, and walked away for 6 months. No Forum, no play games, no WinCraps, NOTHING gambling, other than a home poker game or two. It was a great sanity check for me. After 6 months, I started missing craps and came back, but I also started really analyzing my craps play.

I think you need to decide if you can accept losing the whole $10K bankroll, AND over what time frame would you accept that outcome. You also need to decide if you have other things you would rather do with that money. Those answers will guide you in the right direction.

Quit playing craps...you can never win.

You can't even begin to understand why the numbers come up like they do.

I have realized the best bet is just to flat bet the DP and hope for the best (as I've watched the tables be COLD MUUUUUUUCH more than they're hot.)

If you absolutely HAVE to play..take $100 and just bet $5 on the DP and however long it lasts, it lasts..

Trust me, you're better off taking that $100 bill and lighting it on fire.

Yep, R-craps, from what I hear the droughts with advantage play are even more maddening. I was dickering with +EV in Wincraps for a bit [altering the dice] and with 10x odds you could go 10s of thousands in the red before seeing results way down the road. 0.55% advantage and this could happen.

as far as losing the $10k, yep, prepared for that and would just hope it would take years. As it is, the 'growth' of 4% on it has helped too. But I am thinking about restricting my play less than I have been. A continuance of 14 times EV will mean periods of forced inactivity nevertheless, like you describe. But no forum? [g]

T-speed, yessir, I cannot dispute it. It's eerie sometimes how the dice just seem in the employ of the casino!

I am on the mother of all craps losing streaks. I don't even want to say how much I have lost, because it's embarrassing for someone who purports to be a disciplined player. I just haven't been even able to break even, let alone win. Be prepared to ride out an enormous storm of variance.

"What's been giving me pause has been that actual losses can be 30 to 40 times theoretical in a session, and I can't seem to find what to expect in the long run."

What is your total net loss and your total resolved action?

Yeah, EV and EV just do not show the whole picture.

Learn EV and Standard Deviation.

No math person worth his salt uses EV and EV.

In this thread you claimed to have a clue. What changed??

http://wizardofvegas.com/forum/questions-and-answers/gambling/11680-hourly-expected-loss-for-craps/3/#post190556

""Your total winnings do not converge to your EV as the sample becomes large.

That's a common misconception.

The difference between your actual winnings and your EV becomes infinitely large,

and it actually makes larger and larger fluctuations above and below your EV.

But if you divide that difference by your actual EV, that goes to zero. (A ratio or percentage)

If you divide your total winnings by the number of hands to get winnings per hand, that will converge to your EV per hand."

Concept: Relative Vs Absolute Frequency"

Learn EV and SD and all the rest will fall into place.

Good Luck at the tables

Teddy, seems like you and I wind up on the wrong side of the bell curve on the same games too much. If we played at the same table it might be synergy, but which way would it go? A negative times a negative is a positive!

7craps, I appreciate your input.

Quote:In this thread you claimed to have a clue. What changed??

I thought about that thread, where I acknowledge the dice feel no obligation to reverse your losing streak on the basis of "the long run". Yet it also seems to be true that 40 times EV is not realistically to be seen in the long run.

Quote:Learn EV and Standard Deviation.

No math person worth his salt uses EV and EV.

OK, that'd be a great way for another look at this. But I have problems. The standard deviation in Craps is close to "one" without the odds. Fine. Craps without odds is not my game.

We know variance increases dramatically when free odds enter the picture, thus also SD. What change, exactly, do we expect? Where is the chart or calculator that shows the value for SD in craps with free odds? Where is the statement that says what the SD is for the most common game offered, 3x4x5x taking full odds?

I guess my jaw might drop when you or someone tells me the calculator is at http://i'llbedamned.com/SD/Craps and the chart is on the ask-the-wizard page xyz. [g]

Teddy- I can cure your drought!

I have now had two people from the forum accept my formal craps challenge......where I assure them 1k/day earnings with a bankroll of 10k.

For the record both of these players showed up with 5k (instead of 10k) and we hit our goals each day.

Let me be more specific, 'John", who flew out last Wed & Thursday went home with 2.3k (meaning we won 4.6k with his bankroll) ...and then 'John' returned again from Missouri for a 24 hour visit on Sunday and he left Monday with 1.6k (meaning we won 3.2k since we split all earnings 50/50).....even more impressive we each bought in with 2k (1k in reserve) and never went greater than 25% deep into the bankroll first visit and 40% second visit.

The second person is still here and has plans to relocate from CA to Vegas permanently. I need say no more on this client. With their permission I will post their 'handle' to contact as referrals.

I also have three others pending in early December. I am confident you will not find one negative posting on me ever.

Another interesting stat.....the table was so cold/choppy....never hot during first visit...there was not one other winning player besides us. During his second visit.....some regulars who were getting their butt handed to them finanlly approached us asking for 'assistance'......picked up three additional clients (2 local) who have played with me daily since Monday.

Here is the secret.....first of all, my expertise is blackjack....craps is more fun but less predictable because there is no effect of cards played as history to determine probability of furture outcomes. In craps, all you players with 'systems' may win...you may not win.

The ONLY way to win EVERYTIME (yes, I have ZERO losing sessions ever with clients) is to treat the game no different than 'Waging Business Warfare'. One may have a strategy or system(s) but one MUST be able to tactically adapt to table conditions and player conditions at the table vs just on paper.

What that means is one must be fluent in pre-game preparation...I have a detailed guideline I teach my clients addressing that issue. In addition, one must understand the complete rules & guidelines of 'Being a Professional'. I wrote an SOP detailing everyting from Discipline to Behavior to Money Management to Systems...very important and available to my clients.

Furthermore, one must understand the mathematics of craps, be fluent in SEVERAL 'Off the Shelf' Systems, as interum offset to adapt to changing conditions BUT most important understand that altering play or betting strategy with tactical field changes is ONLY done for reason and/or information and NOT emotionally. Also, remember that if you want to win the war you MUST have the bullets (BANKROLL). The confidence of having far more than you need is key to winning because you cannot win if you do not feel you can win. Don't show up to the gunfight battle with a knife or BB gun.

Simply put, let me say this. If you cannot win 1k per day consistently with a 10k bankroll (5k players $500 per day) you should take up lawn bowling, croquet, or perhaps knitting.

For those interested in winning PM me and I will make it happen.

And FYI, you will be privvy to why I do this for people and what the BIG picture entails.

Mr. Biggins, you can use your own blog ya know.

"OK, that'd be a great way for another look at this. But I have problems. The standard deviation in Craps is close to "one" without the odds. Fine. Craps without odds is not my game.

We know variance increases dramatically when free odds enter the picture, thus also SD. What change, exactly, do we expect? Where is the chart or calculator that shows the value for SD in craps with free odds? Where is the statement that says what the SD is for the most common game offered, 3x4x5x taking full odds?"

Couldn't find i'llbedamned.com or the table on Wizard.com. Just so they're here where people can see them, for $10 pass with different odds multiples:

no odds SD $9.99

single odds SD $19.58

double odds SD $23.34

3, 4, 5X odds SD $49.16

10X odds SD $108.08

Of course, all have the same ev or -$.1414.

25,000 rolls, at 3.375 rolls/comeout would be around 7400 decisions. Since the ev goes up with the number of decisions, ev would be -$1046.36; the SD goes up with the square root of the number of decisions (~86), so the SDs would be:

SD ev/SD

$859.14 1.22

$1683.88 .62

$2007.24 .52

$4227.76 .25

$9294.88 .11

So, with 3, 4, 5X odds, one SD on the "wrong" side would be losing $5274, -2 SD would be losing $9502, which is about 9ev, with a probability of .0228. 20 times ev would be 4.7 SD worse than ev, which is extremely unlikely (my Z table only goes up to 3.49, p .0002).

When the ev/SD is 1.00, you have to have one SD's worth of good luck to break even, p = .1587. That's at 5000 decisions for pass, no odds.

Cheers,

Alan Shank

Oct 21, 2012

## 5 Players Risk $1M, Then Go Back in Time Machine

Right bettors, and roughly $1 Million, that is. Each player risked a total amount of money, as if making bets from a bankroll, but not returning any winnings to that bankroll. The players would go with max odds at a $10 table, 10X odds, and go with 44,000 rolls of the dice, plus enough rolls to finish an unresolved bet. With Wincraps the same player then was able to use the same RGN and go 350,000 rolls with no odds! In this case, of course, only the first 44,000 rolls were the same, but I wanted to look at that too. Bear in mind there is a variation in the dollars actually bet, the consistency is in the number of rolls.See the thread post,

http://wizardofvegas.com/forum/questions-and-answers/gambling/11680-hourly-expected-loss-for-craps/4/#post190954

Clearly we have too few trials, so there is going to be sampling error. But I think this has probative value. It is not surprising that in each case, the free odds meant a better HE in actuality, not just in theory. With 44,000 rolls I'd say that would be a trend only and not a guarantee.

In one case, the Max bettor had positive results after 44,000 rolls. I checked it out and after 350,000 rolls he is up $6010. Want some bad news? At one point he was down $6020. Survivable but would he be so bummed at that point that he would give up? Quite possible.

Note the parameter that only $1 million, roughly, is risked. Thus it still cannot be said that free odds benefit, unless there is such a parameter. This is just not the same as spending the same amount of time at the table as a player would anyway, but adding the free odds to the bets. That is a matter of increasing the amount you are betting.

In regards to "calling out the Wiz" I would have to say none of this would surprise Michael. And it is not a test that tries to show that a betting system does help win or lose; he didn't make it clear he wasn't addressing the expectation by dollar amount?

This does illustrate that a player should not expect the EV by dollars to be consistent with free odds; also, it indicates that variance is a monumental factor with free odds.

Player | Win/Loss with max odds | Win/Loss with no odds | % with max odds | % with no odds |
---|---|---|---|---|

#1 | -$6530 | -$17,020 | -0.66% | -1.65% |

#2 | +$16,350 | -$12,290 | +1.66% | -1.18% |

#3 | -$12,500 | -$14280 | -1.24% | -1.37% |

#4 | -$5040 | -$18,040 | -0.50% | -1.74% |

#5 | -$6970 | -$17,920 | -0.70% | -1.74% |

### Comments

I wish I could be player #2. I'm more like players 1,4, and 5.

I'm not sure if I've ever been down 6 grand, but I have been in a 5 grand hole and climbed out of it. I was bummed but I didn't give up! Clearly the best way to make up losses is to continue playing a -EV game.

Sep 27, 2012

## Another Gracie Allen Moment?

Buzzpaff recently related such a moment by his wife, but she is not the only one.Maybe I should have titled this "a glimpse into the modern young mind" , I wonder if it isn't fair to say it is just the ditzy female mind that gets silly when it comes to cell phones and I-phones and social networks.

My wife and I both recently have been reading various articles about how the up and coming generation is so into their I-phones and such, that they spend so much money on it that [the articles have it] this must be cutting into their disposable income to the degree that it is a choice to do that at the expense of something else. One article said that the housing industry and the car industry both are seeing huge changes with the younger bunch, the latter trending away from fancy cars and houses [but don't think of taking away constant access to the internet!]

Anyway, while we were discussing this, I mentioned that on my irritatingly high but comparatively inexpensive cell phone plan that goes along with buying a phone [for years I was issued a phone by my employer, a thing of the past it seems]. I am shocked to the core when I hear what the typical person is paying.

Anyway, I mention to my wife that I could be paying even another $10 to get unlimited texting. That I go long periods without texting, and that an enormous amount for me would be 20 texts per month, at 20 cents a text. My wife, a pretty sharp girl really, has a Gracie Allen moment and instantly suggested I pay the $10 and get unlimited! It really is her instinct to go for the hokie-doke on these things. I call this interchange a glimpse into the female mind when I talk to other guys.

I just changed my cell phone plan, which took away an hour of my life on the phone I can never get back. But I own the phone now and can pick my plan. Verizon didn't make it easy to change, and I hate using the phone to set stuff like this up [required!] But they actually have some pay-per-use plans that are really about as cheap as anyone's, and they probably have the best service. I signed up for paying for each minute and each text!

I predict this will cut my cost to 1/3 of what it was for 10 out of 12 months; a few months might be 2/3 instead. This for the simple reason I don't use the phone that much. I might go a week without using it at all! I told my wife I signed up for a cheaper plan without giving her the details, she probably would shake her head to think I have no set number of free minutes or "unlimited" anything. One Gracie Allen moment was enough! [g]

### Comments

Track Phone for me. All I want all I need.

I am always amazed at women who rush in to buy a pair of shoes because the second pair is half off. But turn their nose in the air

at a mere 3)5 off on one pair.

Plus where is the second one in a pair of panties ?

LOL, I'm an IT director...and people look at me crazy because I don't own a SmartPhone (I have a phone from StraightTalk for Talk and Txt a little)

When I need computer access I have my Acer Netbook...

Sep 13, 2012

## M-Live Sept. 12

Without much warning, I got a nice offer for free play withing a very narrow window of time, on one day too. I had thought I'd have no problem showing up at the right time [luckily]. Later events have shown that I was showing up for something big, to my surprise. The email said it was to be a "sneak peek", so although I realized it might be busier than usual, turns out it was nightmare overcrowded. Word has it a lot of people were miffed, not getting in, or giving up trying. I almost turned around myself, but the incentive was pretty good and by the time I realized the problem, I could see I was only going to be a little late, within what was likely to be a normal grace period. I parked in a lot nearby and walked a quarter mile, assuming the garage was going to be hellish.Inside, packed, but I usually deal with that OK. It's the bumper to bumper traffic situation I can't stand. Nonetheless, long lines everywhere, and hard to find a machine I wanted. Finally someone gets up from a seat that has e-craps. I sit down, see it is $10 min. Perhaps that was everywhere, and no way can I be picky. I decided to make a few bets and get out of there, knowing there would be long lines at the cashier. Bear in mind too, as far as I knew, information hard to come by, things were only going to get worse, and I wanted to get the hell out before rush hour.

I wanted to do the buffet again [see previous post], but with the line and my anxiety, forget it!

After thinking about it for a while, I have decided that what was going on was purely a situation where Cordish, the big tuna here, was going to speak, and his handlers have learned in order to schmooze him, there must be a big crowd. So they send out this generous free play offer to thousands of people all to come in this narrow little window of time! They really ought to be ashamed of themselves, such BS is un-neighborly and even unsafe due to the traffic mess. Truth be told, if all they did was have some big drawings, that probably would have brought plenty of people in. This was unnecessary and apparently caused more hard feelings than it was worth. Are they going to make it up to their patrons who got pissed?

But the money was there, and I did take it.

### Comments

how did you do w/the free $?

all on a single dont pass (max odds) then leave?

>how did you do w/the free $?

10 DPs/DCs with full odds, lost right off the bat but got on a winning streak and wound up over $100. Naturally, I wanted to continue, but not real happy with a $10 table and my anxiety about traffic when leaving [unfounded] I got up from my seat.

I have to assume they would know you took X amount from them and just tried to cash it, without gambling through it, BTW. At least that would be the rule if it was up to me! [g]

but you did gamble thru it if u put it all on a single dp/full odds

ie: $70 free $

$10 dp/$60 odds

win or lose, you just gambled thru the free $ they gave you

yeah, I know, but I considered just taking the money... doubt if that works. That's why I mentioned it. I wagered enough in just a couple of minutes if you count free odds, and surely they do.

The garage is not a nightmare if you park in the upper floors, especially 6 and 7.

As far as the craps are concerned, I'm sure you noticed you can no longer make 50 cent line and place bets. Now, they have gone to truly $5/10 minimums (except for the prop bets of course). The only unusual craps bets I notice still allowed, is the $1 horn (as opposed to the usual $4 at most tables) and the $5 buy bet on 4 and 10.

The bar is still $5 minimum, but most other rows, and the "island" is now $10.

I still like that you can use the free play on the tables, as opposed to being forced to drop those dollars in slot machines.

I am enjoying your blog, as you seem to hit the same casinos I most frequently visit (M-Live, Harrington)

## Comments

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.

Buzzard, they do fit.

>a failure at something you love

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

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.

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

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

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

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!

please note that the blog post now contains the corrected math