Posted by odiousgambit
Aug 06, 2019

Hapless Happenings

So in the previous blogpost we reviewed that the basic formula for determining the HE of the DP or DC bet in Craps is

the probability of winning
3/36 + (3/36)*(6/9) + (4/36)*(6/10) +(5/36)*(6/11) + (5/36)*(6/11)+ (4/36)*(6/10) + (3/36)*(6/9)
minus prob. of losing
8/36 + (3/36)*(3/9) + (4/36)*(4/10) +(5/36)*(5/11) + (5/36)*(5/11)+ (4/36)*(4/10) + (3/36)*(3/9)

and that deleting parts of this formula will tell us the change in the house edge if a player rejects all the action on the 6/8 points to be resolved. No one has disputed the latter while one member at least, Mission146, has confirmed it [in fact got me past my initial error]. 

So the next question that comes to mind is, assuming it will be the wisest move to bet on the same DP/DC line, and not just stand there and greedily take the declined action only,  " does another player taking that same action from the player declining it, make his overall betting +EV?". Mission hashed a couple of scenarios out.

That number crunching was not preserved and we will see if I can get it right again altering the above formula. I'll call the accommodating player, giving up his action, "Hapless", as surely no one gives up this action unless he has been unlucky either in education or in perception of his "luck", seeing as how no one who knows 7 is easier to roll than 6 or 8 gives it up unless he believes himself to be an unlucky person.*

Scenario #1. Hapless bets the same amount, always is on the same bet as you, and always gives up the 6/8:
Prob. of winning, simply adding the additional action
3/36 + (3/36)*(6/9) + (4/36)*(6/10) +(5/36)*(6/11) + (5/36)*(6/11)+ (4/36)*(6/10) + (3/36)*(6/9) + (5/36)*(6/11) + (5/36)*(6/11)
minus prob. of losing
8/36 + (3/36)*(3/9) + (4/36)*(4/10) +(5/36)*(5/11) + (5/36)*(5/11)+ (4/36)*(4/10) + (3/36)*(3/9) +(5/36)*(5/11) + (5/36)*(5/11)

I get +0.0116161616161616 

Scenario #2. Hapless bets twice as much, same as above otherwise:

3/36 + (3/36)*(6/9) + (4/36)*(6/10) +(5/36)*(6/11) + (5/36)*(6/11)+ (4/36)*(6/10) + (3/36)*(6/9) + (5/36)*(6/11) + (5/36)*(6/11) + (5/36)*(6/11) + (5/36)*(6/11)
minus prob. of losing
8/36 + (3/36)*(3/9) + (4/36)*(4/10) +(5/36)*(5/11) + (5/36)*(5/11)+ (4/36)*(4/10) + (3/36)*(3/9) +(5/36)*(5/11) + (5/36)*(5/11) + (5/36)*(5/11) + (5/36)*(5/11)

I get +0.0368686868686869

Thus it would seem possible every time you would get a cooperative person you will be +EV for your betting even with needing to be betting on the line.  I am not getting the same results as Mission so I am not claiming this is correct yet. Anyone see an error? 

Calling Mission, come in Mission, Mission are you there?

*what is such a person doing in a casino?


Mission146 Aug 06, 2019

Okay, here we go:

The first thing that we want to do is greatly simplify the problem, so let's first get the expected value (per one unit bet) of assuming the hapless action on the six and eight:

(6/11) - (5/11) = 0.0909090909 (Units)

Okay, so that's the expected profit, in units, every time that we get to assume this action. That's also the house edge of the Big 6 or Big 8:


Because you are effectively playing the part of the casino.

Your Expected Loss

Your expected loss betting the Don't Pass is .0136 units, and you make this bet every single time. Looking at it in terms of all 36 possibilities, for each possible initial come out roll your total expected loss is:

.0136 * 36 = 0.4896 (Units)

On ten of these 36 occasions, we will get to assume the action of our friend who would otherwise be pulling the 6 and 8 back:

0.0909090909*10 = 0.909090909 (Units)

(0.909090909 - 0.4896)/36 = 0.01165252525

Therefore, it appears that OdiousGambit is correct and the ability to take the action of our hapless player yields a positive expectation of .01165252525 (Call it .0116 or .0117, difference due to rounding) every time that you make a bet provided that bet is matched by someone who will let you take the 6/8 DP action.

odiousgambit Aug 07, 2019

OK! good to know we get the same answer, might explore it a bit more.

Posted by odiousgambit
Aug 01, 2019

Hall of Fame, Sucker Division

using the Wizard's work at
for the don't pass, and skipping the process of finding the common denominator, I get the same answer he does for the house edge using an online calculator with the formula
[3/36 + (3/36)*(6/9) + (4/36)*(6/10) +(5/36)*(6/11) + (5/36)*(6/11)+ (4/36)*(6/10) + (3/36)*(6/9)] - [8/36 + (3/36)*(3/9) + (4/36)*(4/10) +(5/36)*(5/11) + (5/36)*(5/11)+ (4/36)*(4/10) + (3/36)*(3/9)]
which preserves the details of winning and losing on 4,5,6,8,9, or 10 as numbers to resolve along with the other ways to win and lose. The calc. can handle that just fine. That is, I get  -0.0136363636363636 for house edge, the familiar figure when you count pushes. 

So it occurred to me I can take the segment for 6 and 8 to resolve wins, (5/36)*(6/11) + (5/36)*(6/11), and change that to 0, but also remove the ways to lose that bet and change that to zero! This is what I got wrong in my first go, which I have preserved in the spoiler. We should get the formula for the house edge if 6 and 8 pushed instead of won. That basically is what happens when a player 'takes no action' on darkside 6/8 bets, no?

With the altered formula 
[3/36 + (3/36)*(6/9) + (4/36)*(6/10) +0+ (4/36)*(6/10) + (3/36)*(6/9)] - [8/36 + (3/36)*(3/9) + (4/36)*(4/10) + 0 + (4/36)*(4/10) + (3/36)*(3/9)] .............. putting in a zero there for the missing action in both places.
I get a house edge of -0.0388888888888889 ... which matches Mission's numbers done in a slightly different way in the comments. To be clear, it was Mission who discovered the error, thanks.

-1.36% goes to -3.89% ; not quite tripling the house edge

Still qualifies for the Suckerbet Hall of Fame, on the stupidity of it.  

using the Wizard's work at
for the don't pass, and skipping the process of finding the common denominator, I get the same answer he does for the house edge using an online calculator with the formula
[3/36 + (3/36)*(6/9) + (4/36)*(6/10) + (5/36)*(6/11) + (5/36)*(6/11) + (4/36)*(6/10) + (3/36)*(6/9)]-[2928/5940]
which preserves the details of winning on 4,5,6,8,9, or 10 as numbers to resolve and otherwise just uses his work. That is, I get -0.0136363636363636 for house edge, the familiar figure when you count pushes.

So it occurred to me I can take the segment for 6 and 8 to resolve, (5/36)*(6/11) + (5/36)*(6/11), and change that to (5/36)*(0) + (5/36)*(0), and we should get the formula for the house edge if 6 and 8 pushed instead of won. That basically is what happens when a player 'takes no action' on darkside 6/8 bets, no?

With the altered formula
[3/36 + (3/36)*(6/9) + (4/36)*(6/10) + (5/36)*(0) + (5/36)*(0) + (4/36)*(6/10) + (3/36)*(6/9)]-[2928/5940]
or simply [3/36 + (3/36)*(6/9) + (4/36)*(6/10) + (4/36)*(6/10) + (3/36)*(6/9)]-[2928/5940]
I get a house edge of -0.1651515151515152

We go from -1.36% HE to an amazing -16.5%, turning one of the best bets in Craps into one that rivals the "any 7" bet for Hall of Fame Suckerhood.


Mission146 Aug 01, 2019

Come Out + Point Results and Outcomes:

Come Outs 2 & 3 = Automatic Win (3/36) = 0.08333333333

Come Outs 4 & 10, Point Missed, Win: (6/36) * (6/9) = 0.11111111111

Come Outs 5 & 9, Point Missed, Win: (8/36) * (6/10) = 0.13333333333

Come Outs 6 & 8, Point Missed, Win: (10/36) * (6/11) = 0.15151515151

Come Out 12, Push = 0

Come Outs 7 & 11, Loss: (8/36) = - 0.222222222

Come Outs 4 & 10, Point Made, Loss - (6/36) * (3/9) = -0.05555555555

Come Outs 5 & 9, Point Made, Loss = - (8/36) * (4/10) = -0.08888888888

Come Outs 6 & 8, Point Made, Loss = (10/36) * (5/11) = -0.12626262626

Add them together: (0.08333333333 + 0.11111111111 + 0.13333333333 + 0.15151515151) - (0.222222222 + 0.05555555555 + 0.08888888888 + 0.12626262626) = -0.01363636341

That's the correct house edge, which agrees with the above, now we account for removing the winning AND losing possibilities because the player is pulling back the bet:

The player would win an expected 0.15151515151 units when this happens and the bet is left up and would lose an expected 0.12626262626 when the bet5 is left up and would lose. Combined, this means that the player is giving up, (0.15151515151-0.12626262626) or 0.02525252525 units per initial bet. When we add this to what would be the house edge of .01363636341 or 1.36363636341%, on a bet made basis, we get -(0.0252522525 + .01363636341) = -0.03888861591

Which represents a new house edge, per bet made, of 3.888861591%, or an expected loss of 0.03888861591 units per unit bet.

odiousgambit Aug 01, 2019

the bet can't win if pulled but also doesn't lose, mission points out, i went wrong there

i 'll see if i can now get the same answer stay tuned

Posted by odiousgambit
Jul 23, 2019

Charles Town

TLDR: recently my recreational gambling has been at Hollywood Casino in Charles Town WV. There is a Sportsbook there now, a much appreciated development. The Craps table is another attraction for me; but the Darkside was unkind yet again on my latest trip. Again I'm struck by how impossible it would be to figure out the best way to play without doing the math. 

This year, including recently, I have had reason a couple of times to be in the Charles Town WV area and of course had to hit the casino there. I've just settled with the opinion Craps is the only thing worth playing in the table games, though I don't have any fresh details about the BJ situation. I simply ignore everything else except the sports book, the arrival of which I do indeed consider a very nice development. Seems to me that a dreary mood has settled in ever since this casino lost its geographical advantage to other casinos now closer to DC and suburbs. When it had its advantage, it was notorious for high table minimums, surly service, and the like. After MGM National Harbor opened for business not so long ago, they did respond with things like lower minimums, more games, and increased free odds in Craps; I detected a change in attitude too, as there clearly was a push towards more friendliness. On this last visit, though purely guessing, I'd have to say that's out the window, and upper management instead is flailing about blaming the employees for the decline in profits, and that is having the usual effect on mood. I also get the impression there and at the Greenbrier that WV in particular takes quite a chunk of the proceeds, challenging the ability of these places to make a profit. 


Some things I hadn't noticed before. The Craps table, only one going during the week [can't speak for the weekend], does go 24/7. When I cashed in some chips, the cashier had a device not too different looking than an ink pen that scanned the $100 chips! That I hadn't seen before. Love having the sportsbook there, connected to William Hill. By god if you need a break there are lots of nice chairs to sit at and watch some sports! The minimum bet is $2, so I feel free to just bet on anything I have a notion to, I find it quite fun. And the missus, not a gambler otherwise, will place bets too - that goes over well. So far you can't place bets with a smartphone - that will change. When it does, I could see them getting rid of it, so I'm enjoying it while I can. 

I hit the buffet for dinner instead of lunch for once. Not bad, but not much. Too bad they don't have Indian food, would love that. Just sort of the usual. I did notice the price went up at 4:00, and it seemed to me that you could go in just before 4:00 and get the dinner selections for the lower price. I don't know of course if the selections get better as time goes on?

Crappy Variance:

This time I decided to play the Darkside in Craps and really got clobbered. I really am trying to hone my techniques for taking some of the abandoned action on the 6 and 8 to resolve darkside that occurs with other players. It really is hard to pull off, darkside players being hard to draw out the way they are, not all take 'no action' on 6 and 8, and are enough of a minority of players they are sometimes absent altogether or not near me. I've never been able to take some of that action at Charles Town in fact - I seldom do anywhere in spite of my efforts. So I decided one thing I needed to do is to play the Don't myself to help break the ice, though you would think I would have figured this out long before. 

I always superstitiously stick to the same side, so if I start on the Darkside I don't deviate during that session. I also typically only play the DC, this limits my action compared to what I do playing the Rightside. Sure sounded like a good idea. 

When I approached the table there was a sign that said they were raising the table minimum shortly, but I didn't see where they posted what that min was. I couldn't find a spot and hate squeezing in; but I figured spots would open up once the min was raised. Spots opened up as I figured, though at that place I still couldn't see where the minimum was posted. I looked at what someone was betting on the line, $15, and concluded that what I had suspected was correct, that the min had been $10 and was now $15 [it's never $5 that I have seen]. I played for about an hour and kept my free odds bet to around $40, adjusting it depending on what the number was to resolve. All of a sudden I noticed someone was betting $10! I was making a bigger bet than I needed to at all, as I am a believer in increasing the odds size if I want to bet more, and never increase it on the line if there is room with the odds. I have no idea what that sign I saw about increasing the minimum was about, makes no sense. I just feel that there was no way the min was $5 to being with, as when I've been there at times of day when you seemingly only get a few stragglers playing and the min is never less than $10. But somehow circumstances led me astray* on the matter; I went back to the lower min; naturally this is when I started to get killed. 

Just for the record I did strike up a pretty good accord with another Darksider, and let him know how lucky I usually am with the 6 and 8. Unfortunately, for whatever reason he was not one to give up his action on the 6 and 8 and only nodded at my remark. 

The experience reminded me once again how utterly unable a person would be able to decide which way works best to play Craps just going by his own observations, not knowing the math had been worked out. Even an intelligent person can easily be deluded into thinking he can quickly get some intuition on the matter. I'm fairly sure what I would have concluded from this session. Some of my worst losses previously have occurred playing the Darkside, and that along with the latest would probably have me conclude it is the absolute wrong way to go, intuitively you feel the amount of playing time has been sufficient to make a judgement. And I can say absolutely and positively I could play for eons and not conclude that the only thing that prevents playing the Don't from being a fantastic moneymaker is the fact that the 12 on the comeout pushes. I've never gotten the sense that it matters at all. If I was ignorant that this is actually a fact, I think I would pounce on somebody claiming such a thing with a "No Way!". During this session the 12 pushed for me exactly once; I'm very attuned to the irony of the seeming irrelevance of that and always keep track. In fact during this session I fared pretty well against the 7 and 11 on the comeout too, not getting skewered much with them, though I didn't track those for sure. My impression was definitely that I was getting past the comeout better than usual, quickly setting up three bets to the point where the odds were in my favor, then only to see them get picked off.   The Rightsiders must have done OK, each shooter was killing me, then on the other hand hardly none of them were come bettors, and no doubt lost plenty of money on the sucker bets. I don't remember anyone coloring up with a nice big stash. 

Notice above how easy it is to write something like "naturally this is when I started to get killed. " If I learned Craps the way most people do, from other players and the dealers, and thought I could also learn the best way to play from observation, I'm not sure, seriously, how much superstition would affect me. I certainly have to fight it off, this time having to dismiss the idea that the dice noticed I went from $15 to $10, that I was showing fear in other words. They certainly did go after me at that point, one of the dealers remarking "that's just uncanny" as he scooped away my DC bets one after the other, knowing the odds had been in my favor. So do I really believe that? I do have to keep asking myself that.

*I realized I can't keep saying "hornswoggled"


ChumpChange Jul 23, 2019

Some casinos will grandfather you in at the lower table minimum if it goes up while you're at the rail. So people walking up to the table can't really judge what the table minimum is by what people are betting. The posted signs are what the table minimum is. People can still bet at the lower amount until they leave the table, bathroom breaks excepted. After an hour or so most grandfathered players have left the table.

odiousgambit Jul 25, 2019

Casinos I'm familiar with don't grandfather, those that do are showing they care, not something Hollywood/Charles Town is known for.

You can't see that sign for the minimum where I was. Of course I could have [should have] just asked. It's still a mystery though as I am confident the table was never at $5 minimum. The sign announcing the raise in the min was removed, but has anyone ever heard of the house wanting to raise it at a busy table and then changing their mind?!

Mission146 Jul 26, 2019

Great write-up! I don't have much to add, shame you couldn't pick up too many of those sixes and eights that other Don't players have seemed not to want in the past. It'd certainly be nice to find a table with someone betting substantially over the minimum that would let you take their 6/8 action!

odiousgambit Jul 26, 2019

thanks, Mission, good to see you back too

I'm repeating myself I guess, but the main problem is getting these darkside players to warm up to you.

Will I continue to go darkside every session from now on, to make myself seem more like 'not the enemy'? Still not sure. Snakebit too on that superstitious level. It is true that knowing it's possible one of these days I might get some of that action that I feel at least a little smarter about my gambling, low roller as it is anyway.

FleaStiff Jul 27, 2019

ASK what the minimum is if you can't find the sign. Sometimes its these newfangled signs that look like clear plastic unless viewed from a certain angle.

Nothing is worse than being whipsawed, but I would never want to feel obligated to the dark side.

no action for me on someone else's no action decision.

state's view casinos as tax revenue and later realize that so neighboring states.

gordonm888 Jul 27, 2019

I played Charles Town frequently about 7 years ago. Pai Gow Poker tables were often all at $50 minimum (or higher!) The poker room raked 10% (5% for the bad beat bonus) which is so high that it changes playing strategy. Still, I had fun.

odiousgambit Jul 27, 2019

>$50 minimum (or higher!)

you can see how they had it made! where do you play these days?

Posted by odiousgambit
Dec 31, 2018

John Daly

The guy is not buying the idea that he must now do complete abstinence, which makes me think he didn't go the Gambler's Anonymous route. Expressing some regret, not much, and a claim he quit the high roller bit. We'll see.

He is definitely the guy who nearly broke the bank at the Greenbrier a few years ago [but a loser overall I don't doubt in the slightest]


standbymyman Dec 31, 2018

I don't think he has anything to high roll with.

odiousgambit Jan 01, 2019

I agree, he is not a guy with control over such a thing any other way. Beloved golfer though.

Posted by odiousgambit
Nov 29, 2018

One Field Sobriety Test

ONM's blogpost got me thinking about the one field sobriety test I took in my "career" ... my career of driving under the influence, now over. There's 'somebody up there' who was looking out for me, and he's probably in trouble, as there has to be up there as well those who would say I richly deserved the opposite treatment.

There is one, one!, solitary time I got pulled over. I had made a two lane change to get to an exit I almost missed, and it was a bad place to pull that stunt. I was leaving a racetrack* that was new to me, and it turns out the state police had a station near the track. That's a bad situation, and yes I was later quite mad at my friends who forgot to tell me that; of course the gendarmes naturally decide that they want to nail each and every drunk driver who exits the track.

And I had put away plenty. Martinis. Yet I knew I was OK, and passed the test, including the breathalyzer. The cop was slowly realizing it all along I guess, and when I blew into the tube he said "you've had maybe a couple of drinks" or somesuch, and let me go. Today I feel I can say that the thing that saved me has to be, has to be!, that the bar there was serving watered-down booze. I certainly had more than two in a short enough period of time too; I should have blown something close to the limit on the basis of how many I had.** Somebody looked out for me.

PS: people say 'zero point 8' but it is actually 0.08 and actually I suspect a % sign belongs there too. Looking it up now, of course, and having trouble confirming the % thing. But 0.08 without the % sign means 8 percent, and I think that would kill you.***

*going to racetracks for me back in the day resulted in a bad experience nearly every time. It finally turned me against gambling generally for the longest time. Somebody up there was giving me a message.

**edited - ... depends on time and your weight, one drink being equal to another, and a lot of things, but 4 every hour is more accurate apparently [don't quote me]. My edit is to say I think now that 4 per hour, the first hour, will get you to 0.08 'depending' on this and that, but after that only 1 drink per hour will maintain you at 0.08 That's putting it away. I hear some states are tightening up the 0.08 thing too

*** Edit: yes the % sign belongs there. And 8% is what a strong beer is, so of course it would kill you, as would 1%.


onenickelmiracle Dec 05, 2018

Everyone thinks they were so bad driving after having a few, but I'm beginning to think we're pretty much lied to about what really drunk driving is, and we've probably never done it or just once or twice. Of course then, there is the statistics, but beyond just drunk driving, I don't think they ever subtract bad driving. In other words, the people are drunk, but the drunken part never really played a significant factor, but took all the blame. Some day I'll waste money on a portable breathalyzer device, so I'll presumably never worry again. Accuracy matters though, I'd hate to just assume .07 is good, when the police instrument might read .08 or .09.

odiousgambit Dec 07, 2018

I think if you think you might blow 0.07 it's time to take the advice of those who say "don't take the field sobriety test, or blow into the tube"

I'd say though if you've had, say, 4-5 drinks but over a period of hours [not just one hour], and you were eating too, a guy can assume he'll do OK and take the test and blow into the tube too, but that depends on your weight as well, and being aware some drinks that count as two for one, like the way martinis generally are made