Posted by odiousgambit

Dec 03, 2020

Dec 03, 2020

## Don't You Just Love It Record

the below is from the "don't you just love it" thread and I want a handy record.https://wizardofvegas.com/forum/gambling/dice-setting/35372-dont-you-just-love-it/2/#post787041

>>>

I want to check some assumptions that I am not sure are correct, and my math could be wrong too

the question does come up, how much would a shooter have to deviate from random in order to have an advantage? So I go to the Wizard's pages, see first link, and find that the ratio that is used is called rolls to sevens, and the first increment seems to be a ration of 6.04 versus 6 for random. It strikes me right away as odd, since the change is noted in the denominator, ie 1/6 versus 1/6.04 ............ This is one thing I'm trying to check, can someone confirm that I am interpreting that right?

However if we try to put such a small change in the numerator, I can see why this is done. We get 0.99337748344/6 ........... yeah, that's awkward.

In the meantime it must be noted that the chart in the link shows player advantage at 6.04. For one thousand rolls, 166.667 [1000/6]would be random and 6.04 [1000/6.04] gets you 165.5629 per thousand, or about 1 roll of seven less, per thousand rolls! That's not much for sure.

So I am trying to see if I am interpreting it all correctly, or not.

https://wizardofodds.com/games/craps/appendix/4/

>>>

I'm at the point of being satisfied that my assumptions have been correct, rereading the link about rolls to sevens and also noting 1 divided by 6.04 and 0.99337748344 divided by 6 both equal 0.1655629139, so that has to be right. I also have to say the bit about 166.667 versus 165.5629 per thousand rolls is right, can't see how it would be wrong.

I'm still befuddled a bit by 'skill factor', not so much the idea but the ability to apply the math, so ... Well, anyway, one thing I note in the Wizard's pages on this is that somehow there is no mention of the 'flying V' dice set. If you can stay on axis with that set it rules out a roll of 7 using 5+2 or 6+1. If staying on axis, a big 'if' ha ha, the only possible rolls [will have] 2 sevens out of 16, or 1 out of 8 versus random's 1 out of 6. You can check this out yourself with a pair of dice. I wish we had a chart, then, with the effect of using even a random roll in the comeout and then following up with the flying V after a number is marked to be resolved. This has been my practice, but the Wizard's chart uses hardways sets for some reason.

Craps dot com image for the flying V

Actually any dice that are set as identical pairs, but then have one die turned 180 degrees like that, might produce the 'less 7s' effect, as far as I can tell; it can certainly be flying 2s instead of flying 3s.

>>>

I was thrown for a bit by realizing you can get different sets of numbers, 'depending'. It is easy to intend to start one die rotating and the next thing you know you've got the other one rotating and get lost.

OK, so with a die with 2 and 5 as the axis, giving the axis a right and left side by facing the 6, say, the 2 is on the left and the 5 is on the right, call it the 2-5 die. For the other die with 6 and 1 as the axis, arbitrarily facing the 5, the 6 is on the left and the 1 is on the right. The 6-1 die call it.

With the 2-5 die unchanged after throw, the four numbers we get with the spin of the 6-1 die are 8, 7, 5, 6, the last through double-pitch.

2-5 die making a rotation on axis that 6 comes up, making the four possibles 11, 10, 8, 9 same way.

2-5 die making another rotation the 4 comes, and the four possilbes are 9, 8, 2, 7 ...

2-5 die making last rotation, the 1 comes up and the four we get are 6, 5, 3, 4

we encountered two 7s out of 16

However, there can be a 5-2 die if we choose to face the 1 on the die, that is, 5 on the left, 2 on the right.

Going through the same way with the 6-1 die, 8, 7, 5, 6.... 6,5,3,4... 9,8,6,7... 11,10,8,9............. two 7s

There can be a 1-6 axis die if you choose to face the 2. Against a 2-5 die that does the rotation on axis:

1-6 die unchanged, 9,7,4,6

1-6 die has the 2 come up, 8,6,3,5

1-6 die has the 4 come up, 10,8,5,7

1-6 die has the 5 come up, 11,9,6,8.................... process also has two 7s

1-6 die now needs the numbers from a 5-2 die. Somebody may tell me these are not the only possibles but I hope this is it......................4,7,9,6... 3,6,8,5... 5,8,10,7... 6,9,11,8 ....................... two 7s

So there are 16 possibilities, but only for each of four scenarios, making 64, which has nearly killed me. Note that a player does not need to decide anything but to have the flying V, or even flying 2s, all of which is quickly set.

>>>

I'm still going with this.

I wanted to see just how many less 7s a player needs to roll before it's +EV in rightside Craps. So, I came up with this, and maybe you'll tell me it can't be done this way, but it seems to offer an insight unless I am very much mistaken. So I took the following,

the familiar figures for each number that can be rolled:

2....1/36 rolled and loses 1 unit

3.....2/36 rolled and loses 1

4.....3/36 rolled and wins 3/9 of the time

10.....3/36 rolled and wins 3/9 of the time

5...4/36 rolled and wins 4/10 of the time

9...4/36 rolled and wins 4/10 of the time

6...5/36 rolled and wins 5/11 of the time

8...5/36 rolled and wins 5/11 of the time

7 6/36 wins 1

11 2/36 wins 1

12 1/36 loses 1

I put it in a calculator as

[1/12*1/3]+[1/12*1/3]+[1/9*2/5]+[1/9*2/5]+[5/36*5/11]+[5/36*5/11]+[1/6]+[1/18]

for the winning combinations, in order those are 4,10,5,9,6,8, when winning, then 7,11 in come out

for the losing combinations,

-[1/12*2/3]-[1/12*2/3]-[1/9*3/5]-[1/9*3/5]-[5/36*6/11]-[5/36*6/11]-[1/36]-[1/36]-[1/18]

which is 4,10,5,9,6,8 when losing, then 2,12, 3 in come out

the sum of the winners is +0.4929292929292929

the sum of the losers is -0.5070707070707071

and the sum of both is the familiar -0.0141414141414142 house edge

So after pondering this quite a bit, decided what it would look like if the shooter rolled one less 7 in about one thousand rolls, and chose 972 rolls, a multiple of 36. I then postulated that if the shooter rolled one less 7, it would be when he set the dice for that in numbers to be resolved, while rolling without setting dice in the come outs. So in the equation, only the chances when resolving did I want to alter. To make the shooter slightly more unlucky, what is rolled instead of 7-out will be deemed to be a roll that does not resolve, so only the part of the equation that gives the wins is unchanged while the chances of a loss do indeed decrease slightly for each.

So when rolling to resolve, instead of the ratio 162 per 972 rolls [1/6] such shooter enjoys a mere 161, while the chances, say, for rolling an 8 stay at 5/36 or 135 per 972 rolls. This makes 161 ways to lose and 135 ways to win, 296 total ways, and 161/296, the chances of losing, now to be 0.5439189189189189 instead of the 6/11 that comes with random results, or 0.5454545454545455, a difference of 0.0015356265356266 which seems to fit. So in the losing equation above, the same process for each takes place and I get:

for the 5s and 9s, 4/36, or 108/972, 161 ways to lose vs 108, total of 269, 161/269 checks as 0.5985130111524164 chances instead of the 0.6 of random's 3/5

for the 4s and 10s, 3/36 = 81/972, and 161+81 = 242 total ways, 161/242 = 0.6652892561983471 which is mighty close to 2/3 and 67%

-[1/12*161/242]-[1/12*161/242]-[1/9*161/269]-[1/9*161/269]-[5/36*161/296]-[5/36*161/296]-[1/36]-[1/36]-[1/18] = -0.5060841337666279

that is reduced from -0.5070707070707071 however,

+0.4929292929292929-0.5060841337666279 = -0.013154840837335

I get a house edge of -1.31% for the 6.04 shooter versus -1.41% and that is definitely progress but the shooter has to be better it seems.

Now I do realize that this process is a little wonky, but to me it does not seem totally flawed. Or can somebody tell me that it is? If not totally flawed I am going to continue with it.

>>>

Trial and error continues, to see at what point rolling less 7s in an unknown way gets a player to +EV. The next level of skill noted by the Wizard is a 6.08 rolls to sevens shooter which indeed means we go to about two missing 7s after 1000 in theory if continuing with the assumption this means one 7 per 6.08 rolls, 1/6.08 instead of 1/6. I'll continue with the above stipulations, that the come-out rolls are without setting the dice and random results, and that rolling less 7s helps avoid 7-outs but does not increase the number of wins. That latter stipulation will have to change when we go to higher rolls to sevens, and that is going to give me a headache it looks like. I'm not expecting much change but let's see.

Sticking to the admittedly deviating 972 rolls, again instead of the ratio 162 per 972 rolls [1/6] such shooter enjoys a mere 160, while the chances for rolling a 6 or 8 stay at 5/36 or 135 per 972 rolls, total of 295 possibles for resolving.

for the 5s and 9s, 4/36, or 108/972, 160 ways to lose vs 108, total of 268 possibles.

for the 4s and 10s, 3/36 = 81/972, and 160+81 = 241 total ways.

-[1/12*160/241]-[1/12*160/241]-[1/9*160/268]-[1/9*160/268]-[5/36*160/295]-[5/36*160/295]-[1/36]-[1/36]-[1/18] = -0.5050902973936376

-0.5050902973936376+0.4929292929292929 = -0.0121610044643447

-1.22% ; so we are getting somewhere but not to +EV

How do I solve the need to adjust the winning side of the equation if I go to, say, 6 less rolls than random of seven, per 972? Help accepted!

Posted by odiousgambit

Dec 07, 2019

Dec 07, 2019

## Blasphemy

Posting this as a blog post to show the number-crunching. That has been double checked but please advise if there are errors that survived. I also started a thread, https://wizardofvegas.com/forum/gambling/blackjack/34025-blasphemous-blackjack/#post749278Am I now to be an Apostate now in the Church of the Wizard?

I've considered this for a long time and now I'm going to do it. My next planned opportunity at BJ will be an 8 deck, dealer hits on soft 17s game. In the past a $5 game has been available, but I think that has changed to $10.

For -EV play, which is pretty much what I'm about , it's seemed to me for a long time that it is a reasonable thing to trade increasing the HE in return for greater variance, an un-Wizardly approach it must be admitted. In fact advocating this may actually horrify the Wizard. Yet I submit* for the negative expectation player, Variance can be more valuable than lower house edge, especially when it involves modest surrender of edge. In a game that is too low in variance like Blackjack [flat-betting], I think it may be the way to go, along with some precautions and some caveats.

Previously I was happy with the idea that my BJ play and my Craps play, all I ever do anymore in table games, were about on the same level, i.e., against something around 0.5% HE. But I have really found that I enjoy the Craps play while the BJ? ... not so much. The difference I feel is pretty much around the difference in the Variance, high [because of free odds] in Craps and low [flat-betting] in BJ.

To fix this in BJ, there are plenty of folks who have said to apply card counting techniques, and certainly doing that would be the end of flat-betting and low Variance. I have considered this and have gotten far enough long to have learned BS - but that's it, and not to the level of reflex either. The fact of the matter is that I don't put the time in at the casino like I'd have to, this for a number of reasons, including that I just don't live close enough to one. Yeah, there are ways to learn it outside a casino, but I'm going to say that won't work unless you combine it with casino time - it wouldn't work for me for sure.

Randomly varying bet size on hunches or whatever would increase Variance too, but who is going to advocate that? Nope, not going down that road, even though I wonder if it makes more sense than flat-betting.

I currently believe the way to increase the Variance is to increase doubling and splitting, though it is said that double, double means toil and trouble. Take those 'precautions' ? The cost in HE should be reasonably low.

from Wizard's table, see link, which views it from player's edge:

If the standard for the no-brainer is in a dealer stands on 17, 8 deck game

soft 18, doubling vs 2 [apostasy]0.120669... against standing [BS] 0.123432

the difference [or delta], in absolute value, is 0.002763 ...

... then I will postulate that any similar penalty in HE can also be deemed a low penalty, but how otherwise to define low? On a search for some possibilities [suggestions welcome] with dealer hitting soft 17 I find:

soft 13, doubling vs dealer 4, 0.068239 [apostasy].................. against hitting, 0.104016 [BS]

delta 0.035777

soft 14, doubling vs 4, 0.067545.................. against hitting, 0.082320

delta 0.014775

soft 14, doubling vs 3, 0.050574...................against hitting -0.001503

delta 0.052077

soft 18, doubling vs 7, 0.222746 ............... against standing, 0 .401292

delta 0.178546

soft 19, doubling vs 5, 0.410465 ............. against standing, 0 .438984

delta 0.028519

doubling with 10 vs 10, -0.006376.......... against hitting, 0.026417 [sampling player 6,4]

delta 0.032793

doubling with 9 vs 2, 0.065231.............. against hitting 0.074560 [sampling player 6,3]

delta 0.009329, yes indeed

doubling with 8 vs 6 , 0.080627 ............................against 0.106038 [sampling player 6,2]

delta 0.025411

splitting, das allowed, 4,4 vs 4, 0.003880................ against hitting 0.043972

delta 0.040092

splitting, das allowed, 6,6 vs 7, -0.255866 ...............against hitting -0.218600

delta 0.037266

If low is to be defined as a delta that starts with zeroes in the first two decimal places, then only one, doubling with player 9 vs 2, qualifies. On the other hand, 0.009329 is a sacrifice of 9.3 cents per $10 bet in that circumstance, and I think we can go further than that. A change to a zero in the first decimal space only means getting into dimes, and I am going to declare that to be acceptable.

Should it be no more than about 4 dimes? I'm thinking so, and that will mean [if $10]

soft 13, doubling vs dealer 4, 0.068239 [apostasy].................. against hitting, 0.104016 [BS]

delta 0.035777, less than 40 cents anyway

soft 14, doubling vs 4, 0.067545.................. against hitting, 0.082320

delta 0.014775, it's on!

soft 19, doubling vs 5, 0.410465 ............. against standing, 0 .438984

delta 0.028519, a good qualifier

doubling with 10 vs 10, -0.006376.......... against hitting, 0.026417 [sampling player 6,4]

delta 0.032793, likewise

doubling with 9 vs 2, 0.065231.............. against hitting 0.074560 [sampling player 6,3]

delta 0.009329, yes indeed!!

doubling with 8 vs 6 , 0.080627 ............................against 0.106038 [sampling player 6,2]

delta 0.025411, qualifies

splitting, das allowed, 4,4 vs 4, 0.003880................ against hitting 0.043972

delta 0.040092, squeaking through with round-off

splitting, das allowed, 6,6 vs 7, -0.255866 ...............against hitting -0.218600

delta 0.037266, qualifies

while the below would be rejected:

soft 14, doubling vs 3, 0.050574...................against hitting -0.001503

delta 0.052077, which really isn't too bad but I want to draw the line somewhere

soft 18, doubling vs 7, 0.222746 ............... against standing, 0 .401292

delta 0.178546, whoa, getting into dollars

So that is where I'm at for the moment and for the next anticipated circumstance. It gives me eight additional opportunities to increase my bet and thus the variance; I wish there were more but I do have to mind the cost.

Further caveat has to be to limit amount of total action. Negative expectation betting just turns from 'no big deal' into foolishness. I am thinking I will do one shoe per day, and I hope it means increased enjoyment . I'll go so far with my blasphemy as to say I think every negative expectation player out there should double 9 against a dealer 2. I wish I could calculate EV/SD on this but I don't know what the change in Variance actually is. I'd really be impressed if someone knows.

12-15-19 additions

soft 15, doubling vs 3,-0.002766 .......................... against hitting, 0.029292

delta 0.032058

soft 16, doubling vs 3, -0.005661 -0.005661.............................against hitting, 0.008799 0.008799

delta 0.01446

soft 17, doubling vs 2, -0.005768 ..........................against hitting, -0.000625

delta 0.005143

splitting 2,2 vs 8, das, -0.176800.....................against hitting, -0.157443

delta 0.019357

splitting 3,3 vs 8, das, -0.231032.....................against hitting -0.218685

delta 0.012347

splitting 7,7 vs 8, das, -0.391334............................. against hitting -0.376254

delta 0.01508

This gives me a total of 14 deviations from BS, 15 as it shows up in a strategy chart as 5,5 is shown as a splitting decision on charts even though 5,5 is to be just considered a player 10 .

*I'm curious as to whether anyone has seen a bonafide gambling writer cover this topic

https://wizardofodds.com/games/blackjack/expected-values/

Posted by odiousgambit

Dec 01, 2019

Dec 01, 2019

## Charles Town V

TLDR: Back again at Charles Town, fifth visit, staying at the hotel for the first time. The sportsbook is changing for the worst, but still there. I apologize to the Wizard. Trying to get casino credit was a bummer. Craps went well, but my old quest to find the right kind of darksider is a bust again.I have other business that brings me close to the casino at Charles Town WV, so taking the otherwise-a-little-bit-too-far trip there when I have that other reason was in order again recently. To be honest, I probably could have put this other business off for a while, but my last trip awakened their marketing department and they had been sending me some fairly nice offers, including a room and plenty towards food . It worked, it was on.

This was the first time I had stayed at their associated hotel, which for some reason is not attached to the casino. This has them running a shuttle every 15 minutes, 24/7, and I never heard anyone complain it ever runs late. It also goes to other hotels, but I don't have those details. Room, comped 2 nights, was plenty nice, no complaints from me. The booking desk failed to mention the $10 per night un-comped fee, but I was expecting it from talking with them before. So I don't have a beef, except I think it is worth mentioning such lapses, which just shouldn't happen. The Trip Advisor reviews constantly mention dirty carpet, but I can confirm what the manager, in responses there, is pointing out: the carpet is actually just worn and needs to be replaced, a quality of modern carpet fibers that I was familiar with [they don't wear out, they ugly out]. Some reviews didn't like the continental breakfast, but honestly I don't know what such people are expecting, I never expect much from those things and frankly, judging by the clientele, which I am sure you can picture, I have to believe few of them ever stay at a place nice enough to have something better laid out - sorry. The gripes are just sour grapes from losers? The employees were all trying hard and very nice, and nobody claims otherwise in those reviews.

The sportsbook, while improving the quality of my experience there immensely, is showing signs of WV tax fatigue, I'd say. The last time I was there, just a few months ago, there were tables in front of every piece of furniture with pencil stubs aplenty. There were sheets printed up with betting information on every sport neatly set out, with a special desk there to print up whatever else you needed. This time the tables were nearly gone, and pencils were hard to find, what happened to these things? Pre-printed information sheets had disappeared as well. The electronic board on the back wall was going strong, but that thing is necessarily incomplete. There was no separate desk to provide information, it had turned into a bar [that was closed to boot]. I could see I had to get into line to get information; I asked for NHL this and that. The evidently quite new clerk's only training seemed to be "you should be surly toward these schmucks so they don't bother you too much". She printed out what I asked for on a flimsy slip, looking at me like I had two heads for wanting it.

Bear in mind that so far the operation there, William Hill, does not have the mobile app so you can bet using your phone, so you normally would go to the sportsbook to both bet and collect. It just seems to me the place would be in its heyday now for these reasons. Though there could be other reasons for its evident current depression, possibly there are reasons for the blues I just don't know about, like getting clobbered by Pennsylvania operations that do have the mobile apps going. But I smell the bean counters in operation. Things like removing the pencils just reeks of those guys in action. They get called in when an outfit like this finds out they are doing all the work and the state of West Virginia is making all the money. Plus the casino gets a piece of the action somehow too; the sportsbook runs there independently of the casino, just using their facilities.

In any case, though I doubt he reads my blog much, I have to apologize to the Wizard. At times he has confessed he's found old betting slips past their expiration date. When I heard this sort of thing, from him and others, I was going 'tsk tsk'. Back when I was working I had to be careful about details, and none of them were more important than the ones involving money. I was just convinced no way could I ever be so lax about my bets that I'd just misplace the slips or forget about them, the flimsy little things they are notwithstanding. So when it was time to go, I gathered up the slips - puzzled that there seemed to be more slips than I expected - and stashed them into a briefcase, not wanting to take the time to look at them. Once I got to the book, instead of studying them, I handed them in mass to the clerk and indicated I wanted them all checked though "surely some were losers". To my surprise quite a few got handed back to me as "not resolved yet". I almost couldn't understand what was going on. Naturally I then took to time then to look at them closely and realized they were proposition bets that I had forgotten I had even made! So, yeah, looks like one of these days I'll also find an expired betting slip, though I have a little system that's supposed to prevent that. Ye who have confessed to this already, I humbly apologize for my arrogance, I'm next no doubt.

Although I have resolved to quit using casino credit, mostly due to the irritation of having to renew, I was going to apply for the first time at this particular place. Member Mdawg has been contending that the casinos conduct a hard inquiry on your personal credit, while I have been maintaining they do not, and that this is something I've made sure about with the annual free check we can do. His response is to ask if you have checked with Experian and I've had to admit that I haven't. So, once a player goes to the trouble of getting approved and does have this approved casino credit in his back pocket, it's something you have to admit is plenty convenient, and I could do this and then do a free credit check making sure it's with Experian. Having two reasons to do it I tried to apply. To my surprise, I find out you can't apply at the casino anymore! What? They indicated that now you must apply online only, and that you can forget about getting a quick response too.

I don't want to apply online, that doesn't seem like a safe thing to do though I can't prove it is more secure to use SS numbers etc. in person only, still that is as far as I'd like to go. It seems obvious to me that this casino has gotten itself into some trouble with collections and has decided to discourage the entire practice. This would normally be very shortsighted, in my view, as there is so much about it that is win, win for the casino - I have posted about this many times. However, I think it is possible that it depends on the state as to what happens in the legal process of collecting the bad debts. Clearly in Nevada, what with the District Attorney fully cooperating in treating debt as a crime, ready to throw folks in jail, things are greased along quite well for collecting that money. Perhaps in WV a debt occurred with casino credit is treated like any other debt, and not as the act of writing a bad check as in Nevada and probably other states? But I would say sheer stupidity of the decision makers here, with bean counter led crackdowns already in evidence, is also a possible explanation. In any case Mdawg's contention will just have to be taken at face value for now.

The gambling I did was a bit of sports betting and Craps, which I posted about in a thread named "why you should always make a Come bet". In fact it has been mostly here that I first got a little stingy with the Come betting [or DC betting, depending] due to finding the table minimums to be higher. When it was only $5 [that's never at Charles Town] I have been very free with the Come betting, when it was $15 I only did Come betting, no line bets [which limits your action], and it has been 'something in between' if $10. Now I am vowing to always have a Line plus Come bet going and am going to have to figure out how to keep my total action under control.

My luck at Craps went well this time, all of it against negative expectations. As I've blogged before, currently my only shot at any +EV wagering is concentrated on trying to take some of the discarded darkside action I see. That was a bust again, it is really pretty difficult to get the right circumstance. Once I was right next to a friendly guy [important] who was alternating, going darkside when he thought the table was cold, but he never decided to 'take no action' on his bets, including on the 6 and 8 darkside. That makes him the wrong kind of darksider! Otherwise I hardly saw any darkside action going at all, that happens a lot, and when it does go on you need to be next to it. I'll keep trying.

Posted by odiousgambit

Oct 11, 2019

Oct 11, 2019

## Casino Credit/Markers

In case you missed it, and are following the "Fico score" thread, here are some blog posts covering markers and casino credit. The first link is MDawg's blog on the unique credit bureau casinos use to set you up for markers. Be sure and read the comments, which becomes a timeline for me discovering that he is essentially correct with what he says, perhaps not putting things the way I would.the second link is about my initial experience with markers, again, the comments are interesting.

btw I may have decided to quit getting set up for markers, don't like the process of renewing them.

https://wizardofvegas.com/member/MDawg/blog/

https://wizardofvegas.com/member/odiousgambit/blog/4/#post1387

Posted by odiousgambit

Aug 06, 2019

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 isthe 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?

## Comments

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:

https://wizardofodds.com/games/craps/basics/#toc-DefiningtheHouseEdge

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.

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