odiousgambit's Blog

Mik Ado About Nothing

Nothing but 10 bucks anyway. 

A hearty "hiyo silver!" to anyone who gets the joke in the title. It's a convoluted path to it, and of course having to explain your joke is the sure sign of a bad joke. 

After my previous blogpost about why I had decided against getting in on the goodies offered by the competing online gambling venues newly authorized in my state, highlighting MGM in particular, I decided it was only right to go back and see just what they were up to recently.  The initial $500 freebet offer had timed out, but they replaced it with a $50 freebet offer that required a player to deposit $10... just deposit it, you didn't have to bet it, the 50 bucks was yours to use [though you didn't get to keep that portion, only any winnings]. Additionally there was an assortment of $2.50 freebets up for grabs, and all of these freebets had T&C clearly spelled out, with no play-through to do. 

At this point I felt I might as well just see what happens, I'm thinking blowing $10 just to satisfy my curiosity is worth the price. And it will be $10 down the drain if they hit me with a withdrawal hassle, something they have already said they reserve the right to do. But I paypal them this amount in the hope that since it is paypal, I'll get no hassle when withdrawing, while honestly fully expecting that they will pull that stunt. Yes, I repeat, I think it is a complete scam to freely allow deposits while demanding scrutiny only on withdrawals. 

I was more interested in having more than $10 to cash out than making a 'good bet'.  I figured the trial withdrawal needed to have winnings included or they might OK it without scrutiny if it was only the amount I deposited. I picked a -250 hockey moneyline bet for my $50 freebet.  Hockey this year has featured a few teams at the top of a division winning 75% of their games, while the teams on the bottom have been correspondingly awful. But the day I picked was a good day for upsets and sure enough the $50 freebet went bye-bye. Fortunately not all bets bombed, so I had $13 in the account after all bets were settled. 

I was now ready to test the withdrawal experience and started the withdrawal request March 30th in the morning. An email acknowledgement indicated I might have to wait 5 days for a response. Well, on the morning of April 1st, April Fools, I see the indication that the withdrawal has been "reversed" ... this took 2 days.  This is the way I would expect my account to show if I had cancelled the request myself, since they wanted to give me every opportunity to change my mind every time I checked up on the request, constantly posing for me the icon to click on with the word "reverse" prominent. But I had not clicked on 'reverse'. 

I have a very strong suspicion that this was done in order to claim that I activated the reverse myself. Or perhaps to get an employee's boss off the underling's back. I can easily imagine this going on in such an organization: "you're granting too many requests!"



That no email was received as explanation* amounts to support for my theory. Or perhaps this is even standard procedure, a way of denying my request without having to explain. Might go like this, "Reverse that, just see if the guy drops it, most of them do for that amount, and he might just keep on gambling, many go ahead and deposit more money. When and if he ever wins big and wants his money, that's when we'll finally reveal all of his winnings were just a pipe dream." At least a dream when it comes to getting it without a big hassle. 

Well, as of now, I have put the request in again, it isn't tagged as un-withdrawable, a category that evidently exists. Should it go through this time maybe I'll revisit the whole matter.

*as of 4 days past request date, 2 days after reversal

A Pondering Gambler I

A Pondering [Online] Gambler I ... or actually, An Abstaining Gambler Me [that loses something though].

Apologies to Gilbert & Sullivan in any case

So now there are half a dozen different outfits offering online sports betting in Virginia, generally with fairly lucrative joining offers. Yet I have declined to participate ... so far. 

I've mentioned before I fit the profile for a typical gambler in some ways, but not so in many others. I certainly have a list of types of gambling I simply have no interest in, notably lotteries, and a list of 'just-not-going-to-do' as a matter of self-control. Pertinent here: online casino gaming , ain't doing that. However, though I admit sports betting should make me hesitate for all the same reasons, I confess I'm willing to take that particular plunge. Ummm,  'Depending'. 

I suspected my first problem was going to be that I am a holdout against getting a smartphone. Since I really don't want one, I resent the current trend towards apps exclusive to them. I discovered, however, that even though these outfits favor the use of phones, at least some of them realized there were a few old coots out there without one who might give them some business. Investigating MGM's Virginia venture first, I did see they were attempting to do business using just a home computer.

I signed up with "Bet MGM Virginia", giving name, address, d.o.b., and phone number. Quite eager were they to get a deposit immediately, and boy was that going to be easy, multiple ways to do it. But thanks to paying attention to what people have said at WoV, I knew I was going to have to be happy with terms and conditions. So I did spend some time pouring over them; you know, really, with most internet things I just skip doing this, so it was almost like a new experience. Most of the time just trusting that the other side isn't up to something works fine. But this is gambling, and we know the nature of that. 



As I suspected, there it was, the deal-breaker. They reserve the right to give you a hard time when it comes to withdrawals. Name, address, phone no., some claim about d.o.b., that was fine for deposits, but withdrawals? It seems they need more, a lot more. The perversity of that is remarkable. You might want to defend them and say they need to be sure you are who you say you are, and that you're not fraudulently accessing funds. In order for me to buy this explanation, though, I'd like to find out why they don't insist on this level of scrutiny right from the beginning. That they *do not* suggests a special kind of casino perspective: it's no problem to take in fraudulent funds if you refuse to pay winners. All those winnings, in this case, are just pipe dreams, not affecting the house. When it eventually is revealed the player shouldn't have had access to the funds he used, overall losers included, then there is the possible pain of returning those funds, but it was all make believe money anyway for any wins. But there is also the percentage of those funds that will never have to be returned, almost for sure a nice hefty slice. There's the expression 'easy come, easy go' but this is switched to, 'easy come, ain't gonna go'.  Not all of it anyway, maybe not even most of it, these funds that the online gaming should never have received in the first place. Far be it for Virginia to have insisted all scrutiny be in place for deposits as well as withdrawals, they've just plunged into this allowing the gambling interests to do whatever they want, bringing with them much of the nefarious doings they learned from overseas operations. 

There will be plenty of guys who provided funds legally just deciding to postpone withdrawing in the face of onerous identification demands, while continuing their betting. This means increased likelihood the money will dwindle away in the meantime, of course. Don't think that isn't a known factor. 

I couldn't find anything indicating I might not get the withdrawal scrutiny if I used Paypal. But I did wonder if that might not be the case. A betMGM offer for a free $10 no deposit bet came up, so I thought that might be a good test to see if I'd be hassled if I won the bet and tried to withdraw the winnings. I started the process and found I had to download something to verify my location. My operating system completely rejected this download, with a big warning, and giving no option to bypass the rejection. I waited a couple of days and the problem had been fixed. Unfortunately I was then informed I had already used up my free bet, which I never was able to make. Well, well. 
 
I've read accounts of players getting into it with casinos over disputed this and that on WoV, and sometimes prevailing, but I have to say it is the last thing I want to find myself doing. Depending on the amount, I'd likely be happier kissing the money goodbye rather than going through something like that. It would totally destroy my enjoyment, the only reason I would be betting in the first place. I think this also separates me from many other gamblers. 

A certain person, not a gambler I think, might ask why bother with withdrawing when it is -EV in the long run. Well, I do know that in the long run my bankroll is likely to dwindle away. But I don't know if I'll stick to a particular outfit. But more than that, to decide something like that is just too much, too much. I'd suggest to such a person that if they can make a decision like that to give up any gambling they do or dont start. It's just wrong!

In case I didn't make it clear, if they did have you give extraordinary evidence you are who you say up in front, before making a deposit, I would decline to do so. I don't want them to have that much information on me. I just like the way that is done that is still available at some times in some places. You walk in and anonymously place your bet, keep your slip, and anonymously collect any winnings too. It may be they open such betting parlors in various places near me. Looks like I'll be waiting for that.

Not Loving It

Two developments with the dice-setting:

* It must have been noticeable that I was getting different results than the Wizard with the 6.04 shooter. Then it occurred to me that the Wizard was using a modified formula that incorporated the lower HE you get with full odds using the 3x4x5x free odds. I had dismissed that, thinking someone with skill would not want to use the free odds, since they add variance without changing the EV. That was stupid: if you can shoot with less 7-outs, the free odds benefit from it enormously in fact, in the player's favor that is ... it's no longer the same matter of not changing the EV. So this explains the difference and why such a small change as one less 7 rolled in a thousand rolls can pretty much take away house advantage as the Wizard shows. Though he doesn't put it that way and we are having to rely on my conclusion that 6.04 means one seven rolled per 6.04 rolls, which no one has confirmed.

* I have arrived at the Greenbrier. The Craps minimum has been raised to $25, yuck. And they have decided that a max of three players are allowed, one on each end and one just to the *left* of stick. All this including the $25 min due to the virus I guess. I mentioned it's nuts to think you can accomplish anything from one end of the table [12 ft here] and my new throw is too hard to pull off left-handed [for me] and would be even worse to try right handed from left of stick [it's quite different]. So after getting all worked up over it I can't try it. Great. And the new minimum means minimal time at the Craps table as well ... I've never wanted to spend much time at a $25 Craps table.

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!

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/#post749278


Am 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/