your favorite uncle's questions on blackjack

[hardin county boy]

your favorite uncle is an artist and tells you he knows you count cards, believes that is a way to gain an advantage in the casino, and that he believes if he played a progression system long enough he would be ever more likely to lose, ever-closer, to the calculated disadvantage of the game he chooses. he says his artist-nature is too math-challenged and sensitive to ever count but he plans to play anyway.

he says the best rules he can find have a .5% disadvantage and he will take 2500$ and play no more than 1000 hands on any given day, perfect basic strategy. he read he would lose less flat betting than varying his bet so he plans to flat bet 25$ until it might happen he loses so many flat bets he is not very practically likely to recover back to zero, at which time he plans to increase to 50$, hoping his luck will change and giving him some prospect of getting back to zero. he knows this may instead simply accelerate his appointment with ruin so he pledges NOT to bet 50$ any more bets lost than the 25$ so he figures his bankroll is 66 units of 37.50 each. he read on a website he will lose all his money about one in ten times this way.

he knows you are better at math than he is so he asks your opinion of how many flat bets down would he be when he "is not very practically likely to recover back to zero by continuing flat betting?" ten?, twenty? some other number?

you are tempted to educate him on advantage play but he IS, truly, a gentle soul and as math-clueless as he says and you know he can afford the losses and enjoys playing so you decide to use your math talent and answer his question.

how many units down do you tell him he will be when it will be quite UNLIKELY he is going to recover to zero by flat betting?

[DSchles]

Define "quite unlikely." I'm not being cute. Ten different people will give you ten different answers.

Don

[hardin county boy]

Define "quite unlikely." I'm not being cute. Ten different people will give you ten different answers.

Don

lets say at point where only a 35% chance of return to zero remains.

[DSchles]

"lets say at point where only a 35% chance of return to zero remains."

Boy, you sure do have a pessimistic view of what "highly unlikely" means! Not even a two-to-one underdog, and you already give up!! As I said, different people would answer differently, but that surely wouldn't have been my answer.

The problem with your question is that there are an infinite number of (or, at least, a great many) answers. Let me explain why. This question falls under the heading of achieving a goal, with a time constraint, for which I provided formulas in BJA3 and Norm followed up with online calculators. The one to use for this scenario is here: http://card-counting.com/blackjack-calculator-c5.htm

(Actually, because you're playing at a disadvantage, there is a way to trick the calculators, by using a different one, for risk of ruin, and using a positive edge instead of your negative one of -0.5%, but I'm afraid that is a bit complicated to explain here.)

Anyway, the problem is that being down a certain number of units isn't sufficient to solve the problem. There is a time constraint that you won't play more than 1,000 hands, so it matters how many remain available to you, when you get down a certain number of units. Playing with 100 $25 units as your bank, I'm sure you understand that you could be down the required number of units to "give up" that you seek at many different points in time: with 800 hands left, 500, 200, etc. And, of course, you also understand that, being down x number of units but with 800 hands left, isn't nearly as hopeless as being down the same number of units with, say, only 200 hands left. So, there is an entire sliding scale of answers, all yielding your requisite 35% probability, of the form x units down with y number of hands remaining.

Do you understand the problem?

Don

[hardin county boy]

in an artsy sort of way i ABSOLUTELY understand that the fewer hands left and the deeper in the hole, the lower the probability of return to zero. i also see what you mean by a sliding scale, which would actually be VERY pragmatic for most non-advantage players, especially if derived by individuals with math talent.

before posting i had tried to help myself using the very calculator in your link but am tripping up. since 66 unit start, i entered "132" unit end for a greedy win of double money. the next entry was 66 for units. to me the win rate for disadvantage play was -.5 per hundred hands. i left the 27.72 standard deviation that was, by default, already filled in because i dont understand standard deviation (more on this) and then entered the 1000 hands. it gave the optimistic prospect of 41% likelihood of achieving the goal of 66 unit win, which cant be right? so i plugged in 2 for standard deviation and got ZERO probabilty of achieving goal. the LITTLE i know of standard deviation is something like 95% of "objects" in random distribution are confined within 2 standard deviations so it sounded good (?) but ZERO is not the right answer to ones prospects of doubling their money--is it?

HELP!--i am SOMEONE'S favorite uncle.

[hitthat16]

Just count. There's addition, subtraction, and some basic division.

Hardly too challenging for the "math clueless".

[hardin county boy]

Just count.

BAD NEPHEW! bad boy, bad doggey!

[DSchles]

Will be out this evening (leaving now), so will have to answer later. Sorry.

Suffice it to say that a) you can't use the calculator as described, and b) the standard deviation for a single hand of BJ is 1.15 units; therefore, the s.d. for 100 hands is ten times that value (s.d. being a square-root function), or 11.5 units per 100 hands.

More later.

Don

[hardin county boy]

Will be out this evening (leaving now), so will have to answer later. Sorry.

Suffice it to say that a) you can't use the calculator as described, and b) the standard deviation for a single hand of BJ is 1.15 units; therefore, the s.d. for 100 hands is ten times that value (s.d. being a square-root function), or 11.5 units per 100 hands.

More later.

Don

thanks, i will get to work with what you have told me and look forward to more later.

[bigplayer]

If he absolutely refuses to count he could use a positive progression to try to change his distribution of results. If he plays something like $25-$25-$40-$50-$60-$70 going up by a mild amount after a win like $10 a hand, never going past $100, and dropping back to $25 as soon as he loses a hand, he will most likely be a small loser for the trip, but if he wins it will be a very good sized win and he will get some good entertainment value that comes from having a chance to win big. Positive progressions do not change the nature of the house advantage, but they do sort of work as an automatic money management tool in that they keep you betting the minimum amount until you've won a few hands and return you to betting the minimum amount after any loss. This is preferable to flat betting and then betting 2x as much when you're a loser, this is essentially a negative progression and will usually result in a complete trip wipeout. Using a positive progression the chances of a wipeout are smaller as you are making the minimum bet most of the time.

I don't know why some players think "counting" takes the fun out of the game. Nothing beats knowing most of the cards left are big cards and betting big into them.

[Three]

Probably can't add and subtract by one to more than +/-20 without indecent exposure.

[hardin county boy]

I don't know why some players think "counting" takes the fun out of the game. Nothing beats knowing most of the cards left are big cards and betting big into them.

good post, bigplayer. no doubt, great count, big bets and counting has GOT to be grand--i bet nothing like it. i find counting difficult, though not impossible, and dont doubt i could improve at it BUT, like a lot of folks, it turns an easy, basic strategy, good time into WORK---from reading, i think those with better math skills and a firm grip on logic enjoy counting MORE than they ever could basic strategy/disadvantage.

i think i agree with every word of your progression comments though, if a guy has slogged away, it is late in a trip and he finds himself down quite a bit with not so much time left, i think choosing to up his basic unit size, risking late-trip ruin in hopes of catching late-trip luck, is also rational.

i do not have your math talent so am interested in your continued opinion a bit more: when i consider that if FAVORITE-UNCLE goes and bets his thousand hands at 37.50 average bet, his expected loss is FIVE UNITS and 1 standard deviation is THIRTY-SIX UNITS. you used an interesting phrase: "to try to change his distribution of results"--great phrase. if we focus ONLY on this one, UP TO a thousand-bets, trip, the reasonable progression you described is one tool. a second tool might be to decide to quit early while up or quit later at even, to avoid losing (not talking about the long run nor "sessions"---just focusing on one trip). a third tool to "try to change his distribution results" for this one trip might be my notion that if 600 or 700 hands didnt get him what he wanted AND if far enough down that 300- 400 more hands have diminished prospects at his smallest unit size, upcoming hands might be contested at a somewhat larger unit, albeit with increased risk of ruin.

i really DO completely understand the long run, negative expectation, disadvantage, perpetual motion etc BUT, it does seem clear that distribution of results can be "manipulated" ( though, unfortunately, positive variance cannot be manufactured) such that on many occasions one might meet with desired success and opt in favor of securing a decent-enough outcome based on these few variables and "how it has gone."

the easy dismissal of such conversation includes saying, concretely, that this will result in a number of break-evens, small wins and losses and enough large losses that the inevitable, negative expectation will become ever more likely. i have NO difficulty imagining that such could occur. However, it is not persuasive to suggest that "blind" execution of some, any, progressive system, trip after trip, making it essentially one LONG-run trip, is the same as 500 "trips" of varying length and approach, depending on these few variables, attempting to exploit some positive variance and truncating the trip when favorable, refusing to truncate and count it one of 500 "trials" till either favorable, ruined or out of time. those 2 are NOT the same thing and i wish i could google somewhere, anywhere, and find that talented math folks have batted it around, overcome objections with clear arguments etc. i am skeptical that the large losses that WILL occur will, of necessity, outpace the sometimes very considerable wins that ALSO occur.

your thoughts sir?

[RS]

Playing BJ and not counting is.....absolutely boring and horrific. It's like you're sitting there, naked, defenseless, trying to beat this carnival game -- you look around you and notice something quite intriguing -- everyone else beside is playing the same way, naked and defenseless. The sad part is, that's how they always play -- some of them, SOME OF THEM, even have the nerve to think they have a chance at this game, playing based on luck, fortune, or other hocus pocus. In the end, no matter how great a win they pull out of the hat, and no matter how steep a loss they book, one thing is for certain -- they will return, and yes, they will give it all back.

If someone has a question about how counting works, it can be explained quite simply in a few minutes. Even if the person doesn't quite understand the math, the basic ideas aren't that difficult to understand.



PS: I do not find counting to be "work" or anything like that, at all, while at the table. I'm not calling myself a "pro" or anything like that, at all, but -- it's kind of like a boxer who trains night and day for his fight. When he steps into the ring, he knows he's already put in the time and effort to win the fight, he has already won the battle. He is not nervous or worried -- he is confident and relaxed.