The rollercoaster that is card counting

[sagefr0g]

@ xengrifter "...we are only at ATH 1-2% of the time..."
@KewlJ "...As for the ATH at 1-2% of the time, while this is true. ..."

say what?
those portions of your statements sound illogical and if not illogical then at the very least paradoxical.
what unit of time are we even referring to anyway? hmm, time, that's an interesting subject.
are the above statements in reference to the (not sure what properly schooled mathematicians call it) the mean (maybe) to which various fractions of high and low standard deviation are relative to, far as an idealistic bell curve goes, sorta thing? a bell curve constructed from monetary results for some unit of events (and those events comprising some unit of time?) where the order of the events is what?, meaning less, just randomly 'dosed' with more numbers to fill in the blanks and spread round about some average with respect to some accurate as possible standard deviation? the driver of those events, supposedly some advantage, which is again an average that presents over time and events, that has its own bell curve, in no particular order with respect to the real way time unfolded, with no particular salient rhyme or reason.
sigh, i'm lost.
don't events in real time present in a manner for which cumulative profits add up a given ATH more often than 1-2% of the time, for blackjack? like, ok, perhaps card counting bj offers a, say, 2% advantage, but well that's on money across the table, where bet spreading (so more money across the table at an accelerated rate at the right time & that at around 27% of the time) is conducted, just doesn't seem right one only has a ATH present 1-2% of the time.
even examining and comparing bell curves, say for events where results are positive only and events for which results are negative only, i believe one should find a much greater disparity than one would expect to find if the ATH was reached only 1-2% of the time. example (albeit, it isn't for blackjack only): https://www.blackjackinfo.com/community/threads/question-about-standard-deviation-and-variance.54892/#post-490891
maybe i'm just looking at the whole scenario wrong, just doesn't make sense to me, ATH 1-2% of the time.
edit: does ATH 1-2% of the time mean that bj card counting is spending 99-98% of the time for naught? i must really be missing something here! well if that were the case then the winning for the 1-2% of the time must be immense, i guess.

 

[KewlJ]

Ok, I don't know exactly where that stat came from. I do know ZG, or XG as he is now known, didn't pull that number from thin air. Although I am not sure of the source, I remember reading fairly early in my career and learning process that a player is at his all time high (ATH) only 1.5% of the time. The other 98.5% of the time he is somewhere below his last ATH, trying to get back to, or establish a new ATH. If I had to guess, I would say I read that in either Wong's Professional Blackjack or Don's BJA3, simply because they were my two "go to" reference books, early on.

Now I don't know how that number is calculated. I suppose it is saying that if you tracked and recorded every round played, you would be at an ATH 1.5% of the time. Well I don't track every round played. I don't sit at the BJ table and pull out pen and paper and record every round. What I do, is track sessions and days and I am at ATH, more frequently that 1.5% in both those categories. For example last year, I played 319 days. At the end of 25 of those days I was at my ATH. That is about 8%. Now that is a very small sample size and it is only measuring against other end-of-day stats. And as I said, they were "grouped". In July and August when I when on my big run for the year, I hit 14 ATH's. So I don't know. I don't know where exactly that stat came from or how it is calculated, but I do know I read it from a very reliable source (I think either Wong or Schlesinger) and despite my own personal numbers (small sample size) not falling in line, I feel comfortable saying "while this is true" to ZG/XG referencing of the stat.

 

[sagefr0g]

@KewlJ & @xengrifter
yup, after kewlj's post above regarding he might of read it in Wong's Professional Blackjack, i took a look, at pg. 200, and here it is:
"chance of reaching all time high
unfortunately most of the time you seem to be losing.
according to mathematician Peter Griffith, at most 1.6% of the time your present hand puts you at an all time high.
the other 98.4% or more of your playing time, your current bankroll is lower than it was at some time in the past."

edit: perhaps the salient words in the statement quoted by Wong of Peter Griffith, are the words present hand.
otherwise, all i can say is, YOIKS
end edit.

another edit: also, far as this particular excerpt, no implication of how far below ATH is made. without further reading, i'd venture to guess the significance of how far would be represented by standard deviations, hi or lo, 1sigma 34%, 2sigma 13.5%, 3sigma 2.1%,..., sorta thing. end another edit

 

[London Colin]

The book 'Extra Stuff, Gambling Ramblings', by Peter Griffin has some of the mathematics behind all this.

To begin with there is a proof that, for a simple coin toss-like game, with probability of winning, p > 0.5, 'the chance of being at an all time high sometime long into the future is the same as the chance of always being ahead', which is shown to be 2p-1, which also happens to be the EV.

There are complications for games like BJ, with multiple payoffs, and presumably varying your bet size with the advantage (and sometimes betting with no advantage) all add extra complexities. But maybe your average advantage still approximates to your probability of being at an ATH.


As for the meaning of the words, if we are considering the probability of any given future hand achieving an ATH relative to our current starting point, skipping over the immediate future where the probability will be quite high, then the chance of any one hand resulting in an ATH and the percentage of hands (aka the amount of time) spent at an ATH would seem to be just two ways of saying the same thing.

 

[sagefr0g]

The book 'Extra Stuff, Gambling Ramblings', by Peter Griffin has some of the mathematics behind all this.

To begin with there is a proof that, for a simple coin toss-like game, with probability of winning, p > 0.5, 'the chance of being at an all time high sometime long into the future is the same as the chance of always being ahead', which is shown to be 2p-1, which also happens to be the EV.

1.6% is awfully close to the ‘classic spoken’ advantage a card counter has.

There are complications for games like BJ, with multiple payoffs, and presumably varying your bet size with the advantage (and sometimes betting with no advantage) all add extra complexities. But maybe your average advantage still approximates to your probability of being at an ATH.

yes, getting a blackjack, doubling, splitting & re-splitting or not & maybe doubling or not, hitting or staying, surrendering or not, taking insurance or not, raising & lowering bets, playing or not playing, definitely complex.

As for the meaning of the words, if we are considering the probability of any given future hand achieving an ATH relative to our current starting point, skipping over the immediate future where the probability will be quite high, then the chance of any one hand resulting in an ATH and the percentage of hands (aka the amount of time) spent at an ATH would seem to be just two ways of saying the same thing.

far as the quote of Peter Griffin, “at most 1.6% of the time your present hand puts you at an all time high. the other 98.4% or more of your playing time, your current bankroll is lower than it was at some time in the past.", there doesn’t seem to be a problem replacing the word hand with moment.

or since that 1.6% is so close to the ‘classic spoken’ advantage a card counter has, let the quote read: at most 1.6% of the time your present money across the table puts you at an all time high.
the other 98.4% or more of your playing time, your current bankroll is lower than it was at some time in the past.
might that be acceptable, as well?
at any rate, that word present in the quote makes me feel a bit warmer and fuzzier, lol.
still definitely an rather immense psychological barrier to overcome, imho.

 

[KewlJ]

I still say those ATH's will be bunched. Like I said, I hit 14 in two months in July and August when I was on a roll. When you are near the top of the mountain, each step forward you take, you are higher than before. But slip and slide down the mountain, and it may be a while before you get back to where you were.

And while I had 14 ATH's when I was on a roll back in late summer, I haven't hit one in more than 3 months. And being that I am currently just about $30k off my last ATH, it will not be coming in the immediate future. I mean $30k in blackjack EV is 4-5 months for me. So from an expectation standpoint....I am 4-5 months away. But that is not how variance works. I could go on a roll, just as I did in July and August and various other times in my career and be back to that level in 3-4 weeks. OR, I could have another year like I had a couple years ago where my BJ win was far below expectation at $27,000. If I were to have another 27,000 year, I wouldn't even get back there in 2017. I would have ZERO ATH's in 2017.

But this is all sort of related to variance. Variance and the negative swings, while a pain in the ass, are actually our friend. Without the variance involved, there would be no card counting advantage blackjack. If players just hit their expectation regularly (as some have claimed that they do), everyone and their mother (or brother ) would be a professional card counter/AP and casinos would do away with the game as we know it.

So yeah, it IS a psychological barrier to overcome. Part of the education process needed to be a successful card counter, whether professionally or recreationally. You have to know and accept that there is variance and negative sings and be able to handle and deal with them. It actually took me a while to really be comfortable with some of the big negative swings that is part of this game. I really don't know that there is anyway to prepare for it despite that you read about them. You have to ride that rollercoaster and go through a couple nightmare swings and come out the other side a couple times, before it clicks and you accept that "yep this is the way card counting blackjack works". And if you happen to be depending on your blackjack income to pay your bills as you are learning this lesson, as I was, I think it is 100 times worse. The best scenario is to have another source of income while you really learn these things. But then again, I really believe that blackjack works best as a part-time or supplemental type income anyway, despite that is not my situation.

 

[mcallister3200]

Hey KJ!

Hope you're doing well and your days are filled with positive variance (we know it's a mixed bag, but wish you the best)

That last post is a pretty awesome one covering the realities of the fluctuations that anyone card counting at any sort of substantial stakes will experience at some point.

 

[xengrifter]

That's faulty logic though.

Perhaps, just needs some further refinement.

 

[sagefr0g]

The book 'Extra Stuff, Gambling Ramblings', by Peter Griffin has some of the mathematics behind all this.

To begin with there is a proof that, for a simple coin toss-like game, with probability of winning, p > 0.5, 'the chance of being at an all time high sometime long into the future is the same as the chance of always being ahead', which is shown to be 2p-1, which also happens to be the EV.
..............

that is interesting.
so if i'm understanding that statement correctly, the value for the chance of being at an all time high is equivalent to expected value, no?
for the coin toss-like game where the probability of winning is p > 0.5 . was there a derivation that showed how 2p-1 is the chance of being at an all time high sometime into the future and how it is the same as the chance of always being ahead and how it also happens to be EV?

edit:
i guess for example:
if p = 0.6
then for 2p - 1 , we'd have 2*0.6 - 1 = 0.2
so EV = 0.2
makes sense but the thing is i don't understand the derivation or logic of the statement above the edit.
end edit
edit:
I guess that since if something is definite, it’s probability is p = 1
that then it holds that a certain expectation is 2p – 1 = 1, a for sure event happening
and far as expectation goes, an expectation dealing with uncertainty is going to be p >0 & p <1
so then inserting that value of p into 2p-1 gives one the expectation or EV
end edit

 

[London Colin]

that is interesting.
so if i'm understanding that statement correctly, the value for the chance of being at an all time high is equivalent to expected value, no?

For the coin-toss game, definitely. More generally, I don't know.

for the coin toss-like game where the probability of winning is p > 0.5 . was there a derivation that showed how 2p-1 is the chance of being at an all time high sometime into the future and how it is the same as the chance of always being ahead

Of course. That's what I meant by 'there is a proof that...' [Actually, what's shown is that the chance of always being ahead is 2p-1, and that this is the same as the chance of being at an all time high]

I'd recommend getting the book. It's a slim volume, a compilation of a few magazine articles, and can be had for next to nothing -
https://www.amazon.com/Extra-Stuff-Ramblings-Peter-Griffin/dp/0929712005/ref=sr_1_3?ie=UTF8&qid=1484830547&sr=8-3&keywords=gambling+ramblings

and how it also happens to be EV?

That part is taken for granted. It's just straightforward algebra, from the definition of EV. Your examples, below, show it working in practice for specific numbers.

edit:
i guess for example:
if p = 0.6
then for 2p - 1 , we'd have 2*0.6 - 1 = 0.2
so EV = 0.2
makes sense but the thing is i don't understand the derivation or logic of the statement above the edit.
end edit
edit:
I guess that since if something is definite, it’s probability is p = 1
that then it holds that a certain expectation is 2p – 1 = 1, a for sure event happening
and far as expectation goes, an expectation dealing with uncertainty is going to be p >0 & p <1
so then inserting that value of p into 2p-1 gives one the expectation or EV
end edit

 

[sagefr0g]

@London Colin

i have Griffith's The Theory of Blackjack. tried to read it, i dunno 12 years ago. i was like, huh?
was leafing through it yesterday, trying to find any reference to the information you posted. again, i was like, huh?, but this time, i saw Griffith at least had a modicum of humor.
anyway your revelations on the matter helped me learn something new. just me maybe, it's always good to learn something new. thank you.
may or may not pick up a copy of Extra Stuff, having previously experienced the 'trauma' of trying to read The Theory of Blackjack, lol.

 

[London Colin]

@London Colin
may or may not pick up a copy of Extra Stuff, having previously experienced the 'trauma' of trying to read The Theory of Blackjack, lol.

There's a lot in TOBJ (pretty much everything in the appendices) that goes over my head. This other book is pitched much more down to my level!

 

[Ryemo]

@Ryemo
what was the table min? how many standard deviations was that loss?

Oh btw, I ran the sim on the heavy loss that I took. I was almost -2 standard deviations (-1.91) with a 2.83% chance of of those results occurring. Ugh

 

[sagefr0g]

Oh btw, I ran the sim on the heavy loss that I took. I was almost -2 standard deviations (-1.91) with a 2.83% chance of of those results occurring. Ugh

thank you Ryemo, i was merely curious, no comment, other than i hope you've had similar deviations on the other side of the curve, or at least ones that add up and exceed the loss.

 

[Ryemo]

thank you Ryemo, i was merely curious, no comment, other than i hope you've had similar deviations on the other side of the curve, or at least ones that add up and exceed the loss.

Thank you. Yeah, that's how this game goes I guess. I was very fortunate enough to have went on a 6 month winning period (starting in June) that just barely touched 6 figures, before the big losing streak. So the big negative hit I took in December actually brought me almost right at EV for the year. I guess I can live with that.

 

[sagefr0g]

there's another number, other than the ATH frequency# (frequency for which a type of play generates an all time high cumulative value, that just me maybe, is of interest. that number i call the GTL frequency# . the GTL frequency# is the frequency for which a type of play generates a greater cumulative overall value than the last cumulative overall value generated of a previous (last) play.
from the data of my plays, the GTL frequency# tends to be circa edit 13% end edit or more higher than the ATH frequency# .
the GTL# gives a bit more warmer fuzzier feeling than the ATH#, albeit, it's pretty much the GTL is ever going about catching up with the ATH. it's kind of like walking on an ever lengthening treadmill and every so often pausing, ending up back a bit and having to take GTL steps to get back to another ATH

 

[KewlJ]

There's a lot in TOBJ (pretty much everything in the appendices) that goes over my head.

I am in the same boat. Although I have pretty good basic math skills, I am most definitely not a math freak type guy. I am lost when you get into all the formulas and stuff. And while I understand that blackjack card counting IS math, and all the formulas and stuff, you don't have to know and understand all that to win.

I think it's a little like driving a car. You don't have to know how the engine works inside and out to drive a car. I think this is where I often end up butting heads with the "math geek" type guys on various forums. They want to dissect everything. They want to spend their Sunday afternoon in the driveway taking the engine apart to see how it works, while I would rather go for a nice Sunday afternoon drive.

 

[London Colin]

there's another number, other than the ATH frequency# (frequency for which a type of play generates an all time high cumulative value, that just me maybe, is of interest. that number i call the GTL frequency# . the GTL frequency# is the frequency for which a type of play generates a greater cumulative overall value than the last cumulative overall value generated of a previous (last) play.
from the data of my plays, the GTL frequency# tends to be circa 10% or more higher than the ATH frequency# .
the GTL# gives a bit more warmer fuzzier feeling than the ATH#, albeit, it's pretty much the GTL is ever going about catching up with the ATH. it's kind of like walking on an ever lengthening treadmill and every so often pausing, ending up back a bit and having to take GTL steps to get back to another ATH

Forgive my bluntness, but I literally have no idea what any of that means!

 

[Taff]

Me neither.!!

 

[London Colin]

I think it's a little like driving a car. You don't have to know how the engine works inside and out to drive a car. I think this is where I often end up butting heads with the "math geek" type guys on various forums. They want to dissect everything. They want to spend their Sunday afternoon in the driveway taking the engine apart to see how it works, while I would rather go for a nice Sunday afternoon drive.

It's useful to be able to customise your car if you are going off road (to stretch your metaphor to breaking point)