Score

[London Colin]

I think perhaps there is fault on both sides here. Certainly, I could have found a more polite way to express my very real exasperation, and for that I apologize.

I take my time and try to answer your question, which was not worded very well. I was the only one to try to help you for several days!

Many who have followed with responses repeated basically what I stated.

I agree my question was not worded well, mainly because it was founded on a false assumption - that EV^2/Var is the starting point from which to consider SCORE, and hence a further assumption that the EV and Var in question must refer to the total dollars [and squared dollars] per 100 hands.

In the light of what I now know, I can see that my posts must have seemed very confused. So why not say that at the time? Why not ask me to clarify my meaning? Your every post seemed to be ignoring the actual content of my questions, other than being about the topic of SCORE.

And the unfortunate truth is that yours were virtually the only reponses until after my outburst. Four days of total silence prompted my first moment of tetchiness - "Is there no one who will explain ..." - to which you were again the only respondent, and again didn't seem to be in any way engaging with the actual content of my posts, merely reiterating the one thing I already knew, that SCORE is a measure of both risk and reward.

So I tried again, and you responded again, in much the same manner (complete with yet more :whip: whipping, which I have to admit contributed in some minor, irrational way to my growing annoyance. )

At which point I blew my top, for which again I apologize. I'm not happy at losing my cool, but I'm also not happy that doing so seems to be what it takes to get a discussion going. Within half an hour the other contributors started piling in, and in a very short while all became clear to me. (Because they didn't just repeat what you stated, they made an effort to get to the bottom of the confusion and establish what I was trying to ask, however confusedly.)

If you would have asked your real question.
How do you calculate EV and how does that relate to SCORE!

In bja 2 and 3 Don gives the advantage at each TC and explains how the bet ramps were calculated.

If you read my responses I did answer your question, but did not answer how to calculate EV; nor create a bet ramp, which you did not directly ask!:joker::whip:

The question was as real as I could make it at the time, but with hindsight I'd say my real question was "Why does SCORE, defined as win-rate per 100 hands under specific conditions, also equate to DI^2, which is also 1,000,000 * EV^2/Var?"

I "live in hope" that you can in the future be more precise with your questions and show a little appreciation for those who try to help you!:joker::whip:

I'll endeavour to do both; believe it or not, that would be more normal for me. But please, take a moment to review the sequence of events in this thread. As I said, I think we can both share some blame for the miscommunication.

 

[sagefr0g]

another question about SCORE

my question regarding SCORE has to do with the logic of it.

i mean what the heck is the logic behind the maths of SCORE, how is it putting the maths together for how it's done in computing SCORE delivers the information that it does?

what the heck is this Sharp ratio and m-m modeling stuff?

what's the deal with squaring Di? what's that do?

what's the deal with variance and standard deviation, the squaring and square rooting that goes on with that stuff, lol.

i mean can anyone give a logical practical, layman's sort of explanation of what's going on in the math nerd's heads as far as an understanding of that stuff?

 

[Kasi]

Really, win-rate should be taken as the definition, and how to calculate it should be the first question. ...
To calculate win-rate you just need to sum all the different betsize * EV * frequency, for each true count.

I think you basically have it.

To me, the first question is what is optimal bet ramp? Since SCORE takes into account EV vs risk and figures out the best ratio between the 2. Put another way, it minimizes the size of roll one needs to bet at a given risk.

Win-rate, to me in my mind, usually a %age i picture. But you can express in $'s too, like you say.

Is a game with an avg win-rate of 1.2% = to any other game with an avg win-rate of 1.2% No.
Is a game with an avg win rate of $30/hr = to any other game with a win-rate of $30/hr? No.

Don't just focus on win-rate in other words. It's just one-half of the risk vs reward dilemma lol.

Another very useful function of a sim - it figures out for you the absolute best way to bet your money, maximizes reward while minimizing risk so your roll has the best chance to grow, so you need the fewest units in a roll possible to make that happen.

So you know the best way to bet the same $10K when pen changes from 75% to 83%. Or how much to bet and when should you stumble across a table with mid-shoe-entry allowed.

Then lower risk by adding more units to roll if you want.

I thionk your eqation is basically correct but one won't know the freq, or the EV, or how much to bet without a sim.

Once you get Freq, Adv % and SD at each TC from a sim, all else follows as surely as the night follows day.

 

[Kasi]

i mean can anyone give a logical practical, layman's sort of explanation of what's going on in the math nerd's heads as far as an understanding of that stuff?

Not really lol.

Thank God that means I am not a math nerd .

 

[blackjack avenger]

Flame On?

I did not attack you in any way.

:joker::whip:

The above are just symbols. I like them. I wonder which is the casino and which is the player. I often use them in reference to myself.

Probably no one else responded because they were unsure of your question and/or thought I basically answered you. One of the posters stated such. Anyway, no harm no foul. These are just words on a computer!:joker::whip:

 

[London Colin]

I did not attack you in any way.

I certainly wasn't trying to suggest that. I did say that all the :whip:ing was only a minor (and an irrational) contribution to my overall annoyance.

It's clear you were genuinely trying to be helpful, and I just got the wrong end of the stick. My previous post was just an attempt to give you a little insight into how things looked from this end, so you hopefully don't think I was simply being pointlessly, randomly obnoxious.

P.S. Thank God you never saw the first draft of the post that started the flame war.

 

[London Colin]

Thanks for the feedback, Kasi.

Win-rate, to me in my mind, usually a %age i picture. But you can express in $'s too, like you say.

Is a game with an avg win-rate of 1.2% = to any other game with an avg win-rate of 1.2% No.
Is a game with an avg win rate of $30/hr = to any other game with a win-rate of $30/hr? No.

I think one of the potential seeds of confusion is that both the terms win-rate and EV can be used to mean a percentage or a $ amount, depending on the context.

In this context, we really have to be talking about $ amounts, because the bankroll is one of the variables that affect our calculations - the amount we bet at each TC is proportional to our bankroll. So a bigger bankroll means a bigger score (though not a bigger SCORE, which must by definition assume a $10K bankroll).

Once you get Freq, Adv % and SD at each TC from a sim, all else follows as surely as the night follows day.

Indeed.

 

[London Colin]

my question regarding SCORE has to do with the logic of it.

i mean what the heck is the logic behind the maths of SCORE, how is it putting the maths together for how it's done in computing SCORE delivers the information that it does?

Well I think I've demonstrated that I'm not the best person to answer this. Nevertheless, ...

It sounds like you are in a similar position to mine at the start of this thread. The last few posts clarified things a great deal for me. I can't really offer any further insights, just maybe try to restate a few things slightly differently -

Ultimately, SCORE is just a calculation of the win-rate in dollars, under certain, pre-ordained conditions. The calculation of a win-rate seems to be a pretty straightforward, mechanistic process -

• Run a sim to get the EV and variance at each possible true count, as well as the frequency with which each true count occurs.
• Use that information, together with the amount you intend to bet at each TC, to calculate how much you expect to win, per-hand, on average. (And if you assume 100 hands per hour, then you can also arrive at an hourly win-rate.)

An individual, attempting to compare different games, can use their own personal circumstances - current bankroll, desired level of risk - to formulate personal betting strategies for those games and see which game wins the most money for the same amount of risk.

Don Schlesinger, on the other hand, had to pick numbers to use when generating his tables which would be useful to all readers, even if not matching anybody's personal circumstances. He chose a $10K bankroll and a bet size equal to the full-Kelly bet for that size of bankroll at each true count (meaning a 13.5% RoR). That means that at each TC, the amount bet is 10,000 * EV / Var. [Where EV and Var. are specific to the TC.]

Using those figures, combined with a set of simulation results for various games, the tables in chapter 10 were able to be compiled.

what the heck is this Sharp ratio and m-m modeling stuff?

As I understand it, its the same stuff, but the things being valued are financial products, rather than blackjack games. They too have EVs and variances (though usually called volatility, I think). So you have the same 'which is best?' dilema as you do in blackjack. Apparently the Sharpe Ratio was the inspiration for the Desirability Index, and the Modigliani-squared value inspired SCORE.

what's the deal with squaring Di? what's that do?

I think that was covered pretty well in some of the above posts. It would appear to be just a sort of cosmic coincidence that squaring the DI happens to give the same value as SCORE.

DI was defined as 1000 * EV/SD. The 1000 was purely to give convenient numbers. The DI itself is unitless; the underlying thing being measured is EV/SD. [Again, if I understand correctly, EV and SD is specific to each true count, and you must compute the average, based on all the true-count frequencies, to get an overall answer. This is per-hand, unlike SCORE's per-100-hands.]

Now it just so happens that - only with a bankroll of 10,000 and full-Kelly bet size; i.e. only for SCORE and not for score - the amount of each bet is 10,000 * EV/Var, meaning that the win-rate for each hand is EV * 10,000 * EV / Var. So this is the point at which EV^2 raises its head, as the above can be written as 10,000 * EV^2 /Var, and for 100 hands SCORE is therefore 1,000,0000 * EV^2 / Var.

Now 1,000,0000 just happens to be 1000^2, and Var is SD^2. So the above equals DI^2. That is-

(1000 * EV/SD)^2 = 1,000,000 * EV^2/Var.

what's the deal with variance and standard deviation, the squaring and square rooting that goes on with that stuff, lol.

Not my strong point either, but I think variance and standard deviation both conceptually mean the same thing, the variability of the expected results, but in terms of calculations, variance tends to come first.

If you start out knowing nothing, then you calculate variance and taking the square root gives you the SD. If, on the other hand, someone tells you the SD, then obviously you know the variance too.

In lengthy calculations, I think you tend to have to do all your intermediate working with variance, before taking the sqaure root right at the end, if you require an SD.

i mean can anyone give a logical practical, layman's sort of explanation of what's going on in the math nerd's heads as far as an understanding of that stuff?

I'm certainly a layman, so take all of the above with a pinch of salt. But that represents my current understanding. Hope it helps, or at least doesn't hinder.

 

[blackjack avenger]

Wow

I couldn't have stated the above better myself!:joker::whip:
but
to be more eloquent then me is not that difficult:joker::whip:

 

[sagefr0g]

lost in space, but at least wondering where i'm at

I'm certainly a layman, so take all of the above with a pinch of salt. But that represents my current understanding. Hope it helps, or at least doesn't hinder.

well of course it didn't help, but that's only because when it comes to this maths stuff i'm hopeless, but it certainly didn't hurt.
and well actually it did help since imho that was a great explanation, a great perspective, errhh the whole post, imho.

just yesterday, i read a paper on the EDGE website, (sorry i forget the guys name, ahh, here is the link: http://www.edge.org/3rd_culture/dehaene/index.html ) by a mathematician who became a sort of cognitive scientist. well, anyway, part of what he was trying to say was that humans have a sort of an innate numbers sense, as do other animals to a lesser degree, but that for humans that innate numbers sense only goes so far just as is true with animals. (just humans can contend with a bit larger sized numbers than animals but it is a weakness animals and humans share as number become larger, sort of thing). same sort of thing when it comes to adding, it's an innate sort of thing for relatively small numbers.
thing is the guy was saying, humans have also this language and symbol manipulation sort of evolutionary skill tied to brain physiology.
so we can take this innate number sense, the primal sort of addition capability and fool around with that using the symbol, language manipulation skill where we can build all sorts of complex mathematical operations stuff and whatnot.
thing is though what the guy was saying is we only really have this evolutionary limited innate number sense as far a what we can really get our 'understanding' around, sort of thing. the rest is so complex, that all we do is sort of do it, operation by operations, correct rule by correct procedure sort of thing.
logic in a sense, far as i know, lol.

It sounds like you are in a similar position to mine at the start of this thread. The last few posts clarified things a great deal for me.

right, and perhaps there is a good reason for that,

Ultimately, SCORE is just a calculation of the win-rate in dollars, under certain, pre-ordained conditions. The calculation of a win-rate seems to be a pretty straightforward, mechanistic process -

* Run a sim to get the EV and variance at each possible true count, as well as the frequency with which each true count occurs.
* Use that information, together with the amount you intend to bet at each TC, to calculate how much you expect to win, per-hand, on average. (And if you assume 100 hands per hour, then you can also arrive at an hourly win-rate.)


An individual, attempting to compare different games, can use their own personal circumstances - current bankroll, desired level of risk - to formulate personal betting strategies for those games and see which game wins the most money for the same amount of risk.

Don Schlesinger, on the other hand, had to pick numbers to use when generating his tables which would be useful to all readers, even if not matching anybody's personal circumstances. He chose a $10K bankroll and a bet size equal to the full-Kelly bet for that size of bankroll at each true count (meaning a 13.5% RoR). That means that at each TC, the amount bet is 10,000 * EV / Var. [Where EV and Var. are specific to the TC.]

Using those figures, combined with a set of simulation results for various games, the tables in chapter 10 were able to be compiled.

lmao, i might be a genius cause i think i finally get it!
genius, only because i got you to explain SCORE, something i just could not understand even when it came from the horses mouth, lol, D Schlesinger is just to darned wordy at times, lol.
but all joking aside, yes, your explanation is great because it points out how essentially SCORE and Don's charts is a 'bastardization' of the essential basic process that we might plod our way through if we was gonna figure this stuff out on our own, lol.

As I understand it, its the same stuff, but the things being valued are financial products, rather than blackjack games. They too have EVs and variances (though usually called volatility, I think). So you have the same 'which is best?' dilema as you do in blackjack. Apparently the Sharpe Ratio was the inspiration for the Desirability Index, and the Modigliani-squared value inspired SCORE.

I think that was covered pretty well in some of the above posts. It would appear to be just a sort of cosmic coincidence that squaring the DI happens to give the same value as SCORE.

DI was defined as 1000 * EV/SD. The 1000 was purely to give convenient numbers. The DI itself is unitless; the underlying thing being measured is EV/SD. [Again, if I understand correctly, EV and SD is specific to each true count, and you must compute the average, based on all the true-count frequencies, to get an overall answer. This is per-hand, unlike SCORE's per-100-hands.]

Now it just so happens that - only with a bankroll of 10,000 and full-Kelly bet size; i.e. only for SCORE and not for score - the amount of each bet is 10,000 * EV/Var, meaning that the win-rate for each hand is EV * 10,000 * EV / Var. So this is the point at which EV^2 raises its head, as the above can be written as 10,000 * EV^2 /Var, and for 100 hands SCORE is therefore 1,000,0000 * EV^2 / Var.

Now 1,000,0000 just happens to be 1000^2, and Var is SD^2. So the above equals DI^2. That is-

(1000 * EV/SD)^2 = 1,000,000 * EV^2/Var.

Not my strong point either, but I think variance and standard deviation both conceptually mean the same thing, the variability of the expected results, but in terms of calculations, variance tends to come first.

If you start out knowing nothing, then you calculate variance and taking the square root gives you the SD. If, on the other hand, someone tells you the SD, then obviously you know the variance too.

In lengthy calculations, I think you tend to have to do all your intermediate working with variance, before taking the sqaure root right at the end, if you require an SD.

there you go again, great explanations, imho.
just, one thing i'm still stuck with is the why and wherefore so to speak of the taking the square root of variance.
like it's a step in the operations of mathematics that is obviously useful but i can't understand how the heck we know to do it, and i'm not even really sure why we do it.
same thing for ratios, be they Sharp, M-M modeling or simple probability, lmao, the why and wherefore simply escapes me :whip:
like ok, i've never had a probability or statistics course, yet, but anyway about the best explanation i've found is in this child's link, lol :
http://www.mathsisfun.com/data/standard-deviation.html

i mean i can sort of get (understand) that stuff, but i just can't get my mind around the essence of it, or the primary idea behind it.
i mean, ok, i know for one thing one needs to have the ambition or desire to want to understand the implications of some large group of data.
thing is i get lost in my understanding when they take that darned square root of the variance to get standard deviation.
i kind of don't like the explanation given in the link, seems it's sort of hand waving, lol.
but for me, it's the same confusion when it comes to ratios, the reasoning behind them, that some math nerd three hundred or more years ago, had some epiphany about, lol.

 

[London Colin]

Thank you both for the kind words.

just, one thing i'm still stuck with is the why and wherefore so to speak of the taking the square root of variance.
like it's a step in the operations of mathematics that is obviously useful but i can't understand how the heck we know to do it, and i'm not even really sure why we do it.

The best I can offer is to consider the units that these things are measured in. You'll see a variance quoted as some number of 'squared units', and I jokingly used the phrase 'squared dollars' in an earlier post, wondering what such things might look like. That stems from the way variance is calculated: the average squared difference from the mean.

So if, having calculated the variance, you are looking for a final answer that's measured in units, or in dollars, then at some point you are going to have to head back in the opposite direction and take the square root.

 

[sagefr0g]

no joke

Thank you both for the kind words.


The best I can offer is to consider the units that these things are measured in. You'll see a variance quoted as some number of 'squared units', and I jokingly used the phrase 'squared dollars' and that sort of stuff in an earlier post, wondering what such things might look like. That stems from the way variance is calculated: the average squared difference from the mean.

So if, having calculated the variance, you are looking for a final answer that's measured in units, or in dollars, then at some point you are going to have to head back in the opposite direction and take the square root.

lmao, ok hey way back, i was asking questions about 'squared dollars', no joke.
but ok, thank you, there is at least now for me a stepping stone with your point on the idea of That stems from the way variance is calculated: the average squared difference from the mean.
geesh, i think i wasn't even aware of that factor. :whip:
i'm heading for the hills and think about this stuff some, lol, maybe just maybe, it'll start making some sense.

just leave you with this, further state of confusion in my mind of whats going on with the relationship between variance and standard deviation.
first off, which one is the most elementary phenomenon, or what is the elementary phenomenon being screwed around with here? i'm guessing it's the 'dispersion' of the data values.
but what ever, some where i got the idea that standard deviation, the computation of it beyond variance, is an attempt to sort of 'standardize' matters, too where i guess, then one can get a 'view' of things from a wider perspective and then compare, sort of thing, with out having to worry about the apples and oranges issue, lol.
heading for the hills, thanks for the ear.:cat:

 

[rukus]

the values are squared so as to get a true sense of the deviation from the mean which is not affected by negative distances. Think of a number line with the mean or ev at the center. Now think of two data points, at equal distances on both sides of that mean. If you calculated the differnce between each data point and the mean and took the average, what do you get? ZERO average deviation from the mean! But we know BOTH data points have deviated from the mean so seeing a zero average deviation tells us nothing. So, before taking te average of any deviations, we square the differences between each data point and the mean to remove negative values. Then when all is sai and done, we average all these squared values up and take the square root of to get some average measure of dispersion from the mean. This way we now get a representative contributions to any dviation from the mean from all data points. Did that make any sense?

 

[iCountNTrack]

I have wanted to post something in this thread a while ago, but every time i started writing something i get distracted with other things to find more replies kind of a vicious circle:grin:. But anyway i am going to try to summarize some the ideas presented and try to add another perspective on things.

First a friendly reminder that SCORE as defined by Don Schlesinger in Blackjack Attack is an acronym for Standardized Comparison Of Risk and Expectation. He clearly mentions that this SCORE is nothing but an hourly win rate with $10,000 bankroll, full Kelly fixed betting and 100 hands an hour. He was also clear about his unhappiness with people using SCORE in lower case (score) as if it was a unitless scale to measure the attractiveness of a game when both risk and expectation are taken into account. But what he does not explicitly explain is why he specifically chose the conditions mentioned above to define SCORE. He did so because SCORE in this case would be equal to the square of the NUMERICAL VALUE of Desirability Index (DI). I stress on the words "numerical value" because DI as defined (100*EV/SD) is a unitless number or scale to rate the attractiveness taking into account both expectation and risk. So really there is nothing special about SCORE besides becoming a very popular "number" in the BJ community. You can certainly define your "own SCORE" but this is like defining a new mass unit to impress your weak minded friends that you lost some weight:laugh:

Perhaps it is not the best place to talk about this but it is pertinent to some posts in this thread. There is a large tendency within the community to report the ev of a given AP technique as a percentage. This percentage could unfortunately be unhelpful and even misleading at times. To illustrate this point, you might be shocked if i tell you there is only a mere 0.15% increase in % ev going from (straight card counting) to card (counting+shuffle tracking 1 slug), to a point where some might think why even bother with shuffle tracking, but if we all take a closer at the win rate (or SCORE ) we will realize that STing is very profitable. What we really care about is our win rate not the percentage, but win rate=ev%*(total action or bet per hour), total hourly action is directly proportional to our ability to detect advantageous situations (when i know i have an advantage i put more money on the table), and this exactly what Sting does, it helps identify MORE advantageous situations thus increasing my total action and consequently my win rate (even in the extreme where %ev does not increase).
So the bottom line is we should always report the ev as a win rate and standard deviation (conveniently in betting units), everything after that becomes easy to calculate.

 

[blackjack avenger]

SCORE & score

SCORE is a great way to compare games. The problem is if we don't play just like the variables in SCORE, then we would need to compare games based on how we would actually play them in the real world. However, I would imagine most of the time one's personal score rating of games would be similar to the SCORE rating.:joker::whip:

When looking at games SCORE is a good place to start and then look at your personal score.:joker::whip:

 

[blackjack avenger]

Oh Yeah!

the values are squared so as to get a true sense of the deviation from the mean which is not affected by negative distances. Think of a number line with the mean or ev at the center. Now think of two data points, at equal distances on both sides of that mean. If you calculated the differnce between each data point and the mean and took the average, what do you get? ZERO average deviation from the mean! But we know BOTH data points have deviated from the mean so seeing a zero average deviation tells us nothing. So, before taking te average of any deviations, we square the differences between each data point and the mean to remove negative values. Then when all is sai and done, we average all these squared values up and take the square root of to get some average measure of dispersion from the mean. This way we now get a representative contributions to any dviation from the mean from all data points. Did that make any sense?

Bet I can count down a deck faster then you!:joker::whip:

Well said, I think!:joker::whip:

 

[Nynefingers]

Bet I can count down a deck faster then you!:joker::whip:

Well said, I think!:joker::whip:

Note that the squaring of the difference does something more important than just get rid of the negative signs. What it does is it effectively gives more weight to numbers farther from the mean. In my mind, that's the whole point of the SD or variance is to quantify the "spread" of the data. For example, look at the following two sets of data:

-2 -1 0 1 2
-4 -2 0 2 4

Both have an average of 0.
For the first, the variance is [(-2)^2 + (-1)^2 + 0^2 + 1^2 + 2^2] / 5 = [4 + 1 + 0 + 1 + 4] / 5 = 10 / 5 = 2
The Standard Deviation is the square root of the variance, or sqrt(2)
For the second, the variance is [(-4)^2 + (-2)^2 + 0^2 + 2^2 + 4^2] / 5 = [16 + 4 + 0 + 4 + 16] / 5 = 40 / 5 = 8
The Standard Deviation is sqrt(8) = sqrt(4 * 2) = sqrt(4) * sqrt(2) = 2 * sqrt(2)

As you can see, when we scale the data set by doubling all of the values (positive and negative), this doubles the SD, while the variance goes up by a factor of 4. A practical example would be doubling your betting unit, which doubles your EV and also your SD.

I'm not sure that helped you any at all

One caution... When using SD or Variance to determine things like RoR or a range of possible results, make sure that the data is normally distributed or that the size of the sample is large enough so that the data behaves as a normal distribution. I got into this issue recently in trying to determine what range of results to expect over a given number of hours of counting, such as 50 or 100 hours. For just normal counting, a 50-100 hour "session" is more than adequate for the results to follow a normal distribution. My issue was that I had a side bet with a particular payout that contributed a small but significant amount to the EV, but did so by paying a large amount very infrequently. So infrequently, that it would be only around 6-7% likely to occur during 100 hours of play, but one occurrence was possible and two occurrences would be fairly rare in 100 hours. A normal distribution does not accurately describe the probability distribution for my range of expected results. A more accurate distribution would look like a normal distribution at a lower mean, but with an extra small hump up higher than the mean, with the distance between the humps equal to the amount of the infrequent side bet payout. As the length of time is increased, both humps would move to the right (since we are playing with an advantage), but they would slowly meld together as a new hump arose for the times when we hit 2 of the infrequent payouts. As you continue to increase the timeframe, you would see more of the same movement, with the overall shape becoming more and more like a normal distribution, until we reach a point where we can use the assumptions and the math that goes along with the normal distribution. I know I kind of went off on a tangent here, but my point is that you should not rely on SD or on RoR calculations based on SD if your results depend heavily on something very infrequent.

 

[rukus]

agree with your second point about being careful using tools meant for normal distributions. However in regard to point 1 I

 

[Kasi]

I think one of the potential seeds of confusion is that both the terms win-rate and EV can be used to mean a percentage or a $ amount, depending on the context.

In this context, we really have to be talking about $ amounts, because the bankroll is one of the variables that affect our calculations - the amount we bet at each TC is proportional to our bankroll. So a bigger bankroll means a bigger score (though not a bigger SCORE, which must by definition assume a $10K bankroll).

Don't mean to continue this, not that I can add much, but, you're right I find "win-rate" confusing too. I guess in addition to $'s and %age, you could use min units too.

A bigger bankroll could mean lower score but also with lower risk while still beting optimally. Often this is the case becasue noone bets full-kelly anyway with that 13.5% ROR.

Also, the amt bet at each TC is often not proportional to roll - if playing-all we still often bet something in -counts despite a -EV. It's more like the Kelly-stuff(sim) figures out the best way to bet when so the avg EV compared to avg SD is optimal over all hands played. I don't know how it does it exactly except that, maybe, it's actually a trial-and-error-process, some kind of iterative stuff or something lol.

Don, in his tables, also has a "unit" column. That's the biggie, to me becasue I will always win that many units per hand no matter how many dollars I have as a roll or how many dollars I use as a min unit - I just want to bet x units at each TC kind of thing. It minimizes the number of units I need in a roll

Also, regarding DI vs SCORE, I think one reason of using SCORE was so that, if one only used DI, one might assume a DI of 5 vs a DI of 7.07 might seem like it meant the latter game was only 40% "better" than the "former" game rather than making it easy to see the "latter" game is twice as "good" as the former game if using SCORE. (5 squared is half of 7.07 squared). As Don pointed out somewhere.

Don could have assumed anything he wanted in defining SCORE - it wouldn't change a thing as to determining the best use of one's money in a fixed time period, would it?

All great if you want to know is it worth driving an extra hour to a better game etc, maybe, but at least know exactly as best one can what to expect in whatever game one chooses to play and how.

Whatever, I see no reason to ever bet anything other than an amount that keeps one risk the same, more-or-less, in whatever game while always betting "optimally" in whatever game.

This might actually mean, OMG, running more than one sim might be actually something to do to accomodate "real-life" stuff.

It's not like anyone can play even one round that a sim couldn't tell you what to expect and risk from that one round and how to bet that round.

Theory and reality seem to meet somewhere has been my experience lol.

 

[Kasi]

A practical example would be doubling your betting unit, which doubles your EV and also your SD..

Sure, if u mean EV & SD are in $'s.

If so, "doubling betting unit" means orig $ roll has half as many min-units.

Which, in turn means, your risk is now square root of orig risk.