CE also assumes a penalty for variance. Why not simply choose the conditions that yield the highest CE as opposed to SCORE?

MJ

CE also assumes a penalty for variance. Why not simply choose the conditions that yield the highest CE as opposed to SCORE?

MJ

*CE also assumes a penalty for variance. Why not simply choose the conditions that yield the highest CE as opposed to SCORE?
*

*MJ
*

I don't know the details of how CE is calculated, but if it relates EV to SD, by all means use CE instead of SCORE.

So if your original question had asked for the difference between WR and CE, would you now be asking "Why not simply use SCORE instead of CE?"?

*Or am I mistaken in thinking the RoR choice doesn't need be anything but universal to utilize the SCORE statistics for useful comparison? *

I pretty sure Don S. did not say, "I going to come up with a calculation based on a ROR of 13.533528323661269...%."

I've studied the Harris piece. I use his OBT calculation method in my PowerSim software to derive SCOREs, and I quote it in my manual. That's how I know 13.5% is arbitrary. If you want a different RoR, you simply change the line in the program where it says RoR = e^(-2).

It's arbitrary to choose not to resize your bets when you're invoking a betting method that requires resizing. The fact that a RoR is "oft-quoted" doesn't make it a less arbitrary a choice for a standardized rating system. Harris was NOT reommending its use for this purpose.

MathProf has gone round and round on exactly this issue with DS. As usual, MathProf is correct. It's very important for APs to understand that this is, in fact, an arbitrary number.

ETF

Several years ago, it was not necessary to register a handle in order to post. Apparently the previous "MJ" did not register the handle.

In order to compare the concepts, I found it useful to look at something like bjstats.com, under "calculate", where if you want to know a Score, you input playing strategy (e.g. Hi-Lo, etc.), number of decks, rules (e.g. S17 DAS, etc.), penetration (how many cards cut off), and bet spread. To calculate an expected Win Rate, you have to enter a bankroll you're playing to, which is theoretically tied into your max bet. In other words, Score doesn't take into account a max bet you can get on the table in a particular venue, it just compares all of the games at an equal bankroll level.

To me, an exercise such as this clearly shows the difference between the two numbers. I have had some fun inputting all kinds of numbers and plotting various graphs to find the best games for my bankroll.

And as to whether the "magical" 13.5 percent ROR is arbitrary or not (as discussed at great length off the right side of the screen below), it was my understanding that it can be considered arbitrary becasue it is tied into a specific bankroll size and overall concept of play, but it is not arbitrary because for that bankroll and overall concept of play, it produces the highest expected return balanced against the risk being taken on.

Speaking as a non-theoretician, down in the trenches, I'd be interested to know if these comments are correct.

:: ::

There is nothing optimal about a 13.5% RoR !

There is an amazing amount of confusion about this point.

because someone arbitrarily chose to use the ratio of circumference to the diameter. Instead of the diameter, one could just as easily used the radius or maybe not as easily the secant connecting the ends of 1 radian arc. (The values would be 2*pi ~= 6.28 and pi/sin(0.5) ~= 6.55.)

All I am saying is that 1/e^2 was the result of a calculation, not parameter for the calculation.

Just because pi and 13.5% have non-arbitrary sources does not mean that their use in a given context is non-arbitrary. I thought my choices for BR and ROR in "Back to the matter at hand..." specifically addressed the arbitrariness of pi :-)

Kelly betting has some properties may be considered �optimal�, but what is optimal about them is the resizing strategy. �Optimal Betting�, in the Kelly sense, involves making wagers of Ev*Bank/Variance, where the Bank is constantly changing.

There is nothing optimal about exp(-2) Risk of Ruin. It has a little more EV and a little less Variance than a 10% RoR, and a little less Ev than a 15% RoR. There is not mathematical reason to prefer one over the other, if you are engaged in Fixed Betting.

To follow up you analogy: We know that Pi is involved in the area of a circle. We don�t use it for the area of a square, or a pentagon, etc We use Pi where the mathematics tell us to use Pi.

You can, and should use CE as way of measuring games However, SCORE is used as a benchmark, for comparative purposes. As such, it is computed under some specified conditions: a 13.5% RoR on a 10K Kelly Bank.

If you used CE per hundred hands, and you specified the same conditions, the your CEs would be exactly one-half the SCOREs. You would end up with exactly the same comparisons.

The advantage is employing SCORE is that is a standard, that most palyers understand. When you tell someone you game has a SCORE of 60, most people know what that means.

In Detroit, we still measure power output in horsepower. Why horsepower ? Why not Kilowatts, which might be more logical. We did it because HP has become a standard measure; most car buyers have a n idea of what 150 Hp is.

I use the DI index in BJRM to compare different games using different strategies. I don't see CE or SCORE listed as such in BJRM, and I never use them. Can someone tell me how these correlate to DI? In the end what matters is win rate and the risk you choose, and I found the DI value to be the best index to use to evaluate win rate/risk and compare how good the game is to other games you are considering, or to other strategies you might use for the same game. You can make the DI of a bad game higher for example by increasing the betting ramp, or playing two hands instead of one. Any result with a DI below 5 is bad.

You must have an old copy of BJRM ?

Under the proper assumptions, you can compute SCORE by squaring the DI. It gives a much better representation of the game. A game with a DIU of 10 is 4 times better than one with a DI of 5, in the sense that it takes 4 hours of the latter game to equal one hour of the former game.

Most people would view of game with a DI of 5 (SCORE of 25) as poor. Below mediocre.

... one of them has to stick to the ceiling! Thanks MathProf.

OK, lessee ... SCORE is just the EV for a hundred rounds on a bankroll of $10K if the bets are optimized to RoR = e^-2. So if you want to know the EV for a different RoR, you multiply SCORE by (ln e(-2)) / (ln (new RoR)). For example, if you want to know EV for 100 rounds when RoR = 0.05, you do SCORE x (ln (e^-2)) / (ln 0.05)) = SCORE x -2 / -2.995732274 = SCORE x 0.6676164 .

You just multiply all your SCORE bets by this 0.6676164 constant and your RoR will become 0.05 and your new EV will be 0.6676164 times the SCORE.

But if you start out by optimizing to 0.05 instead of e^-2, then you don't have to do any extra multiplication. You could call it the .05SCORE, and instead of SCORE = EV^2/VAR x 1,000,000, you would use .05SCORE = EV^2/VAR x 667,616.4. You just change a constant. In fact, Sileo used .05 for his "Total Return Index" which was just the original name for .05SCORE. .05SCORE predates e^-2SCORE by approximately 10 years.

ETF

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