What is the difference between WR and SCORE?

If anybody knows please enlighten me. I always thought these were the same but they are not the same concept.

Thanks,
MJ

Win rate is the amount you expect to win in a given time ($/hr, for example). It's a reflection of your betting ramp, your playing skill, and the rules in question.

SCORE is a measure of how favorable a game is. Though related to win rate, SCORE also reflects the variance of a particular set of conditions. If Condition Set A and Condition Set B have the same win rates, but A has a lower variance, A will have the higher SCORE.

SCORE also assumes a particular ROR and bankroll (sort of like assuming standard pressure and temperature in a physics problem), while win rate is affected by whatever bankroll and ROR you happen to have. Since SCORE is standardized and includes a penalty for variance, it's more useful as a comparative tool than is win rate.

SCORE bankroll = $10,000
SCORE ROR ≈ 13.5% (results from Kelly betting ramp)

I'd highly recommend Blackjack Attack, 3rd ed. for a complete explanation of SCORE and values for many, many sets of conditions. You can also see how practical betting ramps affect the SCORE.

That seems a bit too risky. Is SCORE only designed to assume full kelly? The assumption of a 10k BR is reasonable.

But what if your BR is only 5k? Than SCORE is calculated as though you had a 10k BR and played to full kelly with the given bet spread?

MJ

Whether the bankroll is standardized at $10,000 or any other number, and whether the ROR is standardized at 13.5% or something with which you'd be more comfortable, is largely irrelevant. The purpose of standardization is simply to allow fair comparison among conditions; standardization is not meant to mimic anyone's personal BR or ROR.

In other words, SCORE is not telling you how much money you should have in your checking account or how much you should bet; it's just telling you how different conditions compare.

Whether the bankroll is standardized at $10,000 or any other number, and whether the ROR is standardized at 13.5% or something with which you'd be more comfortable, is largely irrelevant. The purpose of standardization is simply to allow fair comparison among conditions; standardization is not meant to mimic anyone's personal BR or ROR.

In other words, SCORE is not telling you how much money you should have in your checking account or how much you should bet; it's just telling you how different conditions compare.

Th 13.5% ROR figure is not an arbitrary figure. It is the result of using the optimal bets for a given spread and never changing it.

Using optimal bets in real life would be difficult because 1) they are usually in fractional dollar amounts and 2) you would have to recalculate your optimal bet based on your new bankroll resulting from the previous won or lost bet.

How friggin' cheap can you be, Mike? Buy the goddamn book already! :-) Can you afford the $24.99? :-)

Don

Are these your real 1st and last names? Do David and Don not like you?

This thread explains the name theory.

OK, I don't understand how it is possible for two posters to use the same handle on the same website, but that seems to be the case here. Perhaps Al Rogers can explain this one.

For the record, my first post on this website was July 4,2004, just use
the search function. Whomever the other MJ was started posting in 2002.
Maybe once a handle is inactive for a certain period it becomes inactive and another user can register the same handle?

BTW, I post at other websites as well...like RGE, BJFO, BJI, hit or stand.net....all under the same handle: MJ.

So David and Don, if you think I'm MB (I'm not) then you guys answer my questions all the time.

MJ

Sorry for thinking you were the "old" MJ--my mistake. Duplicate handles are confusing, though :-)

"Th 13.5% ROR figure is not an arbitrary figure. It is the result of using the optimal bets for a given spread and never changing it."

I'm sorry, Panama, you seem to be struggling to say something, but I don't know what it is. It's optimal, but then you forget to change so it's not optimal? By definition, optimal would be 0%.

Nothing forces the use of 13.5%. You can set RoR to whatever you like -- 5% ... 1% ... As long as you're consistent, the relative rank and merit of every game remains exactly the same. The bets are still perfectly optimal. You just change a constant in the calculation.

ETF

Betting Full Kelly you would normally re-size your bet units if you lost bankroll. The 13.5% ROR assumes NO resizing. Full Kelly with constant re-sizing has much much lower risk of ruin. Even just resizing after you lose 1/4, 1/3, 1/2 etc of your bankroll lowers risk of ruin (I can't quote the exact figure)

Our Team uses 1/4 Kelly + resizing each time we lose 1/3 of the bank, then again when we lose 1/2 of the bank with the final resize when losing 2/3 of the bank. (although usually by that time we have a margin call from the investors). 1/4 Kelly with no resizing has a risk of ruin of 0.03%, with resizing our ROR is essentially zero. Nothing is more frustrating than losing money betting at full stakes and then having to win back the losses at 1.5x or 2x the units at 2/3 or 1/2 stakes. But sometimes it is the only way to keep yourself in the game, and at lower stakes certain games with higher win rates (like certain off-strip double deck games) become playable when the higher bet levels would scare them too much too quickly. (Like you can bet 2x$300 at Palace Station's double deck game whereas 2x$600 would not last long at all).

There are, of course, other things that enter into the risk for a given bankroll, for example, the more often you distribute profits, the more likely you are to experience a dramatic downswing that will cause you to have to resize. If you're betting full kelly and take profits from your bankroll, you're risk of ruin is much higher than advertised. Look in the Archives for a POM by Mathboy regarding Long Term Risk of Ruin.

"Th 13.5% ROR figure is not an arbitrary figure."

13.5% is 100% arbitrary. It's not optimal. It's not simpler to calculate than any other RoR. It provides exactly the same comparative scale as any other RoR. How much more arbitrary can you get?

Betting Full Kelly you would normally re-size your bet units if you lost bankroll. The 13.5% ROR assumes NO resizing.

Right! That's what makes it arbitrary. Kelly has nothing to do with SCORE. Kelly betting means resizing in a particular way.

If you make it sound like 13.5% is the inevitable number because of "Kelly" or something, there's a danger people will think that 13.5% is optimal, or that resizing is not optimal, or even worse, that NOT resizing IS optimal. I'm not saying it's an incorrect choice, just that it's completely arbitrary.

ETF

Thanks, ET Fan, for trying to regain some focus in this thread.

Though Don probably choose BR = $10,000 because it could be close the the BR for some players and is a nice round number, and ROR ≈ 13.5% because it results from an initial, but unchanging, Kelly betting ramp, these choices were still pretty arbitrary, as ET Fan pointed out. Don could have chosen BR = $3,141,592 and ROR = 6.53% as the standards for SCORE with little adverse effect.

SCORE was designed first and foremost (and perhaps exclusively) as a comparative tool. Just as there's nothing magical about setting standard temperature and pressure to 0�C and 760mmHg, there's nothing magical about Don's choices for SCORE. No one needs to argue for a particular ROR, or how such a ROR could be achieved. No rational physicist, for example, would argue, "0�C is unrealistic because it's usually much warmer than that!" Standards are chosen to standardize, nothing more.

All of this discussion about the difficulty of optimal bets in real life, how one particular team resizes its bets, etc. is completely ancillary to the answer to the poster's original question. In a nutshell: WR = how much you expect to win in a given time, SCORE = a very good tool to compare the favorability of different playing rules and conditions. That's it. It's amazing how quickly these discussions seem to derail.

It strictly the result of starting with optimal bets and never resizing them.

You might want to read all about it:

The Theory of Optimal Betting Spreads by Brett Harris
http://www.bjmath.com/bjmath/Betsize/theory.htm

In particular:

A fixed betting scheme differs from a Kelly scheme, in that the betting unit
is not varied as the bankroll changes. As a consequence, the main consideration
for a fixed scheme is Risk of Ruin, where there is a finite chance that the
bankroll may reach zero.

[a bunch of math]

So we get the extremely simple form for the risk of ruin,

R = e ^ (-2 * alpha) (72)

where alpha is simply the ratio between the bankroll C and the system
functional K[B].

One immediate result of Eqn(72) is the often quoted figure that the risk of
ruin for a fixed spread, where the bankroll is given by the 'Kelly' bankroll
K[B], is equal to

R(alpha=1) = e^(-2) = 13.5% . (73)

The fact that it is logical doesn't mean it isn't subjectively arbitrary.

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 suspect ET Fan doesn't require instruction.