Why does SCORE = win rate?

**MercySakesAlive** · 05-06-2018, 10:49 PM

Why does SCORE equal the hourly win rate? Could someone help me with the math on that?

PS referring to pure SCORE with $10,000 bank roll, kelly betting, 13.5% RoR, etc.

**Phoebe** · 05-06-2018, 11:40 PM

By definition

**MercySakesAlive** · 05-07-2018, 05:08 AM

In other words, why does (100 * win rate / sd) ^ 2 = win rate when using kelly betting?

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**Three** · 05-07-2018, 05:14 AM

Originally Posted by MercySakesAlive

(100 * win rate / sd) ^ 2 = win rate

Don't you mean 1.00 instead of 100?

**MercySakesAlive** · 05-07-2018, 05:27 AM

Is (100 * win rate / sd) ^ 2 not the formula for SCORE?

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**Three** · 05-07-2018, 06:34 AM

Hopefully my memory isn't betraying me.

SCORE = (EV/SD)^2

**Three** · 05-07-2018, 06:42 AM

I think you are confusing that the win rate and SD are for 100 rounds of play. To get the 100 round numbers from 1 round numbers you multiply EV/round by 100 and SD/round by the square root of 100, which is 10. So to get SCORE from per round stats you multiply 10 (100/10 = 10) inside the exponent or 100, which is 10^2, outside the exponent. If you just use EV and SD per 100 round stats it is (EV/SD)^2.

**MercySakesAlive** · 05-07-2018, 08:03 AM

Let me rephrase the question in hourly terms in two forms A and B. The question is when kelly betting why does
A. SCORE = win rate per hour.
B. (100 * win rate per hour / sd per hour ) ^ 2 = win rate per hour

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**TomLok** · 05-07-2018, 08:37 AM

score = (ev/sd)^2

**TomLok** · 05-07-2018, 08:39 AM

in stargames you can win by this formula

**MercySakesAlive** · 05-07-2018, 09:18 AM

I am not trying to check a forumla. What I am trying to understand is probably more easily understood if you've ever used CVCX. If you create a c-SCORE by using a non-optimal betting ramp, a RoR other than 13.5%, or a bankroll other than $10,000 then you will see that your c-SCORE is not the same as the win rate per hour. That is the usual because in the real world, not many folks are playing at 13.5% RoR. But if you set up your CVCX sim with the strict restraints that are necessary to produce a true SCORE then you will see that SCORE is equal to win rate per hour (or at least, it is very close). So it is a special situation that SCORE = win rate and my question is how did this come about? Pretty sure it wasn't a happy accident. I think if you have not played around with CVCX this question might be a little confusing, but thanks for the replies nevertheless.

**DSchles** · 05-07-2018, 10:57 AM

Originally Posted by MercySakesAlive

Why does SCORE equal the hourly win rate? Could someone help me with the math on that?

PS referring to pure SCORE with $10,000 bank roll, kelly betting, 13.5% RoR, etc.

Let me see how simple and intuitive I can make it.

To calculate any hourly win rate (with usual assumptions), you would multiply your average wager by your average advantage and then multiply by the number of hands per hour.

If you are betting your correct Kelly wager, it is defined as your bank*e.v./variance. Your edge is e.v. So, your hourly win rate is simply (e.v./variance)* e.v. = e.v.^2/variance, which is the definition of SCORE, assuming a $10,000 bank.

Simple enough?

Don

**MercySakesAlive** · 05-07-2018, 11:54 AM

I'm almost there now... One of my problems here is the language. Are these four statements true? Thanks.
A. win per round = expected value
B. expected value = edge
C. edge = IBA
D. IBA = %W/L (this is the language CVCX uses)