Why does SCORE = win rate?

[DSchles]

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)

Yes, all four are true.

Don

[Phoebe]

Arghhhh !
I tried to edit my 2 last posts with a smartphone (for grammatical mistake) . I deleted them by mistake :-(

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

In short.
A) is THE definition.
B) demonstration is easy

You want to demonstrate that 10000*E²/SD²=E
<=> SD²=10000*E

Well know formula : RoR=exp(-2B*E/SD²)
If RoR=13,53%=exp(-2)

B*E/SD²=1
SD²=10000*E

QED

[MercySakesAlive]

If EV = edge and edge = EV then EV = IBA.

But then the formula... EV = IBA * bet... doesn't make sense when you substitute EV for IBA.

How can EV = IBA? I must be having a semantics problem?

Thanks, Don.

Thanks, Phoebe. I worked through the RoR formula and yes, that makes sense. Thanks for your help.

[Phoebe]

I think that in English EV (Expected Value) is somewhat ambiguous.
For instance, in CVCX it can be Win/round or %W/L

First is in $ (currency unit) as EV=IBA*bet
Second is in % (no unit) as EV=IBA

In mathematic formulas, resolution is obvious by the combination of units.

PS: From a star (private joke) of my knowledge: Sometime, as a shortcut "=" is used as "is"

[MercySakesAlive]

How can EV = IBA = win per round?

I'm hung up because

1. I know that ... win per round = average bet * average advantage

2. average advantage is another way of saying IBA so average advantage = IBA

3. If average advantage = IBA and IBA = win per round then when I substitute these into 1. formula above I get :

4. win per round = average bet * win per round .... which makes no sense.

[Three]

They are the same thing but in different units. IBA is in percentage. Win/round is in dollars so you multiply IBA times your average bet. Your average bet is a constant. It is the average over millions of rounds. So it is like kilometers per hour versus miles per hour. Multiply the number of miles per kilometer and you convert kilometers per hour to miles per hour. That number is a constant. Take IBA and multiply it by average bet /round (another constant) and you get win/round. The unit goes from a percentage to a monetary unit.

[Three]

3. If average advantage = IBA and IBA = win per round then when I substitute these into 1. formula above I get :

IBA doesn't equal win/round in dollars. IBA = win per round as a percentage of your initial bet.

4. win per round = average bet * win per round .... which makes no sense.

win per round = average bet * IBA

[MercySakesAlive]

Thanks, Three. All of that makes perfect sense. My problem comes down to when I try to work out the math for the problem "why does pure SCORE = win rate?". I understood Phoebe's explanation above. And I mostly understood Don's but I can't understand how IBA = Win Rate per round but in different units makes mathematical sense when you start substituting EV's for IBA's... I think I need to just spend time away from it for awhile so I can just have a mental sunrise, but this is the confused place where I am at. See attachment. why does score equal win rate jpeg.jpg

[Three]

And I mostly understood Don's

Reread Don's explanation. It was perfect.

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.

Hourly win rate = average bet/round*EV*100 rounds/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

If you are betting your correct Kelly wager, then average bet = bank*e.v./variance.
SCORE assumes $10K BR and 100 rounds per hour. SCORE = (EV/variance)^2.
So if your win rate is based on a $10K BR Kelly wager and 100 rounds per hour then win rate equals SCORE.

Do you not trust the math figured out by those that blazed the trail ahead of you? Can't you just believe Don when he says win rate = SCORE if it is based on the SCORE standards of $10K Kelly bets at 100 rounds per hour?

[MercySakesAlive]

Do you not trust the math figured out by those that blazed the trail ahead of you? Can't you just believe Don when he says win rate = SCORE if it is based on the SCORE standards of $10K Kelly bets at 100 rounds per hour?

No, no. Of course, I'm not challenging the math or anyone on here. I'm just trying to understand it. My hang up is spelled out in the attachment in my comment above. In short, I don't quite get the difference (or lack of difference) between EV, IBA, and win/ round. But you've explained it and I will spend some time with it tomorrow. Thanks for your help.

[MercySakesAlive]

I guess my confusion in understanding the math behind why SCORE = win rate comes down to :

Is EV the same as win per round or is it the same as IBA? How can it be both?

What am I missing?

The attachment spells out my confusion.

bet x iba = ev.jpg

[Three]

Is EV the same as win per round or is it the same as IBA? How can it be both?

EV can be expressed as a percentage, in which case it is IBA, or in monetary units, in which case it is IBA*average bet.

Which EV to use in a formula is implied by the units required for the formula to work out. So if SD is expressed in dollars so is EV. If SD is a percent then so is EV.

[MercySakesAlive]

I was not able to show that "EV can be expressed as a percentage (in which case it is IBA) or EV can be expressed in monetary units (in which case it is IBA * average bet.) I wish i knew what I'm doing wrong. PS I used page 20 in BJA3 to calculate the "SD percentage value."

sim 2.jpg

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