dog 21: ror ques.

[dog 21]

I believe that to determine half kelly the formula is .135 * .135 = .018225 * 100 = ror of 1.8225
It seems to me this simple formula breaks down if comparing two different risks of ruin. An example 15% ror and 3% ror. .15 * .03 = .0045 * 100 = .45 ror ?
I think this is incorrect. Does the ror gravitate toward the more risky game so much that one should just consider that the risk of ruin? I believe that time spent playing each game would be a major factor? Any thoughts from those gifted in math would be appreciated. thanx

[Don Schlesinger]

> I believe that to determine half kelly the formula is
> .135 * .135 = .018225 * 100 = ror of 1.8225

That's correct.

> It seems to me this simple formula breaks down if
> comparing two different risks of ruin. An example 15%
> ror and 3% ror. .15 * .03 = .0045 * 100 = .45 ror ?
> I think this is incorrect. Does the ror gravitate
> toward the more risky game so much that one should
> just consider that the risk of ruin? I believe that
> time spent playing each game would be a major factor?
> Any thoughts from those gifted in math would be
> appreciated. thanx

You're on the right track. But, this is a tricky concept. Formula for ROR involves e.v. and variance. Each is additive. So, to get global ROR for two different games, I believe you can weight the e.v. and variance of each game, to form a single, "blended," e.v. and variance, and then use the latter to get the blended ROR. As you said, you wouldn't be multiplying the individual RORs.

Don

[Don Schlesinger]

The concept we're discussing is similar to that used to calculate overall volatility of, say, a stock over a certain period when you know the volatilities for the shorter periods of time comprising the total period.

For example, suppose a stock exhibits 20% volatility for month 1 and 40% volatility for month 2. What is the total volatility exhibited by the stock for the two months combined?

Answer: 1. Square .20. 2. Weight it by dividing by 2 (half the time period). 3. Square .40. 4. Weight it by dividing by 2. 5. Add the two values. 6. Take the square root of the result.

{[(.20)^2]/2 + [(.40)^2]/2}^.5 = .316 = 31.6%.

As you can see, this is slightly more than the simple arithmetic average of 20% and 40% (which is 30%).

Don

[ET Fan]

> I believe that to determine half kelly the formula is
> .135 * .135 = .018225 * 100 = ror of 1.8225

1.8225% -- you need the percentage sign on there, or you'll get all twisted up. The precise number is actually e^(-4) = 0.0183156 .. ~= 1.83%

> It seems to me this simple formula breaks down if
> comparing two different risks of ruin. An example 15%
> ror and 3% ror. .15 * .03 = .0045 * 100 = .45 ror ?

0.45% -- but what are you trying to calculate? It's not clear to me. 0.45% would be the small (less than half of 1%) chance you would bust two bankrolls in a row, if the first had an ROR of 15% and the second an ROR of 3%. But is that what you wanted to know?

ETF

[dog 21]

> 1.8225% -- you need the percentage sign on there, or
> you'll get all twisted up. The precise number is
> actually e^(-4) = 0.0183156 .. ~= 1.83%

> 0.45% -- but what are you trying to calculate? It's
> not clear to me. 0.45% would be the small (less than
> half of 1%) chance you would bust two bankrolls in a
> row, if the first had an ROR of 15% and the second an
> ROR of 3%. But is that what you wanted to know?

> ETF

My original question referred to one bankroll, playing 2 different games. What would your ror be for the two games combined. I think Don answered my ques. However, you added another answer to a slightly diffent question? You answered what is the probablilty of losing the one bank and then loading up and losing the second bank? Am I correct to assume the order of the games played would not matter? Also, this would apply to more then 2 different games? thanx

[Don Schlesinger]

[ET Fan]

> My original question referred to one bankroll, playing
> 2 different games. What would your ror be for the two
> games combined.

It would depend on the expectation and variance for each game, and also how your combining the two games.

Suppose you combine the two games equally. You play one hand of game1, then one hand of game2, back and forth. Your answer still depends on the exp and variance of each game. Once you know those you can just add them, and use the standard ROR formulae.

> I think Don answered my ques. However,
> you added another answer to a slightly diffent
> question? You answered what is the probablilty of
> losing the one bank and then loading up and losing the
> second bank? Am I correct to assume the order of the
> games played would not matter?

Correct.

> Also, this would apply
> to more then 2 different games? thanx

Yes. As long as the games are independent of one another, you can multiply all the RORs together. Just to be clear, each game is working on a separate bankroll in this case, so I'm not sure of the practical application.

ETF