Mutli hand variance [VP]

On this page: https://wizardofodds.com/games/video-poker/appendix/3/ it shows how to calculate variance and standard deviation. It says:

Quote:

All numbers on a per individual hand basis.

If I'm interpretting that properly, does this mean I can do calculations as if I'm playing a single-line game with that variance? I'm interested in finding the variance for determining risk / bankroll requirements / full-kelly.

Here's an example, perhaps it'll make more sense with this.

5% advantage, 9/6 JOB, $5 single-line or $0.05 100-line. Single line variance is 19.51 and 100-line variance is 214.18. Question is what is minimum BR requirement to play.

Kelly:
(Edge / Variance) * BR = Wager
:.
Wager * Variance / Edge = BR

Initially, I was doing this:



And I finally re-read the "per individual hand basis" and it clicked -- at least I think so.

So now I'm thinking this is the proper way to do the math:




So, am I doing the math correctly in the second spoiler?




https://wizardofodds.com/gambling/kelly-criterion/
https://wizardofodds.com/games/video-poker/appendix/3/

why isn't it:

BR = (Edge / Variance)/wager

?

assuming your original formula is correct

Quote: odiousgambit

why isn't it:

BR = (Edge / Variance)/wager

?

assuming your original formula is correct

If you divide both sides by Wager, you have to divide both sides by BR -

1/BR = (Edge / Variance) / Wager
1/BR = (Edge) / (Variance * Wager)
BR = (Variance * Wager) / Edge

Quote: odiousgambit

why isn't it:

BR = (Edge / Variance)/wager

?

assuming your original formula is correct

I don't know why. What's the point?

Quote: RS

I don't know why. What's the point?

I'm not really all that boned up on variance but if I had the choice between single line $5 or nickel hundred play I would take the hundred play every time.

Quote: mickeycrimm

I'm not really all that boned up on variance but if I had the choice between single line $5 or nickel hundred play I would take the hundred play every time.

And I agree, I'd rather play 100-play than 1-play for the same total amount wagered. Unfortunately, it isn't always that simple. Most of the time nothing will be consistent. Maybe you have a $5 8/5 BP single line or $2 9/6 JOB 5 lines or $0.10 100-line DDB.


So, if someone is able to and knows how to do the math......is the math I did in the OP (in the second spoiler), the correct way to do it?


odious:

I can't answer your variance question but for bankroll requirements a rough guide for 50 play is that you need 7 times what you need for single line. So for a $1 50 play you need 7 times what you need for a single line $1 play.

I don't know how accurate this is but I was told this from a well respected long time VP pro. For ten play, 3 times single line.

Quote: Hunterhill

I can't answer your variance question but for bankroll requirements a rough guide for 50 play is that you need 7 times what you need for single line. So for a $1 50 play you need 7 times what you need for a single line $1 play.

I don't know how accurate this is but I was told this from a well respected long time VP pro. For ten play, 3 times single line.

Thanks.

Doing the math, according to the way I believe is correct, it says you need 8x for 50-line than you would on 1-line. And 10-line would need about 2x than 1-line. (for the same denom). So this makes sense.

I can't remember what he said for 100 play. What would your numbers say?

I remember spending a significant time studying that page and coming away flabbergasted, and this is from someone with a masters degree in a statistics related field. I remember eventually coming away with some sort of conversion that made things correct like multiplying by the square root of the number of hands. I concluded that the article was giving you a number with an ordinal meaning without something that really had a dollar significance. Notice none of the quiz questions say anything like "if you play 10000 hands of 100 play jacks or better with a 2 cent denomination, then 95% of the time your win loss will approximately be between x and y". That is what people care about. If the Wizard reads this, I would recommend using a rewrite of that article to teach people a lesson on what standard deviation actually means. Reading it again the square root correction is in the article, but I think the tables should be with the correction rather than the way they are.

Quote: Hunterhill

I can't answer your variance question but for bankroll requirements a rough guide for 50 play is that you need 7 times what you need for single line. So for a $1 50 play you need 7 times what you need for a single line $1 play.

I don't know how accurate this is but I was told this from a well respected long time VP pro. For ten play, 3 times single line.

Based on a proper interpretation of the tables, for job the distribution of outcomes is more than 17 times wider for 50 play. But this misses the point. The bankroll requirements depend heavily on your edge on the game. Imagine the extreme case when you get 10% cash back. Then you need a tiny bankroll for both of the two options.

Quote: Hunterhill

I can't remember what he said for 100 play. What would your numbers say?

Not at my computer anymore, but if I remember it correctly, it was only 10x or 11x.

Ie: single line requires $5,000. 100 line requires $50,000-55,000.