Gambling vs. Advantage Play

[SleightOfHand]

I'm not sure we've been on the same wavelengh in this discussion though - I think we've been considering different measures. I've been referring to £/p (or $/c) being represented by x Std Devs derived from the EV of the overall amount I've wagered to date (which in the grand scheme of things isn't very much). Sorry if I didn't make that clear. Of course that won't be the same in £/$ terms as for someone who has wagered much more over x,000,000 hands, and where it's much more likely that the actual results will be nearer the expectation.

Now I'm confused. I'm not quite sure what you are saying. $/c?

As far as being "closer to expectation," that's not true in $ values. The more hands you play, the larger the standard deviation gets. It never decreases. It merely becomes smaller relative to the growth of EV

 

[UK-21]

Now I'm confused. I'm not quite sure what you are saying. $/c?

Well . . . if you play x hands at an average bet of $y and the EV is say +0.5%, the EV equates to $(xy) x 0.5% ?? Three Std Devs either side of this would be a value expressed in $ as well?

 

[SleightOfHand]

Well . . . if you play x hands at an average bet of $y and the EV is say +0.5%, the EV equates to $(xy) x 0.5% ?? Three Std Devs either side of this would be a value expressed in $ as well?

Your calculation for EV is correct, and yes, standard deviation can be, and usually is, measured in $ (or units) for AP. Im still not quite sure what you are getting at though. Looking back at the posts, maybe you are referring to SDs as how many multiples of EV you are experiencing? Standard deviation is not the same as EV, and cannot be calculated primarily by EV alone. A proper way to measure the SD of the game would be to find out the probabilities of the various outcomes of the game (+1 unit, +2 unit, -6 unit, etc) and use some arithmetic on those numbers. You can also use simulation and find the root sum square of the deviations from the mean of the sample you took.