Standard deviation to win per hour ratio: important or not?

[Anubis]

Hey there! I'm fairly new to studying blackjack (a few weeks). While browsing around some other fourms, I came across a comment by someone that the ration of standard deviation to amount won per hour for a playing strategy should ideally be between 10 to 15. As an example, if your win per hour with a given strategy is $20/hour, the standard deviation should ideally be no more than $300/hour.

I hadn't read this anywhere else, so I wanted to see what people here thought. Do you think the ratio of standard deviation to winnings per hour does matter, as with the comment above? Or, as long as ROR is below your desired threshold (1%, 2%, whatever percent you want), does that ratio not really matter? Software I'm using to plan my first trip get me ROR below 1% with a ratio of standard deviation to winnings per hour of about 34, and ROR below 3% with a ratio of standard deviation to per hour of about 28, so if this ratio does matter I might need to plan more.

[JohnGalt007]

Hey there! I'm fairly new to studying blackjack (a few weeks). While browsing around some other fourms, I came across a comment by someone that the ration of standard deviation to amount won per hour for a playing strategy should ideally be between 10 to 15. As an example, if your win per hour with a given strategy is $20/hour, the standard deviation should ideally be no more than $300/hour.

I hadn't read this anywhere else, so I wanted to see what people here thought. Do you think the ratio of standard deviation to winnings per hour does matter, as with the comment above? Or, as long as ROR is below your desired threshold (1%, 2%, whatever percent you want), does that ratio not really matter? Software I'm using to plan my first trip get me ROR below 1% with a ratio of standard deviation to winnings per hour of about 34, and ROR below 3% with a ratio of standard deviation to per hour of about 28, so if this ratio does matter I might need to plan more.

Sounds like you're referring to Don Schlesinger's Desirability Index from BJA. For a blackjack game where the AP is back counting and only makes a bet when he has the edge, the desirability index DI is

DI = 100 x (EV per 100 Hands) / (SD per 100 hands)

For a blackjack game where the AP plays all hands and bets the minimum at non-positive counts,

DI = 1000 x (EV per Hand) / (SD per Hand)

The benchmark value of DI given in BJA is 6.6. Above that, the game is playable. Below that, look for more profitable opportunities. Between 10 and 15 is obviously well above this benchmark value, and any game with a DI above 15 would presumably be so rare as to not consider the possibility of encountering it. I'm of the opinion that ROR being below a certain threshold is just as important as DI being above a certain benchmark, because beginning APs are wiped out by insufficient capital just as often as by improper game selection. Thus, both should be factors you should consider before diving into real-world play.

[Intermediate]

I'll offer another way to look at it. Your SD/Win ratio will be dependent on the number of hands (or the number of hands per hour), and your EV per hand. if you play long enough and get to NO, your have a good chance of your win exceeding one SD.

SD = Bet x 1.6 x sqrt(n) where n = number of hands
Win = Bet x EV x n

SD/Win = 1.6/(EV x sqrt(n)) (so the better your game and EV, and the more hands you play, the lower the ratio)

So if you assume EV = 0.01 (1 percent):

for n=200 (like heads up play) SD/Win = 11.3
for n= 100, SD/Win = 16
for n= 60 (full table, slow game) , SD/Win = 20.7

You will want to maximize EV and the hands/hour in your quest to reach NO.

[Anubis]

Thank you both! I haven't heard of the desirability index, so this was enlightening. For the game examples I listed, the DIs are 2.95 for the 0.7% ROR and 3.56 for the 2.7% ROR, so maybe those aren't good ideas to play. Though those were for playing all hands, so maybe I should consider back counting if possible.

[JohnGalt007]

Thank you both! I haven't heard of the desirability index, so this was enlightening. For the game examples I listed, the DIs are 2.95 for the 0.7% ROR and 3.56 for the 2.7% ROR, so maybe those aren't good ideas to play. Though those were for playing all hands, so maybe I should consider back counting if possible.

Happy to help! Based on the numbers you've cited, your ROR is low enough to feel comfortable playing the game without reasonable fear of going broke, but your DI is not quite high enough to expect to win much relative to your standard deviation. This is part of the reason why blackjack is not a get-rich-quick scheme: you need money to make money, and you need a good game to play a good game.