# Thread: Different Definitions of DI?

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## Different Definitions of DI?

I'm attempting to do my own math for some plays, and I've run into two versions of DI.

In my copy of Blackjack Attack (3rd edition), p.203: "I have christened this ratio the "Desirability Index" (DI) and have defined it, for any game, to be equal to one thousand times (for convenience of expression) the ratio of that game's per-hand-seen win rate to the per-hand-seen standard deviation."

In other words, DI = 1000*EV/SD.

However, here (https://www.888casino.com/blog/side-bets/fear-loathing-and-blackjack-side-bets), Eliot claims to quote from BJA as well, but makes an exception for back-counting plays.

I have christened this ratio the “Desirability Index” (DI) and have defined it, for the play all game, to be equal to one thousand times (for convenience of expression) the ratio of that game’s per-hand win rate to the per-hand standard deviation. Similarly, for the back-counted game, DI = 100 times the ratio of that game’s win rate per 100 hands to the s.d. per 100.

Is there any reason it's reduced by a factor of ten for backcounting games? Is this simply out of date information?

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Did Eliot define his reason for the backcounting adjustment?

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Might be simpler to use
DI^2 = SCORE

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Originally Posted by PitBoss321
I'm attempting to do my own math for some plays, and I've run into two versions of DI.

In my copy of Blackjack Attack (3rd edition), p.203: "I have christened this ratio the "Desirability Index" (DI) and have defined it, for any game, to be equal to one thousand times (for convenience of expression) the ratio of that game's per-hand-seen win rate to the per-hand-seen standard deviation."

In other words, DI = 1000*EV/SD.

However, here (https://www.888casino.com/blog/side-...jack-side-bets), Eliot claims to quote from BJA as well, but makes an exception for back-counting plays.

I have christened this ratio the “Desirability Index” (DI) and have defined it, for the play all game, to be equal to one thousand times (for convenience of expression) the ratio of that game’s per-hand win rate to the per-hand standard deviation. Similarly, for the back-counted game, DI = 100 times the ratio of that game’s win rate per 100 hands to the s.d. per 100.

Is there any reason it's reduced by a factor of ten for backcounting games? Is this simply out of date information?
I am not "claiming to quote from BJA," I quoted BJA. I did not make a "backcounting adjustment." I did did not misquote Don, nor did I change or alter Don's original formulas in my work.

What's the problem?

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Eliot,

The question seems to be why you use a constant of 100 rather than 1000 in your definition of DI for the back-counted game. My guess is that that is simply a typo.

Hope this helps!

Dog Hand

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Originally Posted by Dog Hand
Eliot,

The question seems to be why you use a constant of 100 rather than 1000 in your definition of DI for the back-counted game. My guess is that that is simply a typo.

Hope this helps!

Dog Hand
I believe I quoted Don exactly from BJA and there is no typo. He did use both 100 and 1000. I gave away all of my casino books so I don't have any way to check that now.

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Originally Posted by Eliot
I believe I quoted Don exactly from BJA and there is no typo. He did use both 100 and 1000. I gave away all of my casino books so I don't have any way to check that now.
There is sometimes confusion regarding the DI and SCORE definitions when it comes to back-counting. Starting with play-all, all of the charts in chapter 10 reflect results of either playing 100 hands per hour or seeing 100 hands per hour (and playing fewer, because you're back-counting).

In the first instance, if you look at any chart and take the W/100 (\$) column and divide it by the SD/100 (\$), you will arrive at DI, according to the definition, by first dividing the hourly win by 100, to get the per-hand win, then dividing the hourly s.d. by 10 (square root of 100) to get the per-hand s.d., and finally multiplying that quotient by 1,000, per my page 203 definition. Of course, so doing "undoes" the numbers in the charts, and you can get the DI directly, and more simply, from those chart numbers by simply taking the quotient of Win/SD and multiplying by 100. The results are the same.

Doing the same for the back-counting numbers results in the same, correct, DI, provided you go directly from the numbers in the charts and multiply the quotient by 100, without "decomposing" them to per-hand values. This is because we no longer are PLAYING 100 hands per hour; rather, we're SEEING 100 hands per hour but playing fewer--sometimes, say, 25 or so, and sometimes even fewer, at 15 or 16. So, we "normalize" those values in order to produce the values in the chart, and that may be why Eliot suggests multiplying those back-counting quotients by 100. In reality, ALL the quotients from the charts can be multiplied by 100 to produce the DI, but only the play-all numbers should be broken down to per-hand values and then multiplied by 1,000 (somewhat unnecessarily). Trying that approach for back-counting doesn't work as conveniently.

This is something you need to think about for a couple of minutes. If it isn't instantly clear to all of you, I apologize, but I've tried to make it as straightforward as possible.

Don

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Thank you Don, that makes a lot of sense when you lay it out like that.

DI = 1000*EV(hand)/SD(hand)

For the same value for 100 hands seen (played or not, it appears) EV(100) = 100*EV(hand) and SD(100) = 10*SD(hand), so the normalizing factor drops by 100/10.

DI = 100*EV(100)/SD(100)

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Originally Posted by PitBoss321
Thank you Don, that makes a lot of sense when you lay it out like that.

DI = 1000*EV(hand)/SD(hand)

For the same value for 100 hands seen (played or not, it appears) EV(100) = 100*EV(hand) and SD(100) = 10*SD(hand), so the normalizing factor drops by 100/10.

DI = 100*EV(100)/SD(100)

Don

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