Desiribility Index

Is calculating DI the same for all games? Dividing the win
rate by the standard deviation and multiplying the result by 100?

Is the result really worth anything?

Quote: EvenBob

Is calculating DI the same for all games? Dividing the win
rate by the standard deviation and multiplying the result by 100?

Is the result really worth anything?

For a play all game it is

DI = 1000x(EV-per-hand/SD-per-hand).

For a game that is being back counted it is

DI = 100x(EV-per-100-hands/SD-per-100-hands).

My opinion is that the Sharpe ratio is worth something.

http://en.wikipedia.org/wiki/Sharpe_ratio

Quote: teliot

For a play all game it is

DI = 1000x(EV-per-hand/SD-per-hand).

Isn't this the same as dividing the win
rate by the standard deviation and
multiplying the result by 100?

If a game has a DI of 100, what does
mean to a player.

Quote: EvenBob

Isn't this the same as dividing the win
rate by the standard deviation and
multiplying the result by 100?

I don't understand what you are asking here. Yes, the second formula reduces to the first in the play-all case with certain assumptions on the distribution.

Quote: teliot

I don't understand what you are asking here. Yes, the second formula reduces to the first in the play-all case with certain assumptions on the distribution.

What does the DI number mean to a player? I see
in certain conditions of MS Stud, the DI is 100. Does
this mean you can't lose?

Quote: EvenBob

What does the DI number mean to a player? I see
in certain conditions of MS Stud, the DI is 100. Does
this mean you can't lose?

I'm not going to touch this, maybe someone else can help you.

Quote: teliot

I'm not going to touch this, maybe someone else can help you.

I'm not familiar with DI and don't know what
the DI number means to a player. I'm assuming
the higher the number, the better the game is
for the player. But how reliable is it.

Quote: EvenBob

I'm not familiar with DI and don't know what
the DI number means to a player. I'm assuming
the higher the number, the better the game is
for the player. But how reliable is it.

DI as used in the context of blackjack was "invented" by Donald Schlesinger. Here is a random post I found on the topic:

http://www.bj21.com/boards/free/free_board/index.cgi?noframes;read=155404

DI is a unitless number, so it has meaning only in reference to other DI's. You can find endless exchanges about DI on various gambling message boards if you Google "Don Schlesinger DI". Blackjack card counters obsess over DI's between about 5 and 10, with 5 a fairly poor game and 10 a very good game.

Quote: teliot

DI is a unitless number, so it has meaning only in reference to other DI's..

I understand that. But is it valid? Is a 20 really
better in reality than a 7? Or are there still
a bunch of variables involved.

Quote: EvenBob

I understand that. But is it valid? Is a 20 really
better in reality than a 7? Or are there still
a bunch of variables involved.

Without going into nuance, the most significant variable not included in DI is the table limit for the bet.

Quote: teliot

Without going into nuance, the most significant variable not included in DI is the table limit for the bet.

Meaning things can still go bad if there
isn't a high enough table limit even if
the game has a high DI number?

deleted

Quote: Ibeatyouraces

You can easily lose in this game.

So why does certain situations in the game
have a high DI? I'm just trying to find out
if a DI number is reliable in assessing a
game.

Quote: EvenBob

So why does certain situations in the game
have a high DI? I'm just trying to find out
if a DI number is reliable in assessing a
game.

It is probably the best metric you can find for the AP, as a catch-all measure to apply to all AP opportunities. But, it is easy to argue against its value for any number of reasons. For the sufficiently bankrolled AP or for wagers with a low table limit, it is probably not that important. For the vast middle ground, it aids in determining correct bet sizing.

Enough for me. Join Green Chip over at bj21 and as Don Schlesinger directly. Better yet, post on the free pages at bj21 and ask Don. He loves to talk about it. Bring up the I-18 and he'll be your best friend forever.

Quote: teliot

For the vast middle ground, it aids in determining correct bet sizing.

That's what I wanted to know.

I'm looking at this Sharpe ratio as a total subjective model. Its (gain - "tolerated loss")/SD. If the gain is 1 and the acceptable loss is 1 it solves as zero. If no loss is acceptable (a tie or win) the model reduces to 1/SD. If losses exceed the win, the model suggests a losing scenario as -x/SD.

Quote: EvenBob

So why does certain situations in the game have a high DI? I'm just trying to find out if a DI number is reliable in assessing a game.

Bob,

If we assume that you can bet whatever you want (or, equivalently, that the minimum bet is lower than you want to bet and the max bet is higher than you can afford), then the DI is measuring which game is better for you (with a given bankroll)

The key point here is that the maximum amount that you should bet with a given bankroll is based not only on your edge, but also on the variance of the game. DI combines these together, so you can just look at one number to determine the better game.

In particular, you should NOT always play the game with the highest edge! It may be that a different game with a lower edge but also with lower variance is better for you, because you can afford to bet a lot more in the lower-edge game (enough to make up for the lower-percentage edge with volume). For example, there may be one game with a 3% edge but with a high variance, where you can only afford to bet $100/hand. There may be another game with a 1% edge but with a low variance, where you can afford to bet $1000/hand. Obviously the lower-edge game is better (assuming that all else is equal) because you make $10/hand rather than $3/hand at your optimal betting amount.

But, yes, there are other variables. The first one, as has been pointed out, is max bet size. Once you are betting the max, the ability to afford to make larger bets is useless. Another important variable is game speed. If, in my example above, the $3/hand game deals 200 hands per hour, but the $10/hand game deals only 40 hands/hr, then all of a sudden the $3/hand game is better -- you may not win as much per hand, but you win more per hour. There are other variables which also may not be equal. If you have a copy of Beyond Counting, look inside -- Grosjean gives a pretty good list.

So, basically, DI is a measure of how much you can expect to make per hand with a given bankroll, assuming that you are able to make your optimally-sized bets and also assuming that all other variables are equal.

In the Mississippi Stud example, note that hole-carding can have a player edge of over 100% (depending on which card(s) you can see) which explains the off-the-charts DI. It doesn't mean that you can't lose, of course -- just that you will make more money playing this game than many other games with lower DI, assuming that the betting limits that you want are available.

EV/SD paints a picture, check it out where EV is a high HE game and vice versa . This seems to be a modification of that.

Quote: AxiomOfChoice

you should NOT always play the game with the highest edge

Did you mean lowest edge?

Quote: odiousgambit

Did you mean lowest edge?

No. We are talking about +EV games here. "Edge" means "player edge" here.