CV

[Warren Whitmore]

Excellent article. Do you have any data to suggest the optimal point in a 100 player tourneyment?

[chris_a]

Thanks...

I don't know what you mean by "optimal point in a 100 player tourneyment." Then again, I'm not much of a tournament player so maybe I'm missing out on some lingo. Maybe you can either state precisely what you mean or take it to one of the tournament forums.

Chris

[Warren Whitmore]

What I mean in this case is that playing to maximize ones EV for any given hand in a tourneyment does not appear optimum. Maximizing or minimizing ones standard deviation also does not appear to be optimal. It seems (perhaps I am incorrect on this point) that there must be some ratio that is optimal.

[chris_a]

The thing that you want to maximize is the expected value of your cash prize which is different from the EV in terms of tournament chips.

For instance, if you are in a tournament that pays the top 5 and there are 6 players left and there is a player who will have to go all-in next turn. You have a medium sized stack and everyone folds to you on the button when the two chip leaders are the blinds, you probably don't want to play pocket queens as you would in a no-limit ring game because on next hand the short-stacked guy will have to go all-in and you will cash.

[BillC]

CV has been used for a long time in blackjack world, and is sometimes known as the "desirablity index". It is proportional to the rate of expected bankroll growth when using fractional Kelly betting. It is mentioned in my July magazine article.

The point of this in poker is that if you are playing games with an 'appropriate' bankroll, then your 'CV' is a good way in theory of comparing different games. This is a refinement of the flawed notion of maximizing EV.

BillC

[chris_a]

[ QUOTE ]
The point of this in poker is that if you are playing games with an 'appropriate' bankroll, then your 'CV' is a good way in theory of comparing different games. This is a refinement of the flawed notion of maximizing EV.

[/ QUOTE ]

Be more clear. What do you mean by a good way of comparing different games? It depends how you define good right? If by good you mean most profitable, then CV isn't the best obviously (EV is the most important factor).

If by best you mean the game that makes you most likely be positive, then CV is important.

And what's so flawed about maximizing EV? Maximizing EV makes you maximize your long term bottom line... isn't that what matters in the long run?

[BillC]

When betting Kelly or fraction thereof, you decrease or increase your bets according to your bankroll. The CV is proportional to the rate of growth of your expected bankroll. That is why it is a good measure. It is also related to the Shrape ratio in Portfolio theory.
This stuff has been written about at length (see for example bjmath.com and my July magazine article). The point is that maximizing EV is incorrect. Maximizing EV would have you betting your whole bank with the any advantage whatsoever--a sure path to ruin. I won't elaborate further here. You can read about it yourelf.

[BillC]

I meant Sharpe ratio.

[chris_a]

I think we are arguing separate points. My point is: If you have the sufficient bankroll to have a low chance of going bust in a game, then maximizing EV in that game is clearly your best long term strategy at that game. Your point seems to be: Kelly betting is optimal for bankroll growth.

I'm assuming a fixed betting structure and you're assuming that you can change your betting to whatever you want.

Kelly betting assumes a completely different betting paradigm. That is, that you are able to change your bet to whatever you want. As you said, Kelly betting optimizes the expected rate of your bankroll growth. If this is what you mean by "good" then that's fine.

All that being said, if your bankroll is all you have to live on, then Kelly betting might be too risky. You might be better off finding a game with a risk of ruin that you are comfortable with and maximizing your EV in that game.

[BillC]

Maintaining a constant risk of ruin is equivalent to fractional Kelly betting as explained in our bjmath.com article. We call it "instantaneous" risk of ruin. It gives the ror if you suddenly stopped resizing (like a projectle in a force field has instantanoeus velocity)

So it seems that always having an "appropriate" bankroll for a game is about the same as proportional betting.

Full Kelly corresponds to an instantanous risk of ruin of 1/e^2 or about 13%.

You must take variance into account if risk (of ruin or other drawdown) is a factor. It's a tautology! Balancing risk and reward is the the 2nd most basic financial calculation. EV is the first moment and variance is the second...

You pointed out one interpretation of CV. I am pointing out another one which is directly and clearly related to game choice for those not greatly overbanked for the game in question.