MJ: Certainty Equivalent? Don

[MJ]

I see this term from time to time and am curious to know exactly what it means. On CVCX it is defined as "the value of a wager".

In the "Hot Shoe" DVD Andy Bloch from the MIT team mentions "certainty equivalent" when talking about how the players are paid. He says something along the lines of after a playing session a player would find the EV for various hands via SIM, then subtract the variance to calculate the certainty equivalent. In this fashion players are paid based upon the CE that they generate. So this way players were encouraged to make money and reduce variance at the same time. Does that make sense?

The other time I see it used pertains to indice numbers. For example, splitting 10s if the certainty equivalent is 4.

Does this term have several meanings or am I missing something? Thank you for clarifying.

-MJ

[Don Schlesinger]

> I see this term from time to time and am
> curious to know exactly what it means. On
> CVCX it is defined as "the value of a
> wager".

The math can get a bit complicated, but there is a discussion of CE on pp. 371-74 of BJA3. In general, the notion is one of what fraction of expected value for a risky wager a person would accept with certainty -- that is, with no risk.

> In the "Hot Shoe" DVD Andy Bloch
> from the MIT team mentions "certainty
> equivalent" when talking about how the
> players are paid. He says something along
> the lines of after a playing session a
> player would find the EV for various hands
> via SIM, then subtract the variance to
> calculate the certainty equivalent.

The formulas appear in BJA3.

> In this
> fashion players are paid based upon the CE
> that they generate. So this way players were
> encouraged to make money and reduce variance
> at the same time. Does that make sense?

Yes.

> The other time I see it used pertains to
> indice numbers. For example, splitting 10s
> if the certainty equivalent is 4.

Not a common usage.

> Does this term have several meanings or am I
> missing something? Thank you for clarifying.

There is a paper on the certainty equivalent that was posted on one of the Web sites a long time ago. I'm sorry I don't have the reference, but you should be able to track it down. If I find it, I'll post back here.

Don

[Don Schlesinger]

http://www.bjmath.com/bjmath/kelly/kellyfaq.htm

See Q3 and Q4.

Don

[MJ]

Thanks Don I read the information from the link you provided. If the CE is important enough for the MIT teams to use to figure out how much $$$ to pay the players then howcome other teams don't use it? From what I understand most teams pay their players using either a flat salary(so many dollars/hr) or pay them based upon how much they invest in the bankroll.

I don't think Ken Uston and his teams used the concept of CE nor did any of Tommy Hyland's teams. So was the MIT team the first BJ team to really use this concept? More importantly, if you were running a big money team would you use CE to calculate player payouts or would you use a more traditional approach?

-MJ

> The math can get a bit complicated, but
> there is a discussion of CE on pp. 371-74 of
> BJA3. In general, the notion is one of what
> fraction of expected value for a risky wager
> a person would accept with certainty -- that
> is, with no risk.

> The formulas appear in BJA3.

> Yes.

> Not a common usage.

> There is a paper on the certainty equivalent
> that was posted on one of the Web sites a
> long time ago. I'm sorry I don't have the
> reference, but you should be able to track
> it down. If I find it, I'll post back here.

> Don

[Don Schlesinger]

> Thanks Don I read the information from the
> link you provided. If the CE is important
> enough for the MIT teams to use to figure
> out how much $$$ to pay the players then
> how come other teams don't use it? From what
> I understand most teams pay their players
> using either a flat salary(so many
> dollars/hr) or pay them based upon how much
> they invest in the bankroll.

Your question can be answered on several levels. First, MIT devised their compensation scheme before SCORE became widely used by players to rate the attractiveness of games. Since SCORE incorporates the principles of e.v. and variance, it would be ideal to calculate the "value" or "worth" of a player's game, if such a figure is to be used in the overall compensation calculation.

As for a flat rate, that is usually reserved for the lower-end players who do the "grunt" work for the teams. Finally, not all players are investors, and, conversely, not all investors are players. But, it is quite advantageous for players to be allowed to invest in the team bankroll and to be compensated proportionally to the team's overall win. This privilege is not always extended to beginning players. Sometimes, through longevity, they have to "earn" the right to invest.

> I don't think Ken Uston and his teams used
> the concept of CE nor did any of Tommy
> Hyland's teams. So was the MIT team the
> first BJ team to really use this concept?

Not sure. It's not as big a deal as you think. As you can see from the formulas, CE simply adjusts e.v. for variance. So does SCORE.

> More importantly, if you were running a big
> money team would you use CE to calculate
> player payouts or would you use a more
> traditional approach?

First, I would not compensate players according to what they win individually. It's well-known that I think such a concept is inherently unfair and not grounded in logic or mathematics. But, if there were a small percentage of the overall scheme that rewarded players for the count system they used or the e.v. that the game they're playing brings to the team, I would simply use the SCORE. Nothing could be fairer.

Don

[MJ]