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big word used on 12/12 GWAE radio show

#1

And that big word was “Certainty Equivalence”. It’s so big, you should google it. But the jist is that if your bankroll is unlimited, then CE = EV, but really, who has an unlimited bankroll? With an unlimited bankroll, the CE of say FPDW with perfect play is about 0.76% (of a betting unit). At 10x the Kelly bankroll, the CE is about 19/20ths of the EV or 0.72%. At double the Kelly bankroll, the CE is about 3/4ths or 0.57%. At the Kelly bankroll, the CE is about 1/2 or 0.38%. At half a Kelly bankroll, the CE is 0, and for a smaller bankroll the CE goes negative. Just something to consider.

CE is approximately EV - Variance/2xBankroll betting units
Kelly bankroll is approximately Variance/EV betting units

#2

noti wrote:
And that big word was “Certainty Equivalence”. It’s so big, you
should google it. But the jist is that if your bankroll is unlimited, then CE = EV, but really, who has an unlimited bankroll? With an unlimited bankroll, the CE of say FPDW with perfect play is about 0.76% (of a betting unit). At 10x the Kelly bankroll, the CE is about 19/20ths
of the EV or 0.72%. At double the Kelly bankroll, the CE is about 3/4ths or 0.57%. At the Kelly bankroll, the CE is about 1/2 or 0.38%. At
half a Kelly bankroll, the CE is 0, and for a smaller bankroll the CE goes negative. Just something to consider.

CE is approximately EV - Variance/2xBankroll betting units
Kelly bankroll is approximately Variance/EV betting units

Yes. That show was the interview of John Chang, former manager of the MIT Blackjack Team and Tommy Hyland, manager of a large blackjack team for decades. It was John who used the term. When his wife, Laurie C, was interviewed perhaps a year ago, she used the term a lot — somewhat disparagingly.

I assume NOTI’s definition is correct. I also assume that that John Chang has the ability to do the calculation. When Chang used the term, the expression on Tommy’s face said that they didn’t use that calculation on their team.

Bob

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#3

Interesting. Whoever puts up the money should use CE. I can see why the players would prefer EV, but if that’s the agreement then the players have a bit of advantage over the backers. Also if the agreement is for EV, then the players should play more aggressively (increase variance), which would also favor the players against the backers. Basically, there is a risk penalty for using EV over CE, if the agreement is for EV, the backers take that risk penalty, if the agreement if for CE, then the players take the risk penalty.

#4

I’m not mathematically competent to debate NOTI on this subject. I sent the three posts in this thread (two by NOTI bookending one by me) to John Chang — who was the one who used the reference to CE on the radio show in the first place. I asked if he had a comment that I could post here. Chang responded:

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The VPfree poster is correct, in the context of fixed bet sizes that may be the case for video poker, and assuming Kelly=1. Knowing Kelly betting is actually pretty important, as William Poundstone shows in “Fortune’s Formula”.

I’m
actually not sure how accurate the approximation CE=EV-variance/(2kellybankroll) is for video poker, which has quite a large skew. For me, I think playing errors dominated the question of how
much my video poker play was worth.

For
blackjack, where you can choose your unit, it is optimal to choose a unit so that CE=.5 EV, regardless of the Kelly you choose.