OCP Guessing on Paints/Asymmetric Loss Function

sagefr0g asked that I post a question I raised in a recent chat (the answer appears in Exhibit CAA).

Suppose you and your friend are playing OCP. When your friend sees a picture card, he can't tell whether it is a Jack, Queen, or King, so he uses the correct "agnostic" strategy of Playing only a QJ5 or better.

You, on the other hand, usually have a decent idea whether the picture card is a Jack, Queen, or a King, but you're not certain. You decide to use the "go-with-your-gut" strategy: if you think the card is a King (even though that's just your best guess), you Play K92; if you guess the card is a Queen, you Play Q92; if you think the card is a Jack, you Play any hand. You figure that your guessing accuracy is way better than the 33% accuracy that a random paint-guesser would have, so you think that you will outperform your friend.

Now, we know that your agnostic friend has an overall expectation of 2.408% in this game (as compared to the 3.48% that he would have if he could perfectly distinguish the paints).

Question: how high does your paint-guessing accuracy have to be in order for you to have the same overall expectation as your friend? If your accuracy is 50% (e.g., if you guess that the picture card is a Queen, you are right half the time, as opposed to a monkey who guesses correctly only one third of the time), will you perform better or worse than your agnostic friend?

Question: how high does your paint-guessing accuracy have to be in order for you to have the same overall expectation as your friend?

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75%?

If your accuracy is 50% (e.g., if you guess that the picture card is a Queen, you are right half the time, as opposed to a monkey who guesses correctly only one third of the time), will you perform better or worse than your agnostic friend?

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Worse?

P.D.

Very close guess, PDragon.

If you guess with less than 77% accuracy, you will underperform your friend. Think about that level of accuracy! Suppose you guess the card is a King. If just one in four times the dealer flips over the card and it turns out to be a Queen or Jack, you are playing a worse game overall than your friend who just plays QJ5 against any picture card.

Let's try to dissect the difference between you and your friend. When you guess Queen, you play Q92+ and your friend plays QJ5+. Hardly any difference there. When you guess King, you play K92+ and your friend still plays QJ5+. Again, there isn't much difference there, since there are only a few hands that you will fold that your friend will Play (the hands that are in between QJ5 and K92). Let's pretend that these preceding differences are negligible, and proceed to the meat of the issue:

The big difference comes in when you guess Jack. Now, your friend plays only QJ5 or better, but you play everything. You are playing all those garbage hands that your friend is folding. If you are right that the dealer has a Jack, your Play is marginally better than your friend's fold. It's a gain for you, but not a huge gain if you compare the EV of Playing vs. the EV of folding. BUT, what if you are wrong and the dealer does not have a Jack? The garbage hands that you are Playing are costing you a full unit (your Play bet) compared to your friend who is folding those garbage hands.

When you are right about the Jack, you gain A LITTLE BIT over your friend, but when you are wrong about the Jack, you are losing A LOT compared to your friend. Those capitalized words in the preceding sentence represent what I mean by "asymmetric loss function." Thus, you need to have high guessing accuracy (77 of 100) so that there will be many instances where you gain a little bit, in order to compensate for the occasional (23 of 100) instances where you lose a lot.

Whats OCP?

shadroch said:

Whats OCP?

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ONE CARD POKER

or depending upon your field of study:

obligatory contour principle
oral contraceptive pill
Order Code Processor

BJC

the OCP problem fascinates me. the math to get the answer and an understanding of how one is supposed to play OCP are facets that i don't have competence in.

whatever the "asymmetric loss function" point is clear and appreciated.
lol, clear and appreciated as it is, it's one of those things that can get you if you don't watch out. it's one of those things about gambling that tends to be 'shrouded' from our awareness not entirely unlike the fallacy of the gamblers fallacy.

so but anyway, the OCP problem has a lot of facets of interest with respect to gambling.
there is the probability maths and the question of do we really know what we a doing all bollixed up in it, lol.

so anyway below are some image snippets of further chat on the matter and i included a link and image snippet of some of Taleb's thoughts on the matter of uncertainty. http://www.fooledbyrandomness.com/

i'd be interest in any specific references to game theory texts that concentrate on these sorts of matters.

Moderator - move this thread to the correct forum. zg

I haven't figured out the motive on ZG bumping old CAA threads yet. Anyone?

Edit: Nevermind. Found the unsatisfactory answer in the other thread.

Looks like it's in the right place to me. You can contact me privately if you want to discuss it, but it is probably best to let it be.

-Sonny-

Okay, no big deal, I just happened to notice.
There is no perfect forum currently for this one anyway.

Perhaps change the name of the forum to AP - Theory & Math? zg

covariance

for blackjack we know stuff about covariance, betting more than one hand sort of stuff.
is the methodology for covariance the same sort of approach for OCP as it is for blackjack?
is there information about this in ExhibitCAA?

sagefr0g said:

for blackjack we know stuff about covariance, betting more than one hand sort of stuff.
is the methodology for covariance the same sort of approach for OCP as it is for blackjack?
is there information about this in ExhibitCAA?

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Yes there is covariance and it is explained in CAA. I don't have the book with me right now, but i believe standard deviation drops from something like 1.6 to 1.3 units per hand if playing 2 hands on the same table.

sagefr0g said:

for blackjack we know stuff about covariance, betting more than one hand sort of stuff.
is the methodology for covariance the same sort of approach for OCP as it is for blackjack?
is there information about this in ExhibitCAA?

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