[extropy-chat] About ESP, etc.

[gts]

On Mon, 30 Apr 2007 18:00:53 -0400, Damien Broderick  
<thespike at satx.rr.com> wrote:

> This comment might have had the unfortunate effect of deterring the 
> knowledgeable from further comments that might help disambiguatecheaters  
> from psychics in such games. Please don't be put off!

No problem, I'm still with you...

> A card-counter, according to most of the card-counting strategies I
> have seen, plays the optimal strategy at all times; sticks the
> minimum bet most of the time and increases it minimally when the odds
> favor winning.

Yes.

> Since the optimal strategy is known it can be observed
> that the player is following it; he profits only because he places
> higher bets during his winning streaks.

Not exactly. The counter places higher bets when the odds are in his  
favor. Such favorable conditions may or may not be "during his winning  
streaks" and in fact almost half the time they are not. (Counters believe  
in statistics, not streaks!)

> A psychic, on the other hand, may get cues that cause cardplay to  
> deviate from the optimal strategy:

Yes, that would be a clue that our player has some kind of psychic  
advantage.

> Behavioral clues that a player is a "clairvoyant" who can reliably
> "see through" one thickness of pasteboard:
>
> -Always buys the "insurance" side-bet if the dealer actually does
> have a hidden blackjack, and never buys it otherwise. [Optimal
> strategy never buys insurance -- lacking inside information, it's a
> sucker bet that increases your overall loss rate.]

The insurance bet is a sucker bet only for non-counters. Optimal  
*counting" strategy calls for taking the insurance bet when the count is  
even mildly positive (indicating a probability that the dealer's hole card  
is a ten or a face-card), which is the case about half the time that the  
dealer shows an ace. Optimal *basic* (non-counting) strategy does however  
call for declining the insurance bet every time.

> -Never busts when requesting another card. [This may cause him to
> decline a card when the optimal strategy calls for one.]

Yes, an infallible clairvoyant would never bust, (that is, unless he was  
going to lose anyway and sees that taking a bust card would make some  
future hand a winner, but this supposition starts to get complicated...)

> -Doubles down whenever his third card brings him to 21, or to a
> number that will beat the dealer's initial hand of 17 or better
> (standard rules require the dealer to stand on such a hand). [This
> will almost certainly produce double-down bets when the optimal
> strategy says otherwise.]

Yes.

> -Keeps initial bet at a constant level. [Inconsistent with card  
> counting.]

No, like a card-counter, an optimizing infallible clairvoyant would  
increase his bet when he anticipates a winning hand. Note that he'd also  
bet the table minimum when he anticipates a losing hand, and that losing  
hands would happen quite often even despite his special powers (excluding  
psycho-kinesis).

> Behavioral clues that a player is a "precognitive" who gets ashort-term  
> warning only of good or bad outcomes, without details:

> -Bets the lower limit most of the time, but unpredictably raises betto  
> the upper limit, and is always dealt a blackjack when thishappens.  
> [Inconsistent with card-counting. Over the long run,probably also  
> inconsistent with dealer's sanity. I am assuming thatthe precog gets  
> immediate feedback on the outcome of one decision orevent at a time, and  
> winning on a dealt blackjack is the only*immediate* good outcome  
> possible when deciding whether to play another hand.]

Not sure what you mean here or in what else you wrote.

Seems to me our precog as you define him may or may not play like a  
card-counter, depending on what he is having precognitions *about*. If he  
is intuitive about the statistics of the deck then he would play like a  
counter; but if his intuitions were about the next cards in the deck and  
the dealer's hole card then he would play like a clairvoyant. Of course  
there is some overlap here.

-gts