Stephen Tu, on 2016-July-15, 10:35, said:
Spisu you are just completely off base. RC is just application of Bayes theorem as described above. It is analysis that absolutely *does* depend on play from equals, the probability of a particular holding being held by opponent after the first round play is the *product* of both the a priori odds and the odds that they chose a particular honor. With holding only 1 honor the second term of the product is 100%, with 2 honors it is usually calculated as 50%, though in actuality an opponent might have quite a bit of bias towards one or the other which doesn't affect your best choice of play until it gets really extreme.
If you were playing against an opponent who was known to never randomize, and say always played the K from KQ tight, then on AJt9x vs. xxxx one could do slightly better by playing for the drop every time the first finesse lost to the K rather than taking a second finesse, finessing twice only if the first hook lost to the Q. You would pick up Kxx onside and KQ tight offside, which is better against such an opponent than finessing twice regardless and picking up Kxx and Qxx onside. RC is merely an observation that opponents can and should vary their play from equal cards, and that if you are comparing a priori odds you need to multiply by a factor taking this to account. If your first finesse lost to the K, you compare the odds of stiff K vs. *half* of the odds of KQ tight, or alternately you pretend you had bad vision and can't distinguish between equals and compare odds of KQ tight vs. *both* stiff K and stiff Q. There is nothing fallacious about RC. It does depend on opponent having choices from equals, and not having choices when having only one honor to win with.
I am familiar with Bayes and the restricted choice folks'claim it is based on the Bayes postulate known also by some as the "Equidistribution of Ignorance". The only thing missing I've noted is any confirming data to support a valid basis for that other than the claim. Note that assuming an opponent plays randomly is not mathematically valid. So if you have evidence of a Bayesian basis other than presumptions or guesses, please share. I'd love to see it.
BTW, the freq dist for lone vs double honors shows KQ, K/Q, Q/K, QK each 25%...so the frequency of a specified honor such as the K in East is 1/2 of 25% or 12.5%, while a KQ is 25%, twice that of a specified lone honor. The math of RC depends on your not noticing the frequencies are different.
For 400 hands, East holds 400 total honors 200 are divided( 100 Ks and 100 Qs) and 200 KQ combined honors. Simple math for first finesse shows 100 lone Ks played will match with 100 Ks from KQ (1:1), 100 Qs match with 100 Qs from KQ, leaving 100 KQs to nail you in the 33% of losing second finesses. There is no "half" relationship of KQ.