The “why” of the floating advantage

[ericfarmer]

http://www.edwardothorp.com/wp-conte...rEachRound.pdf

Thanks for the link, this was interesting. I had seen the "Thorp Speaks" article referenced by Don, but I think this does a much better job of cleaning up details that I felt were missing-- when I was in college I wrote a paper (here) that attempted to do this clean-up, that was apparently (at least) three years late. (For those interested, the linked Thorp paper isn't as intimidating as its 26 pages might suggest; the main point of interest here is addressed in the first 5-6 pages.)

[DSchles]

There are "only" 233,715,029 distinct subsets of 52 cards from a 6-deck shoe with RC=0. A lot, but not necessarily intractable. But as k_c says, more than I'm interested in evaluating .

(This is the coefficient of x^52 in the generating function in x and y as shown below.)

SeriesCoefficient[
    Sum[(x/y)^k, {k, 0, 24}]^5
    Sum[x^k, {k, 0, 24}]^3
    Sum[(x y)^k, {k, 0, 96}]
    Sum[(x y)^k, {k, 0, 24}],
  {x, 0, 52}, {y, 0, 0}]

Fewer than I may have imagined. But, the point is, when deciding on whether or not BS at a true count of zero confers an edge to the basic strategist (it does), if you do it by combinametrics, it simply isn't sufficient to choose those "representative" decks that strike your fancy.

Don

[peterlee]

The “why” of the floating advantage

To find the "why", we should look at the higher TC where floating advantage can easily be seen.

z210Chart.jpg

[Freightman]

Freighter, are you not doing the same exact same thing "groveling"? Hoping that your ball scratching side count will appear in the BJ ATTACK 4 EDITION.

Essentially............, I WAS. as previously defined, sucking up and grovelling are related art forms. Please also note usage of the word, “was”, further noting its enclosure front and back with quotation marks.

High level grovelling mixed with just the right amount of suck up has successfully resulted in a voluminous fluid exchange of emails. Further definition of the FBM ASC will in fact, be incorporated in BJA 4. Be sure to note it’s entry in close proximity to verbiage associated with the floating advantage.

[k_c]

Fewer than I may have imagined. But, the point is, when deciding on whether or not BS at a true count of zero confers an edge to the basic strategist (it does), if you do it by combinametrics, it simply isn't sufficient to choose those "representative" decks that strike your fancy.

Don

Yes. However, I have shown that the probability of drawing each non-ten rank is exactly 1/13 and the probability of drawing a ten value card is exactly 4/13 for a HiLo running count of 0 at mid-shoe for any number of decks. The same is true for KO at mid-shoe for a running count of -2*(number of decks). It's true for any count at mid-shoe for the count's "neutral" running count at mid-shoe.

I am not making any conclusion but only showing what the probabilities are for a random deal.

It seems a representative subset might not be too far off in this case. However, there could be a complication in computing overall EV. In completing a round of blackjack some possible random subsets may not be possible. For example in a random 48 card subset from a single deck one of the possibilities is that 4 2's are removed. Clearly this can't happen in a round. Assuming 1 player versus dealer there are probably a lot of subsets that are not possible or less likely especially early in the shoe. How much this may affect random subset probabilities later in the shoe I couldn't say.

I think that random subset probabilities would prove more useful relative to playing strategy because there is no requirement that a round be completed before they are used.

k_c

[Three]

To clarify: I am not a theoretical mathematician. But the statement by Three that, "And until there is proof the BS players advantage never changes throughout the shoe it is an assumption that is almost certainly right" is disingenuous and enraging. THE PROOF EXISTS. I'm sorry if I can't furnish it for you. But then, as you're railing against my failure to understand your convoluted logic, answer this: since the proof exists, but I can't furnish it for you, does that mean it doesn't exist? Oh!

I asked if there was proof or was it an assumption in my first post. Everything after that was based on the fact that you never said there was proof. If you would have said the proof exists that would have good enough for me. I have no issue with your integrity. You repeatedly show it to be above and beyond exemplary. I may not have been real direct with my inquiry but I think it was clearly asked and not answered in the affirmative. It is so obviously the logical conclusion I wouldn't have been surprised if nobody confirmed it. From your nonresponse I simply assumed that was what you meant.