Everybody knows from the books that the Hi-Lo index for 16vT is ZERO. Now, suppose that with a combinatorial analyzer someone decided to find the EXACT index for this play but with all their decimals. Let's say that the game is 1D and the pen is 32/52.
What do you think that index would be?
1) Over ZERO but less than +1
2) Under ZERO but more than -1
3) Exactly ZERO
4) None of the above
Sincerely,
Cacarulo
I guess it would be very composition dependant. I recall John Imming commenting that some plays seemed to coalesce around two points in his simulations and the different compositions produced significantly different answers.
> I guess it would be very composition
> dependant. I recall John Imming commenting
> that some plays seemed to coalesce around
> two points in his simulations and the
> different compositions produced
> significantly different answers.
Nope. I'm thinking about a generic 16vT.
Come on, give it a tryDon't need to justify your answer.
Sincerely,
Cac
I'll say between 0 and 1/2... maybe something like 0.05-0.15...
> Everybody knows from the books that the
> Hi-Lo index for 16vT is ZERO. Now, suppose
> that with a combinatorial analyzer someone
> decided to find the EXACT index for this
> play but with all their decimals. Let's say
> that the game is 1D and the pen is 32/52.
> What do you think that index would be?
> 1) Over ZERO but less than +1
> 2) Under ZERO but more than -1
> 3) Exactly ZERO
> 4) None of the above
> Sincerely,
> Cacarulo
1) Over ZERO but less than +1
My practice is to consider this index to be a RC of 1, so this is my guess.
TW
So, what's the answer? :-)
> Everybody knows from the books that the
> Hi-Lo index for 16vT is ZERO. Now, suppose
> that with a combinatorial analyzer someone
> decided to find the EXACT index for this
> play but with all their decimals. Let's say
> that the game is 1D and the pen is 32/52.
> What do you think that index would be?
> 1) Over ZERO but less than +1
> 2) Under ZERO but more than -1
> 3) Exactly ZERO
> 4) None of the above
Hi,
The idea behind this quiz was to show what happens within the zero bucket when Hi-Lo is used. I chose single deck because it has some interesting properties when floored indices are used. For instance, in single deck there is no "-1" bucket!
Other properties are that within the zero bucket there are not TCs in between! There isn't even an exact TC of +1.0 (or -1.0).
So, if we go by exact indices we would find -1.019608 (-1/51*52) then 0.000000 and then +1.019608 (+1/51*52). There are no possible TCs between -1.019608 and 0.000000 as well as between 0.000000 and +1.019608.
If floored indices were used we would have the following sequence: -2, 0, +1.
If rounded indices were used we would have the following sequence: -1, 0, +1.
Having said that it's obvious that we can dismiss some of the possible answers.
My combinatorial analyzer got the following indices for 16vT (32/52 pen):
Generic 16vT
Exact TC Index = 0.000000
Floored TC Index = 0.000000
Rounded TC Index = 0.000000
Exact RC Index = 0.000000
I have also calculated some composition dependent indices:
T6vT
Exact TC Index = 3.058824
Floored TC Index = 3.000000
Rounded TC Index = 4.000000
Exact RC Index = 2.000000
97vT
Exact TC Index = 0.000000
Floored TC Index = 0.000000
Rounded TC Index = 0.000000
Exact RC Index = 0.000000
There are different approaches for analyzing "generic" indices and depending on the approach used you can get slight different answers. Since the jump here goes from zero to +1 those could be the two possible answers.
OTOH, the composition dependent indices do not admit different answers so I can say for sure that the above are the exact indices.
Sincerely,
Cacarulo
The only "problem" with your analysis is that no player actually computes TC to the exact card.
So, with the best that a normal player can do -- quarter-deck estimation -- you will likely find different answers to the above.
For example, on p. 213 of BJA3, we find the floored hi-lo index for generic 16 v. 10 to be +1, which is why I gave that answer above.
Don
Don
Using our new EoR?s tables from the Theory Page we can get the following comp?dependence algebraic derived indexes:
T, 6 vs T = 3.35825 (3.4)
9, 7 vs T = -0.317554 (-0.3)
Bear in mind that these derivations do not account for penetration and/or cut card effects, thus you won?t be able to approach a bit more Cacarulo?s exact figures for the specific 32/52 penetration.
For single-deck players who are inclined, or do not care about the extra effort of learning comp-dependence indexes, the tables, a pocket calculator and lots of patience is all you?ll need to get a full set of them. From a practical point of view, despite the proven fact that simulated indexes are somehow better (more accurate), in the long run I?ll bet that you shall do equally well with the algebraic ones.
Sincerely
Z
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