John Lewis: Comp dependent 16 v 10 indices

[Zenfighter]

Zenfighter's 2-card composition dependent indices are as follows:

10, 6 v 10: +3.6
9, 7 v 10: +0.3

Not exactly, they are 3.4 and -0.3, which are pretty the same as Wong?s 4 and 0, anyway.

One would presume that 10,6 v 10 hands are almost precisely 4 times more incident than 9,7 v 10 hands,

Almost yes

0.014479638009/0.00386123680242 = 3.75 by rounding

It would be very interesting to examine a 3-card and 4-card composition dependent analysis of this hand.

There are only 29 cases of 4 card 16s. Maybe Cacarulo is going to bite on this academic finesse. :-)

See the Theory page for the 3 cards, 16 vs T.

Sincerely

Z

[Cacarulo]

> Zenfighter's 2-card composition dependent
> indices are as follows:

> 10, 6 v 10: +3.6
> 9, 7 v 10: +0.3 Not exactly, they are 3.4
> and -0.3, which are pretty the same as
> Wong?s 4 and 0, anyway.

As I said in my previous post the indices should be +3 and 0. Besides, EOR-based indices do not take into account penetration and/or cut-card effect.

> It would be very interesting to examine a
> 3-card and 4-card composition dependent
> analysis of this hand. There are only 29
> cases of 4 card 16s. Maybe Cacarulo is going
> to bite on this academic finesse . :-)

Be careful on how you count the cases. You should count "all" the possible hand combinations. As an example take the following 3-card composition:

556 vs T

Assuming this as ONE group comprised of two fives and one six would imply that any combination of these three cards is equally likely to occur which is obviously wrong. 655 and 565 should never occur because we would be doubling 11 v T (American rules)

Having said this I get:

2-card combinations:    4 cases (T6,6T,97 and 79) 

3-card combinations:   60 cases 

4-card combinations:  283 cases 

5-card combinations:  708 cases 

6-card combinations: 1012 cases 

7-card combinations:  834 cases 

8-card combinations:  307 cases 

9-card combinations:   15 cases

Sincerely,
Cacarulo

[John Lewis]

The 3-card hand analysis of 16 v 10 is indeed interesting, and, in my opinion, useful to the player. I have posted a proposed summary of your data on Theory page.

Thank you, JL

[Cacarulo]

> It would be very interesting to examine a
> 3-card and 4-card composition dependent
> analysis of this hand. There are only 29
> cases of 4 card 16s. Maybe Cacarulo is going
> to bite on this academic finesse . :-)

Indeed there are 29 cases of 4 card 16s but, as I said, we have to distinguish the order of the hands. Actually, there are:

2 cards =  2 cases 

3 cards = 15 cases 

4 cards = 29 cases 

5 cards = 35 cases 

6 cards = 31 cases 

7 cards = 20 cases 

8 cards =  9 cases 

9 cards =  2 cases

Sincerely,
Cacarulo