A-Reader: Don: BJ Attack

[A-Reader]

Don,
There seemed many inconsistencies at BJ Attack tables about floating advanatage:
3rd Edition P.86 Table 6.19 versus 6.18
Per hand Expect. Count 4 Table 6.18 4.5D to 4.75D was 1.88 whihc is higher than Table 6.19 4.75D to 5D's 1.73. Same thing on Count 3 Table 6.19 was 1.26 while Table 6.18 was 1.35... Floating DISadvantage??? There were also typo at Table 6.18, 6.18A Count 4 Net Win were the same as Count 5.
For Your Information... may I have the correct numbers?

[Don Schlesinger]

> Don,
> There seemed many inconsistencies at BJ Attack tables
> about floating advanatage:

"Many" is a little harsh. :-)

> 3rd Edition P.86 Table 6.19 versus 6.18
> Per hand Expect. Count 4 Table 6.18 4.5D to 4.75D was
> 1.88 which is higher than Table 6.19 4.75D to 5D's
> 1.73. Same thing on Count 3 Table 6.19 was 1.26 while
> Table 6.18 was 1.35... Floating DISadvantage???

I went back to the original computer printouts that John Gwynn sent me in 1988, and that's the way they are! So, there is no mistake here. You have to understand that, 22 years ago, we didn't have the ability to do billions and billions of hands for each line. So, the samples were relatively small by today's standards. Here, the standard errors, which are furnished to the right, are large enough such that, if you add to the smaller value and subtract from the larger, they will "flip-flop" and become "acceptable." Not much we can do about it.

> There were also typo at Table 6.18, 6.18A Count 4 Net Win
> were the same as Count 5.
> For Your Information... may I have the correct
> numbers?

Now, THAT'S a different story! You will be interested to know that this has been wrong since the first edition!!! No one has ever pointed it out. It seems that, about once a year, someone finds a new typo. Actually, the value was given correctly in the first edition in 6.18A, but was wrong in 6.18. In BJA2 and BJA3, we seem to have compounded the problem and made it wrong in both places!

The correct Net Win value for TC = 4 is 17410.0

Thank you for that.

Don

[Don Schlesinger]

... you can have calculated the correct Net Win by simple multiplication. We have the number of hands given as 924099. And the per-hand expectation is 1.88(%). Multiplying gives 17373, which is just about the 17410 that I gave you. The small difference, of course, is due to rounduing.

Don

[A-Reader]

Were I missing the part explaining where did FA come from? Can it be the same as basic EV difference between 1D and 6D that BJ makes the difference?

[Don Schlesinger]

> Were I missing the part explaining where did FA come
> from? Can it be the same as basic EV difference
> between 1D and 6D that BJ makes the difference?

Read pp. 68-71 of BJA3.

Don

[brownian bridge]

> Read pp. 68-71 of BJA3.

> Don

If, before a round, RC was r, after the round RC was r+a,
the round used n cards.

If there were nonlinear relation between a/n and EV of the game,
and if variance of a/n were depth dependent,
floating advantage might be explained to some degree?

[brownian bridge]

> If, before a round, RC was r, after the round RC was
> r+a,
> the round used n cards.

> If there were nonlinear relation between a/n and EV of
> the game,
> and if variance of a/n were depth dependent,
> floating advantage might be explained to some degree?

additional comment

(1) Suppose, a modified BJ game(=mBJ1).

Its rules are, RC(for example, Hi-Lo) before round is r, and RC after the round is r+a,

always uses 6 cards per 1 round, (n=6)

if a>0, lose

if a=0, push

if a<0, win

in this modified game, relation between a/n and EV is linear and symmetric.

(2) Suppose, for comparison, a modified BJ game(=mBJ2)

always uses 6 cards per 1 round,(n=6)

if a>0, lose

if a=0, push.

if a=-1,-2,-3, win

if a=-4,-5,-6, push

in this game, relation between a/n and EV is nonlinear and asymmetric.

(3) Suppose, for comparison, a modified BJ game(=mBJ3)

always uses 6 cards per 1 round,(n=6)

if a=4,5,6 push

if a=1,2,3, lose

if a=0, push.

if a<0, win

in this game, relation between a/n and EV is nonlinear and asymmetric but opposite way .

Simulation data will suggest something. Perhaps.