yokspot: Frequency of 17, 7, 6 and 5

[yokspot]

I'm looking for the frequency of initial two-card totals of 5, 6, 7 and 17 against dealer upcards of 9, 10 and A. Don's frequency charts (BJA 2 p. 126) range between hard totals of 8 and 16. Can anyone supply?

The reason is I'm trying to calculate the full cost to the player of following John Patrick's basic strategy. I've used Don's charts to cover the double and split errors (0.4%), but want to add his surrender, which is actually much worse.

Thanks if anyone can help.

[Don Schlesinger]

> I'm looking for the frequency of initial two-card
> totals of 5, 6, 7 and 17 against dealer upcards of 9,
> 10 and A. Don's frequency charts (BJA 2 p. 126) range
> between hard totals of 8 and 16. Can anyone supply?

BJA2????? Shame on you! :-)

If you had BJA3 (you're the only one in the world who doesn't! :-)), you'd see from Appendix A (assuming six decks) that the answers to the above are:

Vs. 9

5: 0.092%
6: 0.092%
7: 0.184%
17: 0.456%

Vs. 10

5: 0.339%
6: 0.339%
7: 0.678%
17: 1.681%

Vs. Ace

5: 0.063%
6: 0.063%
7: 0.127%
17: 0.318%

Now, what are you waiting for?? :-)

Don

[yokspot]

Actually, I was expecting a more vitriolic response with the mention of John Patrick :-)

Nice one, Don. Thanks very much.

> BJA2????? Shame on you! :-)

> If you had BJA3 (you're the only one in the world who
> doesn't! :-)), you'd see from Appendix A (assuming six
> decks) that the answers to the above are:

> Vs. 9

> 5: 0.092%
> 6: 0.092%
> 7: 0.184%
> 17: 0.456%

> Vs. 10

> 5: 0.339%
> 6: 0.339%
> 7: 0.678%
> 17: 1.681%

> Vs. Ace

> 5: 0.063%
> 6: 0.063%
> 7: 0.127%
> 17: 0.318%

> Now, what are you waiting for?? :-)

> Don

[yokspot]

Don, since you kindly provided the info above, maybe you can help here. I am stuck on this.

Stanford lists A2 v. 5 double / hit as the closest of the BS plays. In my version of PBJ he even lists it as a hit, saying it makes no difference. I believe you agree on this (the closest decision), as you mentioned it in a brief discussuion we had ages ago.

The Cacarulo EV tables (6D, S17, DOA & DAS) give a difference of 0.0025 for doubling over hitting.

For A4 v. 4, Cacarulo gives 0.0029, so on that basis, even given the slightly greater probability of A2 v. 5, in absolute terms A2 v. 5 is still the closer decision.

However, the tables in BJA seem to give a different picture. Both conditional and absolute penalties are greater for A2 v. 5 than A4 v.4 (pp 127 & 128, v2 still, I'm afraid), which can surely only mean that A4 v. 4 is the closer double / hit decision (and the closest of all).

Can you help me out here?

[Don Schlesinger]

> Don, since you kindly provided the info above, maybe
> you can help here. I am stuck on this.

I have the answer for you. :-)

> Stanford lists A2 v. 5 double / hit as the closest of
> the BS plays. In my version of PBJ he even lists it as
> a hit, saying it makes no difference. I believe you
> agree on this (the closest decision), as you mentioned
> it in a brief discussuion we had ages ago.

It is the closest BS play of all possible plays, but it has to be for an 8-deck game.

> The Cacarulo EV tables (6D, S17, DOA & DAS) give a
> difference of 0.0025 for doubling over hitting.

Right.

> For A4 v. 4, Cacarulo gives 0.0029, so on that basis,
> even given the slightly greater probability of A2 v.
> 5, in absolute terms A2 v. 5 is still the closer
> decision.

Right, for 6-deck, in this case.

> However, the tables in BJA seem to give a different
> picture. Both conditional and absolute penalties are
> greater for A2 v. 5 than A4 v.4 (pp 127 & 128, v2
> still, I'm afraid), which can surely only mean that A4
> v. 4 is the closer double / hit decision (and the
> closest of all).

> Can you help me out here?

The tables you quote are for 4-deck. If you look at Cac's tables for the same plays, but for 4-deck, you'll see that they coincide with the BJA entries you cite.

Don