> No, not at all. By "play on," Kat means that
> you stand and then play on. That isn't the problem.
Ok - I didn't think it was.
> You understand that, if permitted to redouble twice
> after doubling, you wind up with a wager that is eight
> times what you started with, right?
Yep.
> Just checking.
Don't get me wrong, I could have a mistake in my CA with this feature as I have with others in the past (and which I've all corrected), but I obviously don't think I do.
MGP
> When I said 6D, H17,DDD, that meant a bet could be
> doubled, redoubled, and redoubled, for a total of
> either 2, 4, or 8 bets on the table. I think maybe you
> only allowed redouble once for a total of either 2 or
> 4 bets on the table. I look forward to the resolution
> of this.
Yes that's what my CA does. It can allow any number of redoubles. The very initial response was with only 1 redouble allowed, but I also checked with 3 redoubles allowed up to a net bet of 16. The answer is the same.
Ok, here's the analysis in detail of doubling 45 vs 7. I did it partly to double check my calculations and the values came out as I expected them to so I am at least confident that my CA is working as I intendedit to. A few things:
1) The EV is slightly higher than the above post because I've allowed 3 redoubles rather than just 1. It's still not enough to overcome the ev of hitting.
2) I didn't break down the redoubling EV for 345 or 1245 because my CA gives the DEV directly when the strategy doesn't involve redoubling when examining the hand in detail so I just took it from that.
3) I did break down the EV of doubling 245 to show an example calculation of how to deal with redoubling a second time (note the strategy for 1245 is to redouble again).
4) D(hand) is the EV before multiplying by 2 and DoubleEV(hand) is after multiplying by 2. The values in the S column are stand ev's and the values in the D column are double ev's.
HitEV(45) = 0.154061577
DoubleEV(45) = 2xD(45) = 0.149496616
D(45) S D P|457 pev
145 0.753406782 0.084210526 0.063444782
245 0.394997201 0.084210526 0.033262922
345 -0.387603407 0.084210526 -0.032640287
445 -0.464870822 0.080701754 -0.037515891
545 -0.466080796 0.080701754 -0.037613538
645 -0.467098012 0.084210526 -0.039334569
745 -0.467993876 0.080701754 -0.037767927
845 -0.14323071 0.084210526 -0.012061533
945 0.338510373 0.084210526 0.028506137
1045 0.57977001 0.252631579 0.146468213
Sum = 1 0.074748308
D(245) S D P|2457 pev
1245 -0.384390159 0.084507042 -0.032483675
2245 -0.464713949 0.080985915 -0.037635285
3245 -0.464315557 0.084507042 -0.039237934
4245 -0.463938152 0.080985915 -0.037572456
5245 -0.465156775 0.080985915 -0.037671147
6245 -0.14050529 0.084507042 -0.011873687
7245 0.340672363 0.080985915 0.027589663
8245 0.581996352 0.084507042 0.04918279
9245 0.753537251 0.084507042 0.063679204
10245 1 0.253521127 0.253521127
Sum = 1 0.1974986
Double(245) = 2*sum(pev) = 0.394997201
I found a bug in my code specific to hard 12 versus 7, for index generation and BS generation only.
It's a variable misnaming, which makes EV(double) higher than it should be.
It came about because the doubling again on hard 12 thing is an exceptional case, and it was an afterthought on my original code.
Now, I haven't generated the EVs yet, as sims take time (i'll do that this afternoon), but having picked up the bug, I am pretty sure that I will be wrong on the actual play.
I'll redo the indices for redoubling, and post them.
It will mean the the win rates for redoubling will be slightly better than what I quoted in the book.
I apologize to everybody who plays the redoubling game and has bought my book. I tried so hard to mae sure the figures were f perfect, I debugged hundreds of times over three years, but that one got away.
Unfortunately, when I was in the USA, I didn't get the opportunity to play the redoubling game (just H17 and S17 games). Such is the problem with living outside the USA, but writing for an American audience. If I had played it, I would have picked the error up ages ago. It just didn't SEEM right, but I put it down to the redouble on hard 12 versus 7 thing. So the moral of the story is, it helps to play the actual game you're analyzing.
These are the plays for 10 and 11 versus 7 and 8.
7 8
10 D4 D3
11 D4 D4
> These are the plays for 10 and 11 versus 7 and 8.
> 7 8
> 10 D4 D3
> 11 D4 D4
If D4 means to double on 2 and 3 card hands and hit for 4 or more cards, and D3 means only double 2 card hands but hit 3 or more card hands, then that is correct. I had already posted the strategies for 10, 11 vs 7 and double-checked vs 8 and agree.
> I found a bug in my code specific to hard 12 versus 7,
> for index generation and BS generation only.
> It's a variable misnaming, which makes EV(double)
> higher than it should be.
> It came about because the doubling again on hard 12
> thing is an exceptional case, and it was an
> afterthought on my original code.
> Now, I haven't generated the EVs yet, as sims take
> time (i'll do that this afternoon), but having picked
> up the bug, I am pretty sure that I will be wrong on
> the actual play.
I'm glad you found the bug. I've been there and it's frustrating. If you need EV's for regular play you can email me if Don would be kind enough to share my email with you. The CA obviously doesn't do counting EVs/indices.
I'm familiar with your CA's and what they can do from the other forum.
The EOR's in Kat's book I believe are for the H17 game. For the S17 game I suspected the EOR of the ace would be significantly higher due to the fact that the H17 rule is very helpful to the dealer in low counts. I measured it empirically using CVData and got a ratio between the EOR's of the ace and ten of 2.3:1, for the S17 game. Seemed a bit high, but who knows? Do you get something similar? Thanks in advance.
For 9 versus 7, 2 cards (I took an average of the EVs for 4-5, 3-6, and 7-2)
I have EV(hit) = 0.152 SE = 0.0004
EV(double) = 0.142 SE = 0.0008
which is pretty much the same as you.
(Of course, with up card 7, 7-2 would occur slightly less often than 4-5 and 3-6, so it's not perfectly correct to average the three EVs, but the hit and double EVs would have to be infinitesimally close for something like that to actually matter.)
I've corrected all this in my book, and am currently uploading it to the publisher's server (which takes about 4 hours). So anyone who buys the book from tomorrow will get the correct strategy.
I ran the strategy through the house edge calculator and it makes virtually no difference to the house edge. Obviously this is because the hit and double EVs were so close, and 9 versus 7 is not the most common hand.
The good thing is that it means that the error won't afect anyone financially.
Obviously I have to redo my indices. I'm running them overnight, and will upload them to the publisher's server. So to anyone considering buying my book, please wait for 2-3 days to give me enough time to update everything.
For people that already have the book, I will post the indices on this site, plus I will post an Errata sheet on www.spanishcountess.com.
The win rates and SCOREs will probably be unaffected as the two plays are so close in EV.
And to MGP, thank you again for being such a good bloke about it (as we say down here). I only wish that I'd had someone like you to check all my work when I was writing my code and writing my book. It would have saved me months of work.
Good job on finding the error.
With the people here, soon Kat's book will be perfect
Hi,
As you know, my EORs are from my CA and so should be exact. I'm sorry to admit I don't have the book so can't compare.
Please remember that when I do EOR's the values I give are a simple EV(Card Removed) - EV(Full Deck). There is no dividing or normalizing.
In this game, only the CD strategy makes sense for EOR's unless you go through and assign strategies for hands with different numbers of cards which I'm too lazy to do. In other words, the strategy changes slightly during the calculations after a card is removed. The difference is never greater than 0.01% compared to fixing a suboptimal strategy for any given EOR though so it doesn't really matter.
The rules I used included redoubling allowed 3 times and S17 in addition to all the usual SP21 rules.
EOR:
A: -0.16%
T: -0.08%
9: -0.03%
8: -0.03%
7: 0.02%
6: 0.08%
5: 0.14%
4: 0.11%
3: 0.08%
2: 0.05%
MGP
> I'm familiar with your CA's and what they can do from
> the other forum.
> The EOR's in Kat's book I believe are for the H17
> game. For the S17 game I suspected the EOR of the ace
> would be significantly higher due to the fact that the
> H17 rule is very helpful to the dealer in low counts.
> I measured it empirically using CVData and got a ratio
> between the EOR's of the ace and ten of 2.3:1, for the
> S17 game. Seemed a bit high, but who knows? Do you get
> something similar? Thanks in advance.
Interesting, thanks!
Just so you know, the game is never dealt with both S17 and redoubling. That would give it a player edge off the top. I suspect redouble drives the value of the 10 up so without it, the ratio should be closer to my empirical measurements.
> Hi,
> As you know, my EORs are from my CA and so should be
> exact. I'm sorry to admit I don't have the book so
> can't compare.
> Please remember that when I do EOR's the values I give
> are a simple EV(Card Removed) - EV(Full Deck). There
> is no dividing or normalizing.
> In this game, only the CD strategy makes sense for
> EOR's unless you go through and assign strategies for
> hands with different numbers of cards which I'm too
> lazy to do. In other words, the strategy changes
> slightly during the calculations after a card is
> removed. The difference is never greater than 0.01%
> compared to fixing a suboptimal strategy for any given
> EOR though so it doesn't really matter.
> The rules I used included redoubling allowed 3 times
> and S17 in addition to all the usual SP21 rules.
> EOR:
> A: -0.16%
> T: -0.08%
> 9: -0.03%
> 8: -0.03%
> 7: 0.02%
> 6: 0.08%
> 5: 0.14%
> 4: 0.11%
> 3: 0.08%
> 2: 0.05%
> MGP
> Interesting, thanks!
> Just so you know, the game is never dealt with both
> S17 and redoubling. That would give it a player edge
> off the top. I suspect redouble drives the value of
> the 10 up so without it, the ratio should be closer to
> my empirical measurements.
Um, the house still has an edge with S17 and redoubling: the player ev is -0.110151318117587%
I'll run it again though without redoubling a little later.
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