Kat's book has basic strategy a double on 9-7, while Wizard of Odds has it a hit. This is for the 6D,H17,DDD game. I'll go with Kat as she also has it -6 for the play deviation.
A great book. If you don't own it yet , go buy it.
Kat's book has basic strategy a double on 9-7, while Wizard of Odds has it a hit. This is for the 6D,H17,DDD game. I'll go with Kat as she also has it -6 for the play deviation.
A great book. If you don't own it yet , go buy it.
Mike Shackleford used Jeff Wu's redoubling strategy, so Mike did not get it wrong himself.
The reason why wizardofodds.com has a hit for 9 versus 7 and I have a double (the double is the correct play) is because:
if you double and end up with a hard 12, the correct play is to:
1. forfeit against 9, X, A
2. double again againt 7 and 8
3. play on against 2, 3, 4, 5, 6.
This doubling again on hard 12 versus 7 and 8 was something that Jeff Wu overlooked. Because doubling again is the correct play, it increases EV(double) for 9 versus 7 enough to be slightly greater than EV(hit).
Moose from BJ21.com (a computer sim writer that plays the redoubling game in Washington state) has independently confirmed that I am correct.
Hi,
I'm sorry but the Wizard is correct. I'm too tired right now to go into great detail, but my CA shows very clearly that the correct play is to hit 9 vs 7 with the stated rules including redoubling 1 time using CD post-double play.
The EV's vs 7 are:
H D
2,7 0.151347932444458 0.133845873983864
3,6 0.153525098396056 0.142949421048709
4,5 0.154061577180835 0.147254718989207
The ev's are close so a sim would have a hard time picking it up. Again - I used CA and not sim and the results should be exact.
MGP
Hi MGP,
When you're not too tired, I'd love to see the details of your combinatorial analysis.
The reason I ask is that the e.v.s you gave for hit vs. double are actually not that close, and I would expect any sim of decent size to indicate the correct play. It's hard to believe that Katarina's sim or analysis would miss the correct play, given the differences in e.v.s you provided.
David
> Hi,
> I'm sorry but the Wizard is correct. I'm too tired
> right now to go into great detail, but my CA shows
> very clearly that the correct play is to hit 9 vs 7
> with the stated rules including redoubling 1 time
> using CD post-double play.
> The EV's vs 7 are:
> H D
> 2,7 0.151347932444458 0.133845873983864
> 3,6 0.153525098396056 0.142949421048709
> 4,5 0.154061577180835 0.147254718989207
> The ev's are close so a sim would have a hard time
> picking it up. Again - I used CA and not sim and the
> results should be exact.
> MGP
How much detail do you wantDon might be right but I don't think I messed up the rules. One thing that is confusing though is the 3rd option from above:
3. play on against 2, 3, 4, 5, 6
How can you play on after doubling? Are you suggesting hitting is allowed after doubling because if so then my CA doesn't allow that - only standing or redoubling. Maybe that's where the difference is...
In the other thread the rules were stated as DAN, and redoubling but didn't specify how many times you can redouble. I checked both with redoubling allowed once as well as 3 times and the strategy did not change - it's to Hit 9 vs 7.
Anyways, any evs I give would need to be cut and pasted from my ca value by value so obviously I'm not going to put all the ev's for every single possible post-double hand.
Let's start with reviewing the strategies for totals 9-12 vs 7. If we agree on these then we could move on with the analysis - if not then there's a problem.
Note: After doubling the only options are to stand, double and surrender.
Any N Card 9 Pre-Double:
Always Hit (this is where the obvious disagreement is)
Any N Card 9 Post-Double:
Redouble and then redouble again if allowed with a resulting total of 11 or 12, and to stand for all other cards.
10 or 11 vs 7 Pre-double:
3 or less cards Double
4 or more cards Hit
10 or 11 vs 7 Post-double:
Always double then redouble again if allowed with a resulting total of 12
12 vs 7 Pre-double:
Always Hit.
12 vs 7 Post-double:
Always redouble and then stand on any non-busted total.
BTW - the problem with sims in these situations is if they're taken from the whole deck. As you know you need billions of hands to look close evs, so I hope that the sims were forced to start with the 9's vs 7 specifically and not just comparing the overall game EV with a strategy change. If the latter is the case you would need billions and billions of hands.
MGP
> How much detail do you want
> I don't think I messed up the rules. One thing that is
> confusing though is the 3rd option from above:
> 3. play on against 2, 3, 4, 5, 6
I was a bit confused by that wording myself, but, given that Katarina recommends redoubling when hitting would actually be better (but isn't allowed), I take "play on" to mean "stand." It's the only choice that makes sense in context, and I don't think this is the difference.
As far as the rest is concerned, I'm happy to wait for Katarina's response...maybe she'll point out some obvious oversight, or, less likely, find some mistake in her own analysis.
David
> How much detail do you want
> I don't think I messed up the rules. One thing that is
> confusing though is the 3rd option from above:
> 3. play on against 2, 3, 4, 5, 6
> How can you play on after doubling? Are you suggesting
> hitting is allowed after doubling because if so then
> my CA doesn't allow that - only standing or
> redoubling. Maybe that's where the difference is...
No, not at all. By "play on," Kat means that you stand and then play on. That isn't the problem.
> In the other thread the rules were stated as DAN, and
> redoubling but didn't specify how many times you can
> redouble. I checked both with redoubling allowed once
> as well as 3 times and the strategy did not change -
> it's to Hit 9 vs 7.
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?
Just checking.
Don
> 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
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've written to Kat, and I'm sure she'll respond shortly, but I'm guessing that you're missing something in the rules.
She's spent too much time researching all of this, and has also corresponded with Shack on the subject. I doubt that she got this wrong.
To be continued. ...
Don
... you are aware that the player may redouble up to three times and that you may double at any time, right?
So, when you analyze 2-7, 3-6, and 4-5, as starting hands of 9, I wonder if you have considered that this isn't the only way to reach 9, and that multi-card totals are possible, as well. In short, I'm not sure that your analysis is as comprehensive as it should be.
Don
> ... you are aware that the player may redouble up to
> three times and that you may double at any time,
> right?
See my above post - I checked both ways.
> So, when you analyze 2-7, 3-6, and 4-5, as starting
> hands of 9, I wonder if you have considered that this
> isn't the only way to reach 9, and that multi-card
> totals are possible, as well.
Of course my CA can handle that and it even does it automatically. So I don't need to consider anything - it's just taken care of. But I did check to make sure the settings matched the rules posted in the thread down the page including this one.
> In short, I'm not sure
> that your analysis is as comprehensive as it should
> be.
Given that you haven't used my CA yet, how can you be unsure? My CA is comprehensive in this setting.
MGP
> Given that you haven't used my CA yet, how can you be
> unsure?
Wow. That one pretty much answers itself, doesn't it?
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