orster52: 9-7 Span 21

[MGP]

Ok, I ran it in the background - here they are:

Net CD EV: -0.373529465859687%

A: -0.16%
T: -0.06%
9: -0.02%
8: -0.03%
7: 0.01%
6: 0.07%
5: 0.12%
4: 0.1%
3: 0.07%
2: 0.05%

MGP

[Zenfighter]

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.)

Actually MGP claims a difference in advantage of .004565 for the EV (hit) case, which of course is not infinitesimal, exactly.

Putting your sim for the EV (double) in a more readable form we have:

68.3% probability that the true advantage is somewhere between {0.1412 and 0.1428}
95.5% probability between {0.1404 and 0.1436}
99.73% probability between {0.1396 and 0.1444}

With these results in front of us, I am thinking about two possibilities here:

1) Either having averaged the three EVs matters, or
2) Combinatory analyzers, who don?t use a cut-card placement, tend to exaggerate a little bit (0.149497 = 0.15) what?s realistic to expect while playing.

In what I totally agree with you, is in the absence of any real financial harm, even if someone has doubled the bet ?quite often?.

Sincerely,

Zenfighter

[MGP]

The EV example I gave was only for 45 vs 7 so that double EV was higher than the weighted average EV.

The weighted average EVs for 9 vs 7 which my CA also gives are:

Probability: 0.047458618150549
Hit: 0.155697217705006
Double: 0.144131644476505
Difference: 0.011565573228501

So the Net difference in overall game EV between the plays is very small: 0.000548886 and I agree wouldn't make any difference financially.

The averaged values she gives is close but obviously a weighted average would be better and an exact value from a CA is best.

And you are correct that the cut-card effect is not taken into consideration in my (or any) CA.

MGP

[Katarina Walker]

... if you have time. (For me to do it myself would require lengthy simulation.)
Pontoon rules (we'll choose Pontoon 4, as it's the one I play regularly):
8 decks, no hole card, player 21 always wins (even against dealer natural), no resplits, Ace = 1 in a pre-double hand (rather than 1 or 11) which means we never double on soft hands, one card only on each split Ace, lose one bet only to a dealer natural (in addition to any busted bets). If you surrender, and the deaer gets a natural at the end of the round, you still lose your entire bet. All bonuses are the same as American Spanish 21.
Optimal strategy is the same as H17 Spanish 21, EXCEPT: no surrenders (all surrenders replaced by hits), hit A-A versus A, 11 vs X is D4, 11 vs A is D4, always hit soft 17 or less, for soft 18 the strategy is S4 S4 S4 s4 S4 S6 S4 H H H (for 2 through Ace), for soft 19 versus 10 is S5, soft 19 versus Ace is S5.

[Katarina Walker]

It's the digital revolution; I predict that eventually all books on gaming math will be published POD, so that fiddly computational errors can be fixed instantly, instead of having thousands of copies in circulation with errors in them.

[MGP]

> ... if you have time. (For me to do it myself would
> require lengthy simulation.)
> Pontoon rules (we'll choose Pontoon 4, as it's the one
> I play regularly):

My CA can do all the rules you mention but I'm confused because according to the Wizard's site in Pontoon both dealer cards are face down and you can hit after doubling, and you can double on 3-4 card hands but not more (I can do 2 or multicard but not just up to 4 cards) - which are the three aspects of Pontoon my CA can't handle...

Ok so before I run this, we need to clarif a few things. I've rearranged the rules you typed out slightly without changing the text:

> 8 decks
> one card only on each split Ace
> player 21 always wins (even against dealer natural)
> no resplits

So far so good.

> no hole card
> lose one bet only to a dealer natural (in
> addition to any busted bets)

Now this is not ENHC but OBBO (Original and busted bets) or BBO (Busted bets plus 1). My understanding of how this rule is applied is that if you have 3 hands out and 2 bust, the dealer will take the last bet against a natural regardless of where it lies rather than only taking it if it's in the first spot. If that's true it's BBO. If he only takes an extra bet from an unbusted first spot, that's OBBO which is obviously more favorable to the player. Which is it? (I'm assuming it's BBO but my CA does both)

> Ace = 1 in a pre-double hand (rather than 1 or 11) which means we never double on soft hands

Does this mean that doubled Aces count as 1? If so my CA has that. If it means Aces always count as 1 then it can't.

> If you surrender, and the deaer gets a natural at the end of the round, you still lose your entire bet

This is just Late surrender right?

> All bonuses are the same as American Spanish 21.

Please specify them so there's no ambiguity.

Finally, is it H17? Does BJ pay 1.5:1 or 1:1 or 2:1 the latter of which is the payoff for Pontoon on the Wizard's site. Do 5 card hands automatically win like in Pontoon? Do you have to hit for totals <15?

> Optimal strategy is the same as H17 Spanish 21,
> EXCEPT: no surrenders (all surrenders replaced by
> hits), hit A-A versus A, 11 vs X is D4, 11 vs A is D4,
> always hit soft 17 or less, for soft 18 the strategy
> is S4 S4 S4 s4 S4 S6 S4 H H H (for 2 through Ace), for
> soft 19 versus 10 is S5, soft 19 versus Ace is S5.

The problem with an optimal strategy is it's a pain in the ... to go through each total and each number of cards. My CA will show them all but typing them out and cycling through each total vs each upcard is too annoying to do - sorry. What I can do though is just copy the CD or TD strategy for you and paste it here.

Sincerely,
MGP

[AutomaticMonkey]

Thanks man, that's how I figured it would work out. I always enjoy watching sims and CA's converge.

> Ok, I ran it in the background - here they are:

> Net CD EV: -0.373529465859687%

> A: -0.16%
> T: -0.06%
> 9: -0.02%
> 8: -0.03%
> 7: 0.01%
> 6: 0.07%
> 5: 0.12%
> 4: 0.1%
> 3: 0.07%
> 2: 0.05%

> MGP

[Zenfighter]

Can we have precise EoR?s (four decimals will be fine) for both U.S. SP21 standard rules (h17 and s17). Removing six of a kind will produce figures normalized to one-deck values. what are always preferable for easiness of comparison with the regular ones. Btw, I can?t modify my own CA to accomplish for these specifics and Cacarulo seems to be very busy, lately. So, you are the man to do this :-) After, getting accurate BCs for all the different counting systems won?t be, but a piece of cake.

Thanks for your time and efforts.

Sincerely,

Zf

[MGP]

> Can we have precise EoR?s (four decimals will be fine)
> for both U.S. SP21 standard rules (h17 and s17).

I didn't realize that we would need 4 decimal places accuracy with EOR's so my CA rounds to 2 for the outputs in the form for clarity when reading it. That's a really easy modification although it won't look as nice. If you don't mind just explaining what you mean by US rules? I.e. is it S17 no redoubling and H17 redoubling 3 times or some other combination.

> Removing six of a kind will produce figures normalized
> to one-deck values. what are always preferable for
> easiness of comparison with the regular ones.

I'm not sure what you mean by this? I can set it to any number of decks or any shoe composition including suited cards and including infinite decks so just let me know what you'd like me to do. I.e. do you want 1 Spanish deck values?

> Btw, I
> can?t modify my own CA to accomplish for these
> specifics and Cacarulo seems to be very busy, lately.
> So, you are the man to do this :-) After, getting
> accurate BCs for all the different counting systems
> won?t be, but a piece of cake.

Thanks, I my CA was finished a couple of years ago with all of these features, there was just never any interest in it so I'm keeping it to myself and a select few. If you search my posts you'll see a list of all it can do somewhere around here...

Sincerely,
MGP

[MGP]

Do Player BJ's always beat dealer BJ's as well?

Can you double or hit to split aces?

Is there Double Down Rescue?
If yes what about after a split?

Sorry for all the questions but as you know all of these things can make a difference. So without knowing all of the rules explicitly I can't give an accurate answer.

You hooked me btw so I'll try and look at least at the plays you mentioned to see if they're correct or not.

MGP

[Zenfighter]

Don't worry. I think we can work out all the details better by e-mail, provided you won't mind, working a little bit more with this stuff. If you agree on this, then just contact Bettie or Don and ask one of them for my e-address.

Thanks, again.

Zf

[MGP]

Hi,

This forum is fine. If you really want to do it by email they have my email address as well. Just let me know the rules you'd like me to run and it only takes a couple of minutes for each.

Sincerely,
MGP

[Katarina Walker]

Sorry it's taken a while to get back. I started college fulltime on Monday. I'm doing a multimedia course so I can make a pretty website for the book.

> Do Player BJ's always beat dealer BJ's as well?
yes. Always 3;2.

> Can you double or hit to split aces?
No. One card only.

> Is there Double Down Rescue?
Yes. Same as in the US.

> If yes what about after a split?
Yes. Also after a split.

> Sorry for all the questions but as you know all of
> these things can make a difference.
I sure do know.

BTW, I'd love to send you a free copy of my book. Please email me your home address.