1. ## MGP: 678 Bonuses

Hi,

So I was looking at my CA and want to convince myself that I am doing the suited bonuses correctly. Before I get to that though, I was hoping someone could confirm my methodology for regular 678 bonuses because the values I'm getting do not agree with the Wizard's in his 678/777 appendix (see link). Let's look specifically at 1 play, 67 vs 4. He doesn't post his rules, but I assume it's 6D OBO S17, all the other rules don't matter for this play. Even if it's H17 we still have discrepencies so it's the method I'd like to confirm.

The bonus that's described is payed as soon as the hand is reached, and then the hand continues on. If it wins it pays the original bet and if it loses the original bet is lost.

This is what I do and was wondering if it's correct.

Original EV's
67 vs 4 Stand -0.202973227
67 vs 4 Hit -0.274867962
678 vs 4 Stand 0.889935006

p(8 | 67,4) = 24/309 = 0.077669903
p(Bonus | 678) = 1
EV(67, Hit with Bonus) = EV(67, Hit no bonus) + p(8)*p(Bonus | 678)*EV(Bonus | 678)

So if the EV(Bonus | 678) = 1 we have:

EV(67, Hit with Bonus) = -0.274867962 + 0.077669903 = -0.197198059

This value as you can see is better than the original EV of Standing so I would hit 67 vs 4. According to the Wizard's table he wouldn't hit until the Bonus was 2.

So am I doing it correctly? If yes, then I need to double check suited bonuses as well, because my EV's for suited bonuses are consistently higher than what's suggested in that appendix.

Thanks for any input.

Sincerely,
MGP

2. ## Zenfighter: Welcome here

The bonus that's described is payed as soon as the hand is reached, and then the hand continues on. If it wins it pays the original bet and if it loses the original bet is lost.
This is what I do and was wondering if it's correct.
Original EV's
67 vs 4 Stand -0.202973227
67 vs 4 Hit -0.274867962
678 vs 4 Stand 0.889935006

Everything double-checked. Fine expectations. Note that with a bonus 2 to 1 for 6-7-8, even with the dealer being lucky enough to draw after, to a multi-hand 21 (p = 0.110065), table 55, page 127 from PBJ applies. Here Stanford gives us an index of 1, thus basic strategy as an elementary inference points us to hit 6, 7 v 4 for the full 2 to 1 paid.

Your case does not differ in excess, IMO. Note that actually you?re getting paid 1.889935 to 1 no matter what. It?s only a 5.5% of the total bonus less.

EV(67, Hit with Bonus) = EV(67, Hit no bonus) + p(8)*p(Bonus | 678)*EV(Bonus | 678)

I do not see anything strange here. In any case you can always ?open? the hand 6, 7 and work the expectations step by step without forgetting the bonus for the 8. Multiply horizontally and add vertically and voil?.

Glad to see you posting here.

Sincerely,

Zf

3. ## MGP: Re: Welcome here

> Everything double-checked.

Ok, thought so, thank you.

> Your case does not differ in excess, IMO. Note that
> actually you?re getting paid 1.889935 to 1 no matter
> what. It?s only a 5.5% of the total bonus less.

The reason I'm asking is because in the table for deviations in the Wizard's appendix he says to deviate for a bonus of 1 for 67 vs 2-3 but not vs 4. This calculation suggests you should deviate even for a bonus of 1. I always worry when I disagree with his site

Thanks,
MGP

4. ## Zenfighter: Take it easy! :-)

As you can see below yours, there is another slightly inaccuracy for hitting 6,8 v 2. An even bonus is enough to hit the hand. Nothing to blame on Michael, in any case. He?s doing a wonderful job running his web site. It?s almost impossible not having minor errors with this exotic stuff. All these ?bonuses-theory? strikes to me very sensitive, and caution and double-checks look mandatory. In other words, let?s take all this in an easy manner, and without hurries, please.

```

6,7 v 4 Player gets paid an extra bet for any 6-7-8

Stand = -0.202973 p|6,7 v 4	    ev

6,7,A	0.077670	-0.201658	-0.015663
6,7,2	0.077670	-0.202560	-0.015733
6,7,3	0.077670	-0.200221	-0.015551
6,7,4	0.074434	-0.068894	-0.005128
6,7,5	0.077670	 0.186820	 0.014510
6,7,6	0.074434	 0.432407	 0.032186
6,7,7	0.074434	 0.668236	 0.049739
6,7,8	0.077670	 1.889935	 0.146791
6,7,9	0.077670	-1.000000	-0.077670
6,7,T	0.077670	-1.000000	-0.077670
6,7,J	0.077670	-1.000000	-0.077670
6,7,Q	0.077670	-1.000000	-0.077670
6,7,K	0.077670	-1.000000	-0.077670

Hitting        -0.197198

6,8, v 2 Player gets paid an extra bet for any 6-8-7

Stand = -0.289043 p|6,8 v 2	    ev

6,8,A	0.077670	-0.287489	-0.022329
6,8,2	0.074434	-0.288789	-0.021496
6,8,3	0.077670	-0.148757	-0.011554
6,8,4	0.077670	 0.124216	 0.009648
6,8,5	0.077670	 0.387266	 0.030079
6,8,6	0.074434	 0.640075	 0.047643
6,8,7	0.077670	 1.881398	 0.146128
6,8,8	0.074434	-1.000000	-0.074434
6,8,9	0.077670	-1.000000	-0.077670
6,8,T	0.077670	-1.000000	-0.077670
6,8,J	0.077670	-1.000000	-0.077670
6,8,Q	0.077670	-1.000000	-0.077670
6,8,K	0.077670	-1.000000	-0.077670

Hitting  	-0.284664

```

Zf

5. ## MGP: Please don't get me wrong...

Hi,

Please don't get me wrong, I was not criticizing Mike in any way. I've always said his site is amazing and the speed and accuracy with which he analyzes games is amazing to me. He's truly awesome

It's just that I'm working on verifying things with my CA since I've been looking at Spanish 21 and these plays are ones that I have a disagreement with his appendix and I don't know of any other site anywhere that I can compare against.

My CA gets the same EVs for 6,8 vs 2 that you give as well. As I mentioned there are several differences and I only posted the one I did as an example.

If I were doing that appendix I would recommend the following strategy deviations based on S17 6D OBO DAS DOA assuming the hand continues after the bonus. "*" is a difference between what I get and what is in the appendix of the Wizard of Odds' site:

```
6D S17 DAS DOA OBO
Non-suited 678
Hand/UC	2	3	4	5	6
6,7	1	1	1*	2	2
6,8	1*	2	2	3	2*
7,8	2	2*	3*	3	3*

Suited 678.  Hands below are assumed to be suited already.
Hand/UC	2	3	4	5	6
6,7	2	3	4*	6*	5*
6,8	4*	6	7*	9	8*
7,8	7	8*	10*	12	11*

Non-suited 777
Hand/UC	2	3	4	5	6	7
7,7	4	5	6	7	8	5*

Suited 777.  Hands below are assumed to be suited already.
Hand/UC	2	3	4	5	6	7
7,7	20*	26*	32*	38*	44*	22*
```
.

The biggest differences are in the suited 777 bonuses.

Sincerely,
MGP

> As you can see below yours, there is another slightly
> inaccuracy for hitting 6,8 v 2. An even bonus is
> enough to hit the hand. Nothing to blame on Michael,
> in any case. He?s doing a wonderful job running his
> web site. It?s almost impossible not having minor
> errors with this exotic stuff. All these
> ?bonuses-theory? strikes to me very sensitive, and
> caution and double-checks look mandatory. In other
> words, let?s take all this in an easy manner, and

```
> 6,7 v 4 Player gets paid an extra bet for any 6-7-8
> Stand = -0.202973 p|6,7 v 4     ev
>  6,7,A 0.077670 -0.201658 -0.015663
>  6,7,2 0.077670 -0.202560 -0.015733
>  6,7,3 0.077670 -0.200221 -0.015551
>  6,7,4 0.074434 -0.068894 -0.005128
>  6,7,5 0.077670  0.186820  0.014510
>  6,7,6 0.074434  0.432407  0.032186
>  6,7,7 0.074434  0.668236  0.049739
>  6,7,8 0.077670  1.889935  0.146791
>  6,7,9 0.077670 -1.000000 -0.077670
>  6,7,T 0.077670 -1.000000 -0.077670
>  6,7,J 0.077670 -1.000000 -0.077670
>  6,7,Q 0.077670 -1.000000 -0.077670
>  6,7,K 0.077670 -1.000000 -0.077670
>             Hitting         -0.197198
> 6,8, v 2 Player gets paid an extra bet for any 6-8-7
> Stand = -0.289043 p|6,8 v 2     ev
>  6,8,A 0.077670 -0.287489 -0.022329
>  6,8,2 0.074434 -0.288789 -0.021496
>  6,8,3 0.077670 -0.148757 -0.011554
>  6,8,4 0.077670  0.124216  0.009648
>  6,8,5 0.077670  0.387266  0.030079
>  6,8,6 0.074434  0.640075  0.047643
>  6,8,7 0.077670  1.881398  0.146128
>  6,8,8 0.074434 -1.000000 -0.074434
>  6,8,9 0.077670 -1.000000 -0.077670
>  6,8,T 0.077670 -1.000000 -0.077670
>  6,8,J 0.077670 -1.000000 -0.077670
>  6,8,Q 0.077670 -1.000000 -0.077670
>  6,8,K 0.077670 -1.000000 -0.077670
>              Hitting    -0.284664
```
.
> Zf
>

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