Prob dealer BJ = 24/309Originally Posted by Cacarulo
24/309*(-1)+285/309*(-.5) = -.5388
k_c
No, this makes no sense. Your explanation is correct, but stating the EV the way you do is wrong. Late surrender with ENHC means that, if you attempt to surrender but the dealer ultimately has a natural, you never surrendered in the first place! The overall EV for the initial holding doesn't ALL accrue to the surrender play! The EV for any surrender play is, by definition, -.50. The reason that the index for late surrendering 7,7 vs. T in an ENCH game is identical to the index for late surrendering in a non-ENHC game is precisely because the EVs, namely -.50, are identical. In other words, losing your whole bet of 7,7, vs. T because the dealer has a natural has nothing whatsoever to do with surrender, and I have never seen anyone try to explain it that way!
Don
I would rather use unconditional EV computation meaning non-player blackjack is a loss to dealer blackjack. The only reason I compute conditional EV where dealer has checked for blackjack and doesn't have it as the condition is that is the traditional way it has been expressed. In the desktop version of my CA unchecking the choice to compute conditionally instantaneously changes EV to unconditional and vice versa if it is again checked. Either set of EVs leads to the same strategy.
To me it doesn't make sense to say dealer has checked for blackjack in the case of early surrender although I think it could be done that way. I also only display unconditional EV for ENHC whether or not user has chosen to compute player hands conditionally.
The relationship is:
conditional EV = (unconditional EV + prob dealer BJ) / (1 - prob dealer BJ)
k_c
With ENHC player loses all to dealer blackjack for doubles.
You need unconditional values for apples to apples comparison of EVs in this case.
Consider A-4 versus T, single deck.
Say for some reason you only have options to stand, double, or late surrender.
Using conditional EV:
Stand EV = -.5363
Double EV = -.4963
Late surrender EV = -.5
Using unconditional EV:
Stand EV = -.5666
Double EV = -.5883
Late surrender EV = -.5306
Since you can't hit late surrender would be your best option, not double and using unconditional EV shows this.
Maybe not the best example but shows effect of ENHC rules for doubles.
k_c
I think I see the source of the confusion.
We have to consider the mechanics of the game if there were to be late surrender in an ENHC game. The player would surrender, but the action would not be resolved right away. Instead some sort of marker would probably be placed on the initial bet. Therefore, at the time of the surrender action, the EV is the sum of
3/49 x -1 = -0.06122 --- the dealer eventually draws an ace for a natural and the entire bet is lost despite the attempt to surrender
46/49 x -0.5 = -0.46938 --- the dealer does not draw an ace and we lose only half of our bet
The EV for surrendering is -0.5306 as k_c proposes.
There is absolutely no difference whatsoever in the late surrender EV of an ENHC game or that of a regular game! In a regular game, if the dealer has a BJ, we have no option to surrender. If we're allowed to surrender, it's that he doesn't have a natural, and the surrender EV is, therefore, -.50.
In an ENHC, you're simply fooling yourself (playing with yourself might be a better term!), if you think that, vs. dealer T, you have surrendered simply because you speak the words. You haven't! If you say "surrender," what the words mean are, "If you don't have a natural later, I will then surrender." You haven't done ANYTHING until the dealer takes a hole card! If he has a natural, you NEVER surrendered in the first place. So, to claim that your loss somehow accrues to the surrender option makes no sense whatsoever. It doesn't! The dealer had a natural and you lost 100% of your bet. Period. End of story. Surrender doesn't enter into the discussion.
If the dealer doesn't have a natural, then you have surrendered and lost 50% of your wager. You can't lose 53% of your wager by surrendering!
Don
I have no argument with what you say. If dealer does not have blackjack LS EV = -.5.
The point I am trying to make is that in determining the relative VALUE of LS the hand EV for all of the options (stand, hit, double, split, LS, ES) needs to be computed one way (either conditionally or unconditionally.) It isn't right to mix them. Unconditional EV is pretty simple. For ENHC if conditional EV can be used at all you may be looking at jumping through a lot of hoops to get a valid result because of the requirement that splits and doubles are at risk to dealer blackjack.
For full peek conditional EV is pretty simple and results in exactly the same strategy as unconditional EV, which assumes non-blackjack loses to dealer blackjack. Conditional EVs are computed assuming dealer has checked for blackjack and does not have it. Full peek splits and doubles are not at risk as they are in no peek.
I prefer to use unconditional EV for everything. Conditional EV is the traditional option but to me is problematic if ENHC.
k_c
This is getting a bit confusing. Let's look at the same example A4vT from the following scenarios:
1) USA rules
2) ENHC rules (lose all to a natural)
Your conditional EV does not seem to correspond to ENHC. I know this is confusing.Code:1) USA rules Standing = -53.83142398119472% | -56.65807149255014% Hitting = -17.04237712783513% | -22.12141526286563% Doubling = -49.62640116322295% | -52.71049905118890% Surrender = -50.00000000000000% | -53.06122448979592% 2) ENHC rules (lose all to a natural) Standing = -56.65807149255014% | -56.65807149255014% Hitting = -22.12141526286563% | -22.12141526286563% Doubling = -58.83294803078072% | -58.83294803078072% Surrender = -50.00000000000000% | -50.00000000000000%
Sincerely,
Cac
And I realize we should stop and not go around in circles, because we understand each other, and I don't mean to be condescending, but ... when you say, "If dealer does not have blackjack LS EV = -.5," you imply that, if the dealer DOES have blackjack, LS can have a different expectation, and I'm trying to get you to understand that that simply is NOT true. If the dealer has blackjack, and there is no ES, the RULES OF THE GAME do not permit you to surrender. So, to speak of late surrender in the same sentence as the dealer's having a blackjack simply is a non sequitur; one cannot logically follow the other.
I'll be happy to allow you or anyone else to have the last word, but I've more or less said everything I can think of to be said to get the point across. I will add that perhaps I have a little more perspective on all this than most, having played exactly such a game both in Puerto Rico for many years and in A.C., after they eliminated ES but continued to allow surrender even as the dealer continued not to take a hole card.
Don
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