MGP CA: DD S17 DAS LS - 16 vs 9

[Gronbog]

The value of any card as the next card when hitting depends on what you already have. For example, if you have hard 12, then the value of a 10 is -100% of your bet, since you are guaranteed to bust. The 10 is significantly more valuable if you have 11, for example. It also depends on how you play your hand if it is still alive after hitting. Reasonable assumptions can be applied, such as that you will continue on using basic strategy.

Are you asking for the value of each card for each possible holding?

[Freightman]

The value of any card as the next card when hitting depends on what you already have. For example, if you have hard 12, then the value of a 10 is -100% of your bet, since you are guaranteed to bust. The 10 is significantly more valuable if you have 11, for example. It also depends on how you play your hand if it is still alive after hitting. Reasonable assumptions can be applied, such as that you will continue on using basic strategy.

Are you asking for the value of each card for each possible holding?

True enough and is an absolute on a one time occurrence. Now, you’re still minus EV with the occurrence happening 100, 1000 times or more. That value is no longer -100%. What it is can be categorized is as a range between 2 minus EV points, that range which is variable not only to True Count, but QTC. The Law of Large numbers will lead us to the correct answers.

[2Bornot2B]

The value of any card as the next card when hitting depends on what you already have. For example, if you have hard 12, then the value of a 10 is -100% of your bet, since you are guaranteed to bust. The 10 is significantly more valuable if you have 11, for example. It also depends on how you play your hand if it is still alive after hitting. Reasonable assumptions can be applied, such as that you will continue on using basic strategy.

Are you asking for the value of each card for each possible holding?

Yes, I guess I am...I am familiar with Griffin's tables of "complete strategy", as he puts it, so is there a way to adapt those tables?...and I also need to know those individual values for the dealer's hand. Any hints on how to accomplish this will be greatly appreciated. Thanks.

[2Bornot2B]

Point well taken. Comments made were a generality VS an absolute. Similarly, I18 captures most of index value available - good enough for most as a generality - though it is an absolute that additional value is available simply by study and execution. Is that an analogy?

Using 118 is a practical shortcut for players to use rather than learn all of the indices...not a good analogy really...I am aiming at "absolute" because when I have that info I may be able to find a good use for it, theoretical or practical. Does that make sense?

[Freightman]

Does that make sense?

Yup

[MGP]

The values and strategies are all correct as are some of the explanations. To clear things up and get back to the original thread:

1) The TD tab shows the weighted average of all hands for that total. Since surrender and double can only be made on 2 card hands, the net ev vs the surrender/double EV can be deceptive.

2) Even with a TD strategy, it picks the best double/surrender/hit/stand strategy for the given specific hand where options are available. So using the A,6 vs 2 example, it is better to Hit A,6 vs 2 when the player is using a TD strategy. A,7 vs A in this setting is actually interesting because if you use a TD strategy you should Stand but if you use a 2C or CD strategy you get just enough extra EV that you should Hit.

3) For Total Dependent playing on 3 or more cards with the rules you posted Double/Surrender are not options. You can only Hit or Stand on a 3 or more card hand. The 2 card specifics are appropriately found in the CD tabs.

4) 5,5 vs 2-9 are double regardless of the strategy type and that is what is shown so I'm not sure what you mean by "that only gets me soft doubles"? The CD doubles for 2C And CD strategies are shown on the CD Hard tab.

I think that should answer all of the questions that came up before the thread was hijacked.

I'm going to chalk this up to me just not understanding what MGP is displaying.

With some offline input, I'm now guessing that the TD strategy includes all possible hands including multi-card hands. In that case, it's showing that the EV of hitting 16 vs 9 is worse than surrender when all of those hands are included and that it's just showing surrender in the detailed EVs as a reference, since you can't surrender multi-card hands in the configured game.

But that still does not explain why, when I select the TD Hard/Soft tab and select 2-Card Strategy at the bottom, it doesn't show any doubles or surrenders. Doubles are shown only if I select the CD Soft/Pairs tab along with any of the strategies at the bottom, but that only gets me soft doubles.

Attachment 4572

[aceside]

The values and strategies are all correct as are some of the explanations. To clear things up and get back to the original thread:

1) The TD tab shows the weighted average of all hands for that total. Since surrender and double can only be made on 2 card hands, the net ev vs the surrender/double EV can be deceptive.

2) Even with a TD strategy, it picks the best double/surrender/hit/stand strategy for the given specific hand where options are available. So using the A,6 vs 2 example, it is better to Hit A,6 vs 2 when the player is using a TD strategy. A,7 vs A in this setting is actually interesting because if you use a TD strategy you should Stand but if you use a 2C or CD strategy you get just enough extra EV that you should Hit.

3) For Total Dependent playing on 3 or more cards with the rules you posted Double/Surrender are not options. You can only Hit or Stand on a 3 or more card hand. The 2 card specifics are appropriately found in the CD tabs.

4) 5,5 vs 2-9 are double regardless of the strategy type and that is what is shown so I'm not sure what you mean by "that only gets me soft doubles"? The CD doubles for 2C And CD strategies are shown on the CD Hard tab.

I think that should answer all of the questions that came up before the thread was hijacked.

You explained a lot to clarify but need to be more specific. Just look at the numbers for this particular hand of 16 vs 9:
Probability: 0.123
Stand EV: -0.539
Hit EV: -0.504
Double EV: -0.991
Surrender EV: -0.5
These numbers say that your total-dependent strategy for this hand should be "Surrender," but you picked "Hit" anyway. What numbers do you use to pick the "Hit" decision?

[Gronbog]

I think there's an echo in here.

[aceside]

I think there's an echo in here.

Hi Gronbog, Can you look into these probability numbers calculated from the MGP CA program? Each probability is exceptionally large and there is also a huge jump from the hand of 16 vs 6 to 16 vs 7. I don't understand at all.
From MGP CA, Hard TD Strategy, Probability:
16 vs 2: 0.092
16 vs 3: 0.091
16 vs 4: 0.083
16 vs 5: 0.079
16 vs 6: 0.073
16 vs 7: 0.120
16 vs 8: 0.121
16 vs 9: 0.123
16 vs 10: 0.127
16 vs A: 0.128

[Dog Hand]

Hi Gronbog, Can you look into these probability numbers calculated from the MGP CA program? Each probability is exceptionally large and there is also a huge jump from the hand of 16 vs 6 to 16 vs 7. I don't understand at all.
From MGP CA, Hard TD Strategy, Probability:
16 vs 2: 0.092
16 vs 3: 0.091
16 vs 4: 0.083
16 vs 5: 0.079
16 vs 6: 0.073
16 vs 7: 0.120
16 vs 8: 0.121
16 vs 9: 0.123
16 vs 10: 0.127
16 vs A: 0.128

aceside,

The "jump" that occurs when the dealer's upcard moves from 6 to 7 is easy: say you're dealt a 6-8. If the dealer is showing a 6 (or less), B.S. says to stand, but if the dealer is showing a 7 (or more), B.S. says to hit. Thus, this hand will never become a 16 vs. 6, because you stood, but it may become a 16 vs. 7, if your hit card is a deuce.

To a lesser extent you can see this same phenomenon in the "drop" that occurs when the dealer's upcard moves from a 3 to a 4: this is because is you have 12 vs. a 2 or 3, you'll hit (and perhaps draw a 4 to make 16), but vs. a 4, 5, or 6, you'll stand.

Hope this helps!

Dog Hand

[k_c]

Hi Gronbog, Can you look into these probability numbers calculated from the MGP CA program? Each probability is exceptionally large and there is also a huge jump from the hand of 16 vs 6 to 16 vs 7. I don't understand at all.
From MGP CA, Hard TD Strategy, Probability:
16 vs 2: 0.092
16 vs 3: 0.091
16 vs 4: 0.083
16 vs 5: 0.079
16 vs 6: 0.073
16 vs 7: 0.120
16 vs 8: 0.121
16 vs 9: 0.123
16 vs 10: 0.127
16 vs A: 0.128

It makes sense because versus 5 and 6 for example 12,13,14,15 wouldn't be hit whereas versus 7,8,9,10,A those hands are hit so there's a greater probability of winding up with 16.

k_c

[aceside]

It makes sense because versus 5 and 6 for example 12,13,14,15 wouldn't be hit whereas versus 7,8,9,10,A those hands are hit so there's a greater probability of winding up with 16.

k_c

If you compare the probabilities of the two hands
16 vs 9: 0.123
16 vs 10: 0.127,
Shouldn't the 16 vs 10 probability be 4 times of the 16 vs 9 probability? I don't understand this part either.

[k_c]

If you compare the probabilities of the two hands
16 vs 9: 0.123
16 vs 10: 0.127,
Shouldn't the 16 vs 10 probability be 4 times of the 16 vs 9 probability? I don't understand this part either.

Let's create a theoretical deck and deal:

deck composition: one 9, 4 tens, and one theoretical 16 card
both player and dealer are dealt one card

It's 4 times more likely that player will get 16 versus ten rather than versus 9 from a fresh deal

After dealer card is dealt whether dealer's card is 9 or ten, the probability of player's card being 16 is just the same.

This is an example of a conditional probability.

Hope this helps

k_c