Griffin - EOR vs. Betting Effect

[DSchles]

good catch sir, either i did a typo on the four card or an arithmetic error. it should have been 0.5536 . close to the value for a four in table D17, but not exactly the same, whereas the table has 0.5582 (1st line of table D17)
by the way, the settings i used are depicted in the image below:

View attachment 9024

Settings look good. But, I'd also check at the top that the dealer doesn't have a natural.

Don

 

[sagefr0g]

Settings look good. But, I'd also check at the top that the dealer doesn't have a natural.

Don

did so and all of the values came out the same as in my previous attempt (other than for the four card which was in fact 0.5536 )
interesting that the one card rank that was checked was the one i loused up.

 

[Spyros Acebos]

good catch sir, either i did a typo on the four card or an arithmetic error. it should have been 0.5536 . close to the value for a four in table D17, but not exactly the same, whereas the table has 0.5582 (1st line of table D17)
by the way, the settings i used are depicted in the image below:

View attachment 9024

sagefrog, would you please explain the impact of the two options from the EV optional box at the top right hand corner of cdca?

I ask because Don suggested that he would suggest checking the box to check that the dealer doesn't have a natural.

 

[DSchles]

sagefrog, would you please explain the impact of the two options from the EV optional box at the top right hand corner of cdca?

I ask because Don suggested that he would suggest checking the box to check that the dealer doesn't have a natural.

For the American game, all EORs are based on the initial premise that the dealer has checked under tens and aces and doesn't have a natural. Calculating your edge in the game has to be for a playable hand that you have. If playing ENHC, where the dealer might have a blackjack revealed after you play your hand, the odds are obviously different.

So, for our purposes in this discussion, you need to check off that the calculations are conditional upon the dealer's NOT having a natural.

Don

 

[Spyros Acebos]

Thank you. That makes sense, and is what I used when generating EVs in order to generate EORs for US-based H17 and S17 games.

 

[sagefr0g]

sagefrog, would you please explain the impact of the two options from the EV optional box at the top right hand corner of cdca?

I ask because Don suggested that he would suggest checking the box to check that the dealer doesn't have a natural.

frankly sir, i haven't a clue. combinatorial (speiling?) analysis is a fascinating area of maths that is beyond my capability at my level of formal education, study and understanding.
i originally left it blank because those check boxes are precluded by the title ENHC (european no hole card).
ahhh, i see while i was struggling to post an answer that Don has offered an explanation.........

note: i also noted that you'd ask a question that Don may not have observed. i'll repost it below:

" Don, does the box for: "Depleted shoe split strat (Re: basic strat)" matter.

If so, what impact do the options have: "Pre-split" OR "Optimal strat of 1st split hand"? What should it be set for when generating EVs for 1D game to then use in determining EORs?

I used Pre-split, but figured that I may as well ask."

 

[DSchles]

frankly sir, i haven't a clue. combinatorial (speiling?) analysis is a fascinating area of maths that is beyond my capability at my level of formal education, study and understanding.
i originally left it blank because those check boxes are precluded by the title ENHC (european no hole card).
ahhh, i see while i was struggling to post an answer that Don has offered an explanation.........

note: i also noted that you'd ask a question that Don may not have observed. i'll repost it below:

" Don, does the box for: "Depleted shoe split strat (Re: basic strat)" matter.

If so, what impact do the options have: "Pre-split" OR "Optimal strat of 1st split hand"? What should it be set for when generating EVs for 1D game to then use in determining EORs?

I used Pre-split, but figured that I may as well ask."

Yes, I used Pre-Split, as well. You can see a complete discussion and explanation of all of this "What is basic strategy?" stuff in BJA3, pp. 387-391.

Don

 

[DSchles]

This is from the Help section of the analyzer: "Depleted shoe split strat - Only applies if Basic strat is selected. Selecting Pre-split directs the program to compute basic strategy split hands using the same basic full shoe CD strategy as is used on non-pair hands. Selecting Optimal strat of 1st split hand directs the program to compute basic strategy splits using the best strategy of the 1st hand of a split in a full shoe."

Don

 

[London Colin]

For the American game, all EORs are based on the initial premise that the dealer has checked under tens and aces and doesn't have a natural. Calculating your edge in the game has to be for a playable hand that you have. If playing ENHC, where the dealer might have a blackjack revealed after you play your hand, the odds are obviously different.

So, for our purposes in this discussion, you need to check off that the calculations are conditional upon the dealer's NOT having a natural.

Don

How so? Surely we are seeking to calculate the change in EV of a hand yet to be dealt (i.e. the betting EORs). And part of that hand's EV calculation is the possibility of losing to a dealer natural.

Also, as a practical matter, as Sagefrog pointed out, the checkbox makes no difference. It says in the help text-

Also overall EV is always the unconditional pre-deal expected value. For a player hand of 2 or more cards overall EV of the hand versus all up cards is displayed in the upper left corner of the 'Player Expected Values' section. When number of player cards input is 0 or 1 then EV displayed in the 'EV' row at the bottom versus each up card is always the unconditional expected value as is the value displayed in the upper left corner which is the overall expected value versus all up cards

 

[DSchles]

How so? Surely we are seeking to calculate the change in EV of a hand yet to be dealt (i.e. the betting EORs). And part of that hand's EV calculation is the possibility of losing to a dealer natural.

Also, as a practical matter, as Sagefrog pointed out, the checkbox makes no difference. It says in the help text-

Yes, you're right. I thought this box served a different function. Sorry.

Don

 

[Spyros Acebos]

Yes, you're right. I thought this box served a different function. Sorry.

Don

So in light of London Colin's comments, should I rerun the computations for each card, with that box remaining unchecked, or checked?

By the way, please elaborate on what you perceived as the significance of that box.

 

[DSchles]

So in light of London Colin's comments, should I rerun the computations for each card, with that box remaining unchecked, or checked?

By the way, please elaborate on what you perceived as the significance of that box.

Doesn't matter. What matters is that you check Basic Strategy and that you stay away from ENHC, which is what I was confusing the upper right box with.

Don

 

[London Colin]

In addition, Spanish 21 is patented as a 6 or 8 deck game. Single deck EORs are not useful because of this and because some Spanish 21 bonus hands are not even possible with fewer than 3 decks. For example, any bonus hand requiring suited 777.

I hadn't considered the possibility of 1 deck not being enough for certain hands (and hence their payoffs) to even be possible in some games, but in a more general sense I've wondered why the starting point always seems to be 1-deck EORs.

I guess in the old days -

• 1-deck games were the norm.
• A CA would take ages to run (with multi-deck taking even longer than single deck).

So it would make sense to compute 1-deck EORs and scale theses figures to get approximate EORs for other numbers of decks, should they be required.

But today multi-deck is the norm and a CA takes only a few minutes to run. So would it not be better to compute the EORs for every possible number of decks a game might be played with (e.g., 1, 2, 4, 6, 8)? And if only one set is to be computed, why not make it the 4-deck case (in the middle of the range of possibilities), which can then be scaled up or down?

To put it another way, if you want to calculate the change in EV due to removing, say, eight 5s from an 8-deck game, I'm assuming it would be more accurate to calculate 8 times the EOR of a single 5 from eight decks, rather than to take the EOR of a single 5 from a single deck.

 

[sagefr0g]

I hadn't considered the possibility of 1 deck not being enough for certain hands (and hence their payoffs) to even be possible in some games, but in a more general sense I've wondered why the starting point always seems to be 1-deck EORs.

I guess in the old days -

• 1-deck games were the norm.
• A CA would take ages to run (with multi-deck taking even longer than single deck).

So it would make sense to compute 1-deck EORs and scale theses figures to get approximate EORs for other numbers of decks, should they be required.

But today multi-deck is the norm and a CA takes only a few minutes to run. So would it not be better to compute the EORs for every possible number of decks a game might be played with (e.g., 1, 2, 4, 6, 8)? And if only one set is to be computed, why not make it the 4-deck case (in the middle of the range of possibilities), which can then be scaled up or down?

To put it another way, if you want to calculate the change in EV due to removing, say, eight 5s from an 8-deck game, I'm assuming it would be more accurate to calculate 8 times the EOR of a single 5 from eight decks, rather than to take the EOR of a single 5 from a single deck.

lost as i am (and that's really lost), i was wondering the same thing far as single deck then multiple decks. leafing through ToB & BJA, somewhere in there was mention of infinite decks.
also, i'm lost as to what the m# values are in the tables. mean values maybe? dunno how to interpret that.

 

[London Colin]

lost as i am (and that's really lost), i was wondering the same thing far as single deck then multiple decks. leafing through ToB & BJA, somewhere in there was mention of infinite decks.

The EORs for infinite deck would, by definition, be zero.

also, i'm lost as to what the m# values are in the tables. mean values maybe? dunno how to interpret that.

Yep, mean value (a.k.a. EV, or 'full-deck favourability'). m1 is the 1-deck EV; m8 is the 8-deck EV. (It is all explained in the chapter that precedes the tables.)

The point I'm driving at is that the basis for using EORs is the 'assumption of linearity' - the idea that if removing a single card deflects the EV by a given amount, removing 2 cards of that denomination has twice the effect. This is not true, but is generally close enough to give a useful approximation.

So I would have thought it would be more accurate to use EORs for the exact number of decks you are looking at (or a generic multi-deck case, such as 4-deck, scaled appropriately) as the basis for any EOR-related calculations, rather than take the 1-deck figures and scale those. [On the basis that the bigger the scaling factor, the more any inaccuracies will be amplified.]

 

[DSchles]

The EORs for infinite deck would, by definition, be zero.

Yep, mean value (a.k.a. EV, or 'full-deck favourability'). m1 is the 1-deck EV; m8 is the 8-deck EV. (It is all explained in the chapter that precedes the tables.)

The point I'm driving at is that the basis for using EORs is the 'assumption of linearity' - the idea that if removing a single card deflects the EV by a given amount, removing 2 cards of that denomination has twice the effect. This is not true, but is generally close enough to give a useful approximation.

So I would have thought it would be more accurate to use EORs for the exact number of decks you are looking at (or a generic multi-deck case, such as 4-deck, scaled appropriately) as the basis for any EOR-related calculations, rather than take the 1-deck figures and scale those. [On the basis that the bigger the scaling factor, the more any inaccuracies will be amplified.]

Try using the combinatorial analyzer to test your theory.

Don

 

[London Colin]

Try using the combinatorial analyzer to test your theory.

Don

I may well do, but I was hoping there might be some theoretical background that I am missing which would give me a better understanding. [Or, to put it another way, have I revealed any gaps in my understanding through what I've said so far?]

Also, as highlighted by Gronbog's Sp21 example, I was wondering if some games (whether BJ variants or completely different games) have a much greater degree of non-linearity, making 1-deck EORs a particularly poor choice for those games.

In actual fact, I do already have a result from my own CA for the Special BJ rule - re-doubling/tripling game that has me slightly perplexed and is partly responsible for this line of enquiry. I generated 1-deck and 6-deck EORs. The most surprising parts of the results were -

1-deck -
2 : 0.336842
....
7 : 0.379046
8 : 0.034771

6-deck -
2 : 0.0609781
....
7 : 0.0568221
8 : -0.00965977

So the EOR of a 2 is apparently less than that of a 7 in 1-deck, but more in 6-deck.
And the EOR of an 8 (close to zero in both cases) actually changes sign!