Indexes

**Cacarulo** · 03-27-2022, 02:16 PM

Originally Posted by Zenfighter

Hi all

A quite old controversy if I must recall my fancy memory about precise one-decimal indices,
and their possible gains over floored ones. Nada, rien de rien. Nothing to write home.

Just two cents:

T,6 v T-----0.643179-----0.6

9,7 v T-----0.017786-----0.0

8,8 v T-----0.027440-----0.0

T,5 v T -----3.74246-----3.7

9,6 v T----- 3.75459-----3.8

8,7 v T -----3.75484-----3.8

Your way to riches? Too late for the dream.

Best regards,

Zenfighter

Yes, your one-decimal indices are correct.

I got pretty much the same thing:

16vT: 0.0 (0,04) Generic
T6vT: 0.7 (0.66)
97vT: 0.0 (0,02)
88vT: 0.0 (0,03)

15vT: 3.9 (3,87) Generic
T5vT: 3.8 (3,79)
96vT: 3.8 (3,80)
87vT: 3.8 (3,80)

Sincerely,
Cac

**k_c** · 03-27-2022, 06:49 PM

During the worst times of this virus insanity I had nothing better to do but to teach my CA to approximate indexes depending upon counting system, running count, and cards remaining. This is what I get for T-6 versus 10 for 2 and 6 decks using Hi-Lo.

Code:

T-6 versus 10, Hi-Lo

** 2 decks **
Cards remaining (before up card)     RC (after up card)    TC ref (afer up card)

102-98                               hit                   ------------
97-89                                stand >= 4            2.2 to 2.4
88-62                                stand >= 3            1.8 to 2.6
61-36                                stand >= 2            1.7 to 3.0
35-8                                 stand >= 1            1.5 to 7.4


** 6 decks **
Cards remaining (before up card)     RC (after up card)    TC ref (afer up card)

310-306                              hit                   ------------
305-243                              stand >= 4            0.7 to 0.9
242-168                              stand >= 3            0.6 to 0.9
167-94                               stand >= 2            0.6 to 1.1
93-17                                stand >= 1            0.7 to 3.2 
16-14                                stand >= 0            0.0 to 0.0
13-8                                 stand >= 1            4.3 to 7.4

k_c

**aceside** · 03-27-2022, 07:44 PM

Originally Posted by k_c

During the worst times of this virus insanity I had nothing better to do but to teach my CA to approximate indexes depending upon counting system, running count, and cards remaining. This is what I get for T-6 versus 10 for 2 and 6 decks using Hi-Lo.

Code:

T-6 versus 10, Hi-Lo

** 2 decks **
Cards remaining (before up card)     RC (after up card)    TC ref (afer up card)

102-98                               hit                   ------------
97-89                                stand >= 4            2.17 to 2.35
88-62                                stand >= 3            1.79 to 2.56
61-36                                stand >= 2            1.73 to 2.97
35-8                                 stand >= 1            1.53 to 7.43


** 6 decks **
Cards remaining (before up card)     RC (after up card)    TC ref (afer up card)

310-306                              hit                   ------------
305-243                              stand >= 4            0.68 to 0.86
242-168                              stand >= 3            0.65 to 0.93
167-94                               stand >= 2            0.63 to 1.12
93-17                                stand >= 1            0.67 to 3.25 
16-14                                stand >= 0            0.00 to 0.00
13-8                                 stand >= 1            4.33 to 7.43

k_c

I like your work.
Last time you showed the insurance TC index decreases as the number of remaining cards decreases.
Today you showed the 16vs10 TC index increases as the number of remaining cards decreases.

Let us just fix to a 6-deck game and evaluate this HiLo only at two different deck levels: at 156 remaining cards and at 52 cards remaining. These two levels are money levels. Hope to see more of these.

**Cacarulo** · 03-28-2022, 08:04 AM

Interesting! You're on the right track. For 2D I get similar results:

16vT = -0,03 (Generic)
T6vT = 1,78
97vT = -0,11
88vT = -0,08

15vT = 3,78 (Generic)
T5vT = 3,53
96vT = 3,54
87vT = 3,55

Sincerely,
Cac

**Zenfighter** · 04-01-2022, 10:06 AM

Yes, your one-decimal indices are correct.

I got pretty much the same thing:

16vT: 0.0 (0,04) Generic
T6vT: 0.7 (0.66)
97vT: 0.0 (0,02)
88vT: 0.0 (0,03)

15vT: 3.9 (3,87) Generic
T5vT: 3.8 (3,79)
96vT: 3.8 (3,80)
87vT: 3.8 (3,80)

Sincerely,
Cac

Cac, see if you can lower T6 vs T and T5 vs T just one decimal point.
A hint: use the European more menacing ten, as I have.

Best

Zenfighter

**Cacarulo** · 04-01-2022, 11:28 AM

Originally Posted by Zenfighter

Yes, your one-decimal indices are correct.

I got pretty much the same thing:

16vT: 0.0 (0,04) Generic
T6vT: 0.7 (0.66)
97vT: 0.0 (0,02)
88vT: 0.0 (0,03)

15vT: 3.9 (3,87) Generic
T5vT: 3.8 (3,79)
96vT: 3.8 (3,80)
87vT: 3.8 (3,80)

Sincerely,
Cac

Cac, see if you can lower T6 vs T and T5 vs T just one decimal point.
A hint: use the European more menacing ten, as I have.

Best

Zenfighter

I don't understand. What do you want me to do?

Cac

**Zenfighter** · 04-01-2022, 02:26 PM

Hand Hitting Standing Difference Rules

T,6 v T -0.570817 -0.576608 0.005791 ENHC
T,6 v T -0.534676 -0.540954 0.006278 USA

Thus, hitting T,6 v T is a little bit more favorable under US rules,
and therefore, the corresponding index to stand ( a.k.a. to do the opposite) is a little bit higher than the European one, as your figures correctly show.

Do we agree now?

Zenfighter

**Cacarulo** · 04-02-2022, 06:55 AM

Originally Posted by Zenfighter

Hand Hitting Standing Difference Rules

T,6 v T -0.570817 -0.576608 0.005791 ENHC
T,6 v T -0.534676 -0.540954 0.006278 USA

Thus, hitting T,6 v T is a little bit more favorable under US rules,
and therefore, the corresponding index to stand ( a.k.a. to do the opposite) is a little bit higher than the European one, as your figures correctly show.

Do we agree now?

Zenfighter

Hi ZF,

6D, ENHC/USA

16vT = 0.04 / 0.04 (Generic)
T6vT = 0.66 / 0.66
97vT = 0.02 / 0.02
88vT = 0.03 / 0.03

15vT = 3.84 / 3.87(Generic)
T5vT = 3.75 / 3.79
96vT = 3.77 / 3.80
87vT = 3.77 / 3.80

As you can see, there are NO changes in 16vT but in 15vT there is a tiny bit difference (insignificant) in favor of USA rules.
Perhaps the differences you are seeing have nothing to do with the rules but with the EORs. One thing I didn't mention in my post is that the EORs used in this analysis were calculated from a 6-deck pack and to 10 decimal places of precision. Something I discovered years ago is that precision in the number of decimal places and using the correct number of decks is much more accurate than using 1-deck EORs for everything.

Sincerely,
Cac

**Zenfighter** · 04-04-2022, 01:49 AM

Originally Posted by Cacarulo

Hi ZF,

6D, ENHC/USA

16vT = 0.04 / 0.04 (Generic)
T6vT = 0.66 / 0.66
97vT = 0.02 / 0.02
88vT = 0.03 / 0.03

15vT = 3.84 / 3.87(Generic)
T5vT = 3.75 / 3.79
96vT = 3.77 / 3.80
87vT = 3.77 / 3.80

As you can see, there are NO changes in 16vT but in 15vT there is a tiny bit difference (insignificant) in favor of USA rules.
Perhaps the differences you are seeing have nothing to do with the rules but with the EORs. One thing I didn't mention in my post is that the EORs used in this analysis were calculated from a 6-deck pack and to 10 decimal places of precision. Something I discovered years ago is that precision in the number of decimal places and using the correct number of decks is much more accurate than using 1-deck EORs for everything.

Sincerely,
Cac

Well done, Cac. My apologies for the extra efforts added, while dealing with this stuff. I like this table more. More clarifying.

Thanks,

Zenfighter

**k_c** · 04-04-2022, 09:28 AM

Originally Posted by Zenfighter

Hand Hitting Standing Difference Rules

T,6 v T -0.570817 -0.576608 0.005791 ENHC
T,6 v T -0.534676 -0.540954 0.006278 USA

Thus, hitting T,6 v T is a little bit more favorable under US rules,
and therefore, the corresponding index to stand ( a.k.a. to do the opposite) is a little bit higher than the European one, as your figures correctly show.

Do we agree now?

Zenfighter

I don't believe there are any differences for hit/stand indexes for USA versus ENHC rules, only for doubling and splitting. ENHC takes all additional bets added after doubling or splitting in the case of dealer blackjack where USA does not.

Relationship: USA = ENHC + "rebate" for doubles/splits added bets

USA player gets his money back for doubles/splits. For hit/stand there is no difference.

Of course in actuality USA player never gets a chance to add extra bets for doubles/splits if dealer flips over blackjack and just takes initial bets but the principle is the same.

k_c

**Zenfighter** · 04-04-2022, 11:22 AM

Originally Posted by k_c

I don't believe there are any differences for hit/stand indexes for USA versus ENHC rules, only for doubling and splitting. ENHC takes all additional bets added after doubling or splitting in the case of dealer blackjack where USA does not.

Relationship: USA = ENHC + "rebate" for doubles/splits added bets

USA player gets his money back for doubles/splits. For hit/stand there is no difference.

Of course in actuality USA player never gets a chance to add extra bets for doubles/splits if dealer flips over blackjack and just takes initial bets but the principle is the same.

k_c

You are right, provided these indices are extracted with Monte-Carlo sims. We are talking here about algebraic derived ones with the employment of exact Eor’s for both rules. See last Cac’s post about this. Thus, if ENHC effects of removal differ from US ones for the hand in question, and I’m using a fixed formulae (a courtesy of “The Bish“,btw) to extract them, you can`t expect both indices to match perfectly, unless you think that I’m a sort of magician who can do that.

Sincerely

Zenfighter

**k_c** · 04-04-2022, 11:51 AM

Originally Posted by Zenfighter

You are right, provided these indices are extracted with Monte-Carlo sims. We are talking here about algebraic derived ones with the employment of exact Eor’s for both rules. See last Cac’s post about this. Thus, if ENHC effects of removal differ from US ones for the hand in question, and I’m using a fixed formulae (a courtesy of “The Bish“,btw) to extract them, you can`t expect both indices to match perfectly, unless you think that I’m a sort of magician who can do that.

Sincerely

Zenfighter

OK.

These are the EVs you quoted which it looks like are from 6 decks:
T,6 v T -0.570817 -0.576608 0.005791 ENHC
T,6 v T -0.534676 -0.540954 0.006278 USA

It depends on how eor is computed. USA EV above is computed as conditional EV given dealer has checked for blackjack and doesn't have it. If instead unconditional EV is used then USA EVs would exactly match ENHC EVs. Unconditional EV means player non-BJ loses and player BJ pushes if dealer has blackjack.

Hopefully helpful,
k_c