First two cards with TC3 but hitting with TC0

[peterlee]

Replaced by a new story...

This is not a real case, will not happen in the casino.
(Maybe I use only one table is better.)
Imagine...
6 decks played until 3 decks left, RC=+9, that is TC+3
I make my bet.
Before that hand starts, a pit boss come to the table, and give me an offer....
I can choose #1 or #2 (I have to choose before the hand starts) ...
#1, play as normal
#2, after my first two cards and the dealer's up card are dealt, the dealer will take away the shoe(with cards inside), and bring in another shoe, with 6 full decks inside, shuffled, of course it is RC=0, TC=0. Then I hit/split/double using this 6 full decks shoe, and also the dealer would use this shoe to complete her hand.

I would only play one hand and then leave the table. (I add this to simplify the conditions)

Question:
#1 or #2 is better?
How is the difference in EV?
Table #1, TC+3, bet and play as normal.
+++

Below is the old story that I described not so clear what I want to ask.

Table #2, TC+3, bet and deal player's two cards and dealer's up card with no hole card.

Then change the shoe with six deck full and new shuffled, TC0.

Player's hit/double/split and dealer second card/hit, all from the new shuffled full shoe.


Which table is better?

How different between two tables, in EV?
Rules: No hole card, ES10, DOA, DAS, SPL3, OBO, 6D.

[ZenMaster_Flash]

The difference in e.v. is ZERO as it is ENHC OBO.

Why on earth would you think otherwise ?

Your post is confusing as I cannot fathom:

"Then change the shoe with six deck full and new shuffled, TC0."

Then again, the title of your thread is also confusing -- First two cards with TC3 but hitting with TC0

Please elaborate in clear language.

[peterlee]

Sorry for my poor English writing.
I try again here...
This is not a real case, will not happen in the casino.
(Maybe I use only one table is better.)
Imagine...
6 decks played until 3 decks left, RC=+9, that is TC+3
I make my bet.
Before that hand starts, a pit boss come to the table, and give me an offer....
I can choose #1 or #2 (I have to choose before the hand starts) ...
#1, play as normal
#2, after my first two cards and the dealer's up card are dealt, the dealer will take away the shoe(with cards inside), and bring in another shoe, with 6 full decks inside, shuffled, of course it is RC=0, TC=0. Then I hit/split/double using this 6 full decks shoe, and also the dealer would use this shoe to complete her hand.

Question:
#1 or #2 is better?
How is the difference in EV?

[Freightman]

The difference in e.v. is ZERO as it is ENHC OBO.

Why on earth would you think otherwise ?

Your post is confusing as I cannot fathom:

"Then change the shoe with six deck full and new shuffled, TC0."

Then again, the title of your thread is also confusing -- First two cards with TC3 but hitting with TC0

Please elaborate in clear language.

Heads up, 1 deck left, 3 face cards or aces dealt, would create the scenario described.

[BJGenius007]

The difference in e.v. is ZERO as it is ENHC OBO.

Why on earth would you think otherwise ?

Your post is confusing as I cannot fathom:

"Then change the shoe with six deck full and new shuffled, TC0."

Then again, the title of your thread is also confusing -- First two cards with TC3 but hitting with TC0

Please elaborate in clear language.

I agree with ZM_F. The difference between the two is zero. You just modify your index play based on value of TC. In your case, either 0 or +3. The index play values are determined by optimizing the ev on each individual type of hands.

[ZenMaster_Flash]

#1 permits you to continue play with a good modest advantage.
#2 removes your advantage, returning you to a disadvantage.

If you are trying to win, why would you give up your advantage ?

It appears that either I am still not understanding your (revised)

post or ... ?

[DSchles]

Your question is a subtle and interesting one -- one that I've never seen before. I'm sorry that your perfectly valid -- albeit hypothetical -- question has met with so much opposition. People do that a lot here -- tend to answer questions that weren't asked.

In any event, here is my answer. You surely have an advantage in both situations, as both hands are dealt from an original TC of +3, which gives at least a 1% edge to the player. But, in the first case, you get to play your hand with a TC of +3, while in the second case, you must play your hand with a TC of 0, from a fresh shoe. In the shoe game, depending on your spread, the edge from the bet is worth 3-4 times as much as the edge from the play of the hand. But the latter surely has value as well. You would prefer to play your random hand from a TC of +3 as you might: insure, double more, split more, and surrender more, if offered.

The difference in the two situations is that while both hands were dealt from an advantageous situation and thus have positive expectation as to the bet, the second hand is PLAYED as if from an infinite deck, as the effect of removal of the three cards seen is zero, since a full 312 cards remain.

Don't let the naysayers criticize you. You question was perfectly valid from a theoretical point of view. Not every question has to have practical applications.

Don

[Three]

Before that hand starts, a pit boss come to the table, and give me an offer....
I can choose #1 or #2 (I have to choose before the hand starts) ...
#1, play as normal
#2, after my first two cards and the dealer's up card are dealt, the dealer will take away the shoe(with cards inside), and bring in another shoe, with 6 full decks inside, shuffled, of course it is RC=0, TC=0. Then I hit/split/double using this 6 full decks shoe, and also the dealer would use this shoe to complete her hand.

Question:
#1 or #2 is better?
How is the difference in EV?

I think I understand what you are thinking about. You get 2 cards from a TC +3 and the dealer gets 1 card and then plus his hole card (no hole card game) from TC 0. But then you play your hand from TC 0. You are wondering if the gain in EV by the dealer not getting 2 cards at TC 0 (first card from TC +3 and 2nd from TC 0) is higher than the loss in EV from playing your hand at TC 0 rather than TC +3. I don't have an answer for you but the things to consider:

First you give up a nice positive count by getting the fresh shoe option. That is not good.
Your first 2 cards: dealer chance change if switch to fresh shoe:
1) BJ: dealer is less likely to also have a BJ (One for choice #2)
2) Made hand 17-20: Dealer less likely to have a pat hand and less likely to bust a stiff (Sort of a wash)
3) Double: You are hurting your chances for getting the big card you want and dealer is less likely to bust the likely weak upward you are doubling against. Also you make a doubling decision at TC 0 (Sort of a triple whammy, 3 for choice #1)
4) Offensive split: May not be an offensive split any longer but likely hurts EV if it is. (One for choice #1)
5) Defensive split: This one is hard to peg which is better. (sort of a toss up)
6) You get a weak hand that you have to hit: You are less likely to bust but you have a big bet out instead of small one. (Sort of a wash)
7) You get a weak hand that you stand on: The dealer is less likely to bust. (One for #1)

I can't quantify anything for you but I think it is safe to say almost everything favors option #1.

[peterlee]

Don,
Thanks for the advice and encourage.

[peterlee]

I think I understand what you are thinking about. You get 2 cards from a TC +3 and the dealer gets 1 card and then plus his hole card (no hole card game) from TC 0. But then you play your hand from TC 0. You are wondering if the gain in EV by the dealer not getting 2 cards at TC 0 (first card from TC +3 and 2nd from TC 0) is higher than the loss in EV from playing your hand at TC 0 rather than TC +3. I don't have an answer for you but the things to consider:

First you give up a nice positive count by getting the fresh shoe option. That is not good.
Your first 2 cards: dealer chance change if switch to fresh shoe:
1) BJ: dealer is less likely to also have a BJ (One for choice #2)
2) Made hand 17-20: Dealer less likely to have a pat hand and less likely to bust a stiff (Sort of a wash)
3) Double: You are hurting your chances for getting the big card you want and dealer is less likely to bust the likely weak upward you are doubling against. Also you make a doubling decision at TC 0 (Sort of a triple whammy, 3 for choice #1)
4) Offensive split: May not be an offensive split any longer but likely hurts EV if it is. (One for choice #1)
5) Defensive split: This one is hard to peg which is better. (sort of a toss up)
6) You get a weak hand that you have to hit: You are less likely to bust but you have a big bet out instead of small one. (Sort of a wash)
7) You get a weak hand that you stand on: The dealer is less likely to bust. (One for #1)

I can't quantify anything for you but I think it is safe to say almost everything favors option #1.

Yes, that is what I want to know.
This is really help.

So I tried to find so answer with numbers...

http://www.bewersdorff-online.de/black-jack/
I checked on this page - Blackjack Calculator
6D,resplit and double-after-split allowed, S17

Dealer checks hole card=Yes(USA)

Dealer	2	3	4	5	6	7	8	9	10	A	cards remained
EV_1	9.2%	12.4%	15.8%	19.4%	23.0%	14.5%	5.9%	-4.0%	-17.3%	-33.7%	312	RC=0
EV_2	9.3%	14.4%	20.7%	27.9%	31.3%	19.1%	9.2%	-2.6%	-17.7%	-35.6%	168	RC=10

Dealer checks hole card=No(Europe)

Dealer	2	3	4	5	6	7	8	9	10	A	cards remained
EV_1	9.2%	12.4%	15.8%	19.4%	23.0%	14.5%	5.9%	-4.0%	-17.6%	-33.9%	312	RC=0
EV_2	9.3%	14.4%	20.7%	27.9%	31.3%	19.1%	9.2%	-2.6%	-18.1%	-35.8%	168	RC=10

EV_1=EV on full 6 decks depending on dealer's up card
EV_2=EV on 168 cards remained with RC=10(take away 5 small cards and add 5 big cards)

From the above numbers, it seems that I can gain something on [RC+10 shoe] when dealer's up card is 4~8
But it did not show how much I gain on [lower the chance of dealer's getting BJ], if I change the [RC=0 shoe]

[peterlee]

#1 permits you to continue play with a good modest advantage.
#2 removes your advantage, returning you to a disadvantage.

If you are trying to win, why would you give up your advantage ?

It appears that either I am still not understanding your (revised)

post or ... ?

Tthree gave a very good explanation.

Sorry again.

[Dog Hand]

<snip>Imagine...
6 decks played until 3 decks left, RC=+9, that is TC+3
I make my bet.
Before that hand starts, a pit boss come to the table, and give me an offer....
I can choose #1 or #2 (I have to choose before the hand starts) ...
#1, play as normal
#2, after my first two cards and the dealer's up card are dealt, the dealer will take away the shoe(with cards inside), and bring in another shoe, with 6 full decks inside, shuffled, of course it is RC=0, TC=0. Then I hit/split/double using this 6 full decks shoe, and also the dealer would use this shoe to complete her hand.

I would only play one hand and then leave the table. (I add this to simplify the conditions)

Question:
#1 or #2 is better?
How is the difference in EV?<snip>Rules: No hole card, ES10, DOA, DAS, SPL3, OBO, 6D.

peterlee,

First of all, an apology: I made all the calculations shown below for 6D S17 DA2 DAS ES10 ENHC rules, rather than OBO, so the results will be slightly different for OBO.

I first ran a CVData sim for a game with 75% penetration for a heads-up HiLo counter. From these results I found that the TC is +3 at the start of the round on 3.657% of the rounds, and on those rounds the player's IBA is 1.842%.

I then ran another CVData sim with the pen set to only 1 card (to force a shuffle on each round) to determine the IBA for each two-card starting total vs. each dealer's upcard: I'll call this set of values "IBA-Shuffle".

I finally ran a 10-billion-round CVData sim with the "MRI" option set to a TC of +3 to determine the number of each starting hand vs. each dealer's upcard that is dealt when the TC is +3. From these numbers I calculated the percentage of +3 TC rounds that each starting total vs. each dealer's upcard occurs: I'll call this set of values the "MRI+3 Percents". For example, at a TC of +3 the player will be dealt a hard 13 vs. an X 2.6786% of the time... though, in my experience, I'm well above-average :-(

Now we can answer your question!

If you take Option #1, your IBA is simply 1.842%.

If you take Option #2, your two cards and the dealer's upcard all come from a +3 shoe, so the distribution of resulting matchups will be given by the "MRI+3 Percents" results. However, the EV for each matchup will be determined by the "IBA-Shuffle" EV's, since any draws by you as well as the dealer's 2nd card will come from a freshly-shuffled shoe. This fact actually helps you in the situation above, since you'd rather draw to your hard 13 vs. X from a freshly-shuffled shoe (rather than a shoe enriched in X's), and you'd prefer the dealer's 2nd card also come from a shoe NOT enriched in X's and A's.

Thus, your IBA is found by multiplying each value of the "MRI+3 Percents" data by the corresponding entry in the "IBA-Shuffle" data, then summing over the results. I exported the CVData results to Excel and used its "SUMPRODUCT" function to find the resulting EV, which is 1.140%.

Therefore, while either option is +EV, clearly option #1 is superior by a large margin.

I'll post the "MRI+3 Percents" below.

Hope this helps!

Dog Hand

2
3
4
5
6
7
8
9
10
Ace
Totals

5
0.0661%
0.0661%
0.0688%
0.0688%
0.0685%
0.0764%
0.0762%
0.0764%
0.3347%
0.0839%
0.9858%

6
0.0660%
0.0688%
0.0660%
0.0686%
0.0686%
0.0762%
0.0765%
0.0760%
0.3347%
0.0839%
0.9854%

7
0.1346%
0.1342%
0.1344%
0.1346%
0.1369%
0.1526%
0.1526%
0.1526%
0.6701%
0.1676%
1.9701%

8
0.1343%
0.1347%
0.1369%
0.1342%
0.1341%
0.1523%
0.1527%
0.1523%
0.6693%
0.1676%
1.9684%

9
0.2106%
0.2107%
0.2107%
0.2102%
0.2101%
0.2331%
0.2362%
0.2365%
1.0356%
0.2589%
3.0528%

10
0.2180%
0.2177%
0.2185%
0.2213%
0.2180%
0.2407%
0.2404%
0.2443%
1.0685%
0.2671%
3.1544%

11
0.2943%
0.2942%
0.2947%
0.2938%
0.2945%
0.3246%
0.3244%
0.3246%
1.4350%
0.3594%
4.2393%

12
0.5500%
0.5609%
0.5600%
0.5593%
0.5638%
0.6167%
0.6157%
0.6155%
2.6796%
0.6750%
7.9966%

13
0.5644%
0.5492%
0.5608%
0.5601%
0.5596%
0.6155%
0.6153%
0.6154%
2.6786%
0.6753%
7.9943%

14
0.4877%
0.4865%
0.4726%
0.4833%
0.4830%
0.5347%
0.5310%
0.5306%
2.3131%
0.5829%
6.9054%

15
0.4953%
0.4943%
0.4934%
0.4796%
0.4904%
0.5386%
0.5391%
0.5391%
2.3430%
0.5909%
7.0038%

16
0.4189%
0.4184%
0.4187%
0.4184%
0.4039%
0.4550%
0.4585%
0.4542%
1.9769%
0.4988%
5.9216%

17
0.4514%
0.4508%
0.4507%
0.4512%
0.4503%
0.4751%
0.4878%
0.4877%
2.1105%
0.5328%
6.3483%

18
0.3671%
0.3672%
0.3668%
0.3668%
0.3664%
0.4000%
0.3828%
0.3998%
1.7113%
0.4331%
5.1612%

19
0.3672%
0.3671%
0.3671%
0.3666%
0.3662%
0.4001%
0.3993%
0.3832%
1.7087%
0.4320%
5.1575%

A2
0.0805%
0.0841%
0.0840%
0.0839%
0.0836%
0.0917%
0.0919%
0.0918%
0.4000%
0.0958%
1.1873%

A3
0.0839%
0.0805%
0.0839%
0.0838%
0.0838%
0.0920%
0.0919%
0.0918%
0.3992%
0.0957%
1.1865%

A4
0.0836%
0.0837%
0.0804%
0.0837%
0.0838%
0.0916%
0.0918%
0.0922%
0.3991%
0.0960%
1.1860%

A5
0.0838%
0.0838%
0.0839%
0.0802%
0.0835%
0.0920%
0.0918%
0.0919%
0.3993%
0.0957%
1.1858%

A6
0.0838%
0.0837%
0.0838%
0.0837%
0.0804%
0.0917%
0.0918%
0.0920%
0.3990%
0.0956%
1.1854%

A7
0.0916%
0.0917%
0.0917%
0.0918%
0.0918%
0.0962%
0.1001%
0.1001%
0.4324%
0.1039%
1.2912%

A8
0.0922%
0.0919%
0.0919%
0.0919%
0.0920%
0.1000%
0.0957%
0.0999%
0.4333%
0.1039%
1.2927%

A9
0.0919%
0.0916%
0.0919%
0.0918%
0.0916%
0.1003%
0.1001%
0.0960%
0.4326%
0.1035%
1.2912%

AT
0.3998%
0.3995%
0.3992%
0.3985%
0.3994%
0.4329%
0.4326%
0.4326%
1.8410%
0.4468%
5.5824%

AA
0.0479%
0.0478%
0.0480%
0.0480%
0.0479%
0.0518%
0.0519%
0.0520%
0.2232%
0.0512%
0.6696%

22
0.0302%
0.0331%
0.0329%
0.0329%
0.0329%
0.0366%
0.0365%
0.0366%
0.1604%
0.0403%
0.4725%

33
0.0330%
0.0303%
0.0330%
0.0329%
0.0330%
0.0365%
0.0365%
0.0367%
0.1602%
0.0404%
0.4726%

44
0.0330%
0.0329%
0.0302%
0.0328%
0.0329%
0.0365%
0.0365%
0.0364%
0.1603%
0.0401%
0.4716%

55
0.0330%
0.0329%
0.0328%
0.0298%
0.0327%
0.0365%
0.0365%
0.0365%
0.1597%
0.0402%
0.4705%

66
0.0328%
0.0329%
0.0327%
0.0329%
0.0302%
0.0365%
0.0366%
0.0365%
0.1601%
0.0399%
0.4710%

77
0.0402%
0.0403%
0.0402%
0.0402%
0.0401%
0.0403%
0.0441%
0.0441%
0.1917%
0.0479%
0.5691%

88
0.0403%
0.0402%
0.0402%
0.0402%
0.0401%
0.0441%
0.0405%
0.0440%
0.1915%
0.0479%
0.5689%

99
0.0402%
0.0402%
0.0402%
0.0401%
0.0399%
0.0440%
0.0441%
0.0403%
0.1917%
0.0480%
0.5687%

TT
0.7900%
0.7902%
0.7895%
0.7890%
0.7882%
0.8547%
0.8552%
0.8545%
3.6012%
0.9196%
11.0323%

Tot
7.0375%
7.0319%
7.0304%
7.0250%
7.0223%
7.6976%
7.6946%
7.6937%
33.4053%
8.3617%
100.0000%

[peterlee]

Dog Hand,

Wow! I did not expect I can get an answer in so details.
Thank you so much!

I asked this because I discussed this with my friend on "How many hands to play" on a CSM.

I assume there are fixed 15 cards(I guess it is keep changing from 11 to 20 cards) at the [exit] of the CSM, that these 15 cards will never be mixed with the cards used last hand.

If there is RC+10 last hand, I have some advantage, so should I play 1 or 2 hands to make sure those 15 cards is enough for this hand? Or should I play four or five hands to make the dealer get only her face card can enjoy that RC+10?