Deck Composition and Round Depth

[Cacarulo]

This is what I said:
[Taking away an Ace from the remaining cards after the first round breaks the mapping.]
Not a random any rank card. Not a ranodm card maybe an Ace.
But choice an ace from the remaining cards.
Of course, we don't find a real game like that. I made this example just to tell how to break the "one to one maping".
+++
Have anyone said about how to break the mapping before? I have not seen any. Even no one said anything about one to one maping.

If you permanently remove an Ace from the shoe, the EV will naturally decrease. On the other hand, permanently removing a Five will actually increase the EV.
However, it's a different situation when an Ace or a Five is dealt during normal play. That doesn't affect the EV for a basic strategy player, because they don't track
which cards have already been played.


Sincerely,
Cac

[peterlee]

If you permanently remove an Ace from the shoe, the EV will naturally decrease. On the other hand, permanently removing a Five will actually increase the EV.
However, it's a different situation when an Ace or a Five is dealt during normal play. That doesn't affect the EV for a basic strategy player, because they don't track
which cards have already been played.


Sincerely,
Cac

I agree all of these.
+++

How about giving me some advice on whether a card count would affect a BSer's overall EV, that the CC likes to open more boxes when +EV, and goes to the toilet when -EV.

[lij45o6]

[ why “rules changes” are important here]

The rules—by which I mean the entire procedure for playing the game, not just specific blackjack rules like DOA, H17, or SP3, but something more akin to Don’s thought experiment.

In a standard blackjack dealing method, the EV (expected value) remains consistent from round to round. However, certain conditions must be met: enough cards to finish the hand, a randomly shuffled deck, consistent strategy use, and a few other requirements

Again, I fail to see how this is relevant.

A cut card affects the EV because it prevents a round from being guaranteed to finish.

This is false. The shuffle point, when breached, does not effectively "end the round". It merely signals to the house that cards need to be reshuffled into a new show.

Now, consider a card counter who joins the table and only bets when the running count is positive. By selectively eating away high cards, they reduce the basic strategy player's EV in the long run. But is this just another form of cut-card effect (CCE)?

No, they don't. What happens is the number of rounds *everyone* experiences is reduced, not their EV's. And, no, it is not "just another cut-card effect."

To maintain the same EV as in the first round, the remaining cards must have a one-to-one mapping to the cards used in the first round. If this mapping is broken, the EV will no longer stay the same.

For example:
Taking away an Ace from the remaining cards after the first round breaks the mapping.
Discarding 5 decks before the first round does not break it.

What exactly causes this mapping to break? This is something I need to study further.

What is this "mapping" you are talking about? The only thing that "breaks" is that you transition from a full shoe to a depleted shoe, but that's standard for dealing cards from a finite shoe.

[Cacarulo]

I agree all of these.
+++

How about giving me some advice on whether a card count would affect a BSer's overall EV, that the CC likes to open more boxes when +EV, and goes to the toilet when -EV.

The EV of a player using a fixed strategy (BS) is not necessarily affected. It's important to focus on long-term results. Some shoes may have a positive or negative impact,
but these differences usually even out over time, as long as the cut card hasn't been reached or the shoe hasn't run out of cards.

Sincerely,
Cac

[lij45o6]

How about this: only one BJ table in a city, a team of 6 card counters sit all six spots, betting max, a BSer waiting the chance to make a bet. Whenever the the table is TC-1 or lower, the team stop betting, then the BSer make his bet.
Did that team of card counters affect the EV of the BSer compare with the EV if he can play the whole shoe all the time?

No because, again, the BS player uses an invariant strategy and does not run out of cards. As per Thorp. They're not card counting. The remaining residue of the shoe has no effect on their overall EV per round...because they are effectively playing the same strategy for each round.

[DSchles]

Do you think we've all said the same thing enough times already, or do we suggest another five pages of repetitious nothings?

Don

[Freightman]

do we suggest another five pages of repetitious nothings?

Like Government - doesn’t matter what side of the 49th

[peterlee]

The EV of a player using a fixed strategy (BS) is not necessarily affected. It's important to focus on long-term results. Some shoes may have a positive or negative impact,
but these differences usually even out over time, as long as the cut card hasn't been reached or the shoe hasn't run out of cards.

Sincerely,
Cac

No because, again, the BS player uses an invariant strategy and does not run out of cards. As per Thorp. They're not card counting. The remaining residue of the shoe has no effect on their overall EV per round...because they are effectively playing the same strategy for each round.

Extreme Case:
If a card-counting team forces a Basic Strategy (BS) player to only bet at True Count (TC) -1 or lower, does the BS player’s overall EV shift closer to the EV of TC -1 rather than remaining near TC 0 EV?

Less Extreme Case:
Now, consider a Wonging card counter who opens 3 boxes at TC ? +2, reducing the number of hands the BS player can bet on at high counts. This decreases the BS player’s overall EV.

Therefore, the card counter’s actions affect the BS player’s EV.

(This is quite simular to the concept of why CCE drops BSer EV.)

[peterlee]

Do you think we've all said the same thing enough times already, or do we suggest another five pages of repetitious nothings?

Don

Does "we" include Thorp?

Words by AI:
Situations Violating Thorp’s Framework:
Non-Myopic Strategies by Other Players
Description: If other players use non-myopic strategies (violating D3 for them), such as adjusting decisions based on cards seen in prior rounds (e.g., card counting or other tracking methods), the deck’s evolution is altered.

[Norm]

See: https://www.blackjackincolor.com/othereffects1.htm

[peterlee]

Again, I fail to see how this is relevant.



This is false. The shuffle point, when breached, does not effectively "end the round". It merely signals to the house that cards need to be reshuffled into a new show.



No, they don't. What happens is the number of rounds *everyone* experiences is reduced, not their EV's. And, no, it is not "just another cut-card effect."



What is this "mapping" you are talking about? The only thing that "breaks" is that you transition from a full shoe to a depleted shoe, but that's standard for dealing cards from a finite shoe.

[This is false. The shuffle point, when breached, does not effectively "end the round". It merely signals to the house that cards need to be reshuffled into a new show.]
Why a fixed rounds shoe has the same EV on later rounds, but not with a cut card?
A fixed rounds shoe, compare round 1 with round 50, their EV always the same.
Cut card shoe, compare round 1 with round 50, round 50 is not garentee to reach.

[What is this "mapping" you are talking about? ]
The one-to-one mapping concept in Thorp’s paper explains why the EV of the first round remains the same as in later rounds.

[peterlee]

See: https://www.blackjackincolor.com/othereffects1.htm

[The backcounter is stealing some of his good cards. Overall, the Hi-Lo player's edge drops from 1.37% to 1.23% when the backcounter appears at the table.

The Blackjack basic strategy player is not charted here but is also impacted. For the basic strategy player, the house edge increased from .38% to .42%. ]

5 pages saved.

[lij45o6]

Extreme Case:
If a card-counting team forces a Basic Strategy (BS) player to only bet at True Count (TC) -1 or lower, does the BS player’s overall EV shift closer to the EV of TC -1 rather than remaining near TC 0 EV?

Less Extreme Case:
Now, consider a Wonging card counter who opens 3 boxes at TC ? +2, reducing the number of hands the BS player can bet on at high counts. This decreases the BS player’s overall EV.

Therefore, the card counter’s actions affect the BS player’s EV.

(This is quite simular to the concept of why CCE drops BSer EV.)

I'm sorry...none of what you wrote is correct.

Here: explain the *exact* mechanisms in which these change the BS players EV. What you will find is, in fact, nothing will change the BS players EV.

There is really nothing to argue here.