Deck Composition and Round Depth

[DSchles]

Let's consider another thought experiment: Shuffle a 52 card deck. Throw a card on the floor, if it is NOT a picture, throw another one, until it is a picture. Then start to deal a blackjack game.
Would the edge in the blackjack game be different compared to a game that started without any cards being thrown away first?

No! That's the entire concept behind Thorp's paper.

Thorp's paper suggests that the insurance EV should be the same.

No, it suggests more than that. It suggests that the EV for the BJ game is the same, as well. Why are we rehashing this when the entire idea was thoroughly discussed before? This belongs to the realm of probability concepts called "stopping problems," and what Thorp and I are trying to tell you is that you can't devise such a stopping methodology that will change the EV of the overall game. You read the red-card example, no?

But what about the blackjack game? I don't know the answer because I don't completely understand the theory behind it.

With the greatest respect for your considerable knowledge of the game, may I suggest that just because you don't understand the theory doesn't mean that it isn't true.

Don

[peterlee]

There are some conditions are needed to fullfill the "same EV" results:
Enough cards to finish the hand, and the same rules for the two hands.

Throwing card(s) and blackjack are two different set of rules.
Two tables:
Table A, we play two hands, two hands are the same EV for long run. (No doubt about this)
Table B, throw away a picture(might need more than one card), then a blackjack game. Or..
Play one hand, throw away a picture, then play the second hand.
Are the two tables together four hands have the same EV? I don't know. But I think they are not all the same, because the rules are not the same.

[you read the red-card example, no?]
The red-card example fullfills the two conditions.
My thought experiment has two sets of rules.

[With the greatest respect for your considerable knowledge of the game, may I suggest that just because you don't understand the theory doesn't mean that it isn't true.]
I don't fully understand it, so I can only know the answer of the example in the paper. Therefor if a new example came in, I am not sure if I can apply the same theory to the new example.

[lij45o6]

If you are playing straight basic strategy then yes, the EV should be the same.

You seem to be mixing basic play with card counting and ending up confusing yourself. If you take into consideration any additional information than simply your strategy and the current player hand, then you are now card counting.

[peterlee]

If you are playing straight basic strategy then yes, the EV should be the same.

You seem to be mixing basic play with card counting and ending up confusing yourself. If you take into consideration any additional information than simply your strategy and the current player hand, then you are now card counting.

[If you are playing straight basic strategy then yes, the EV should be the same.]
Thorp says EV will be the same under certain conditions.
Don seems to say "no matter how", EV will be the same.
What is your reasons behide, to say the EV should be the same?

My question is not about adding informaton, but adding or changing rules.
The main point is when rules are changed, is the game still in the category of what Thorp says?
If we add a cut card, the cut card effect changes the EV of BS play, but we would say that CCE is not in the Thorp's category, only a fixed rounds game is.

So how to tell which is which? Just like I play snooker everyday, an action is a foul or not, sometimes is not easy to say.

[lij45o6]

Yes, those conditions are what Don and I outlined: using an invariant (read: non-changing) strategy and not running out of cards. You still experience the same EV at each point in the shoe. The only difference between a fixed number of rounds and the cut-card is that the cut card has a conditioning effect on how many rounds you experience and what cards are drawn by virtue of low cards sprinting you towards the CC vs high cards crawling you towards said CC.

I don’t know why “rules changes” are important here; of course changing rules changes the EV, that’s a given. So forgive me if I don’t see the need of your question on why EV changes with different rules.

As long as you use the prescribed basic strategy for the given rules, the strategy does not change, and you don’t run out of cards, your EV should be the same at each level of the deck/shoe for each round.

As I said multiple times: the cut-card does change the expected value of the basic player. I do t recall Thorp nor Griffin explicitly mentioning the CCE.

[peterlee]

Yes, those conditions are what Don and I outlined: using an invariant (read: non-changing) strategy and not running out of cards. You still experience the same EV at each point in the shoe. The only difference between a fixed number of rounds and the cut-card is that the cut card has a conditioning effect on how many rounds you experience and what cards are drawn by virtue of low cards sprinting you towards the CC vs high cards crawling you towards said CC.

I don’t know why “rules changes” are important here; of course changing rules changes the EV, that’s a given. So forgive me if I don’t see the need of your question on why EV changes with different rules.

As long as you use the prescribed basic strategy for the given rules, the strategy does not change, and you don’t run out of cards, your EV should be the same at each level of the deck/shoe for each round.

As I said multiple times: the cut-card does change the expected value of the basic player. I do t recall Thorp nor Griffin explicitly mentioning the CCE.

[ 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

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

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)?

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.

[DSchles]

Knock yourself out! People joining the table--whether card counters or not--doesn't matter either. We're not talking about reducing the number of rounds you play per hour; this isn't about hourly win or loss playing BS. It's about whether or not the per-hand EV for a BS player changes from round to round. The answer is that it doesn't, given the above-mentioned conditions we've already established and beaten to death.

It's a free country, so feel free to "study mappings" further. You seem intent on trying to reinvent the wheel, and that's fine. But when you come to the conclusion that we've all already told you, don't be surprised. There's NOTHING you can do to change the individual-round expectations.

Don

[Cacarulo]

[ 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

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

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)?

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.

Hi peterlee,

I'd like to offer an example using CA that may help clarify this topic. For the purposes of this example, I’ll apply the following rules: 6D, S17, DOA, DAS, SPA1, SPL3, LS,
along with a fixed, total-dependent basic strategy. Under these conditions, the off-the-top expected value (EV) of the game is: EV = -0.3317035785

Now, consider the effect of removing a single, randomly selected card. What impact does this have on the expected value?
We know that the card removed could be any rank from Ace to Ten (where Ten also represents J, Q, and K).
Let’s examine the EV associated with removing each individual card, assuming we know in advance which one is removed:

• EV [A] = -0.4245165255
  
• EV [2] = -0.2619103255
  
• EV [3] = -0.2476875354
  
• EV [4] = -0.2170750840
  
• EV [5] = -0.1853267626
  
• EV [6] = -0.2562006321
  
• EV [7] = -0.2912666188
  
• EV [8] = -0.3431801739
  
• EV [9] = -0.3742086172
  
• EV [T] = -0.4276935613
  

Since we do not know in advance which card will be removed, and each rank appears 24 times in a 312-card shoe (6 decks), the probability of removing any given rank is 1/13.
To determine the average expected value, we compute the weighted mean across all possible ranks:

EV = (-0.4245165255 - 0.2619103255 - 0.2476875354 - 0.2170750840 - 0.1853267626 - 0.2562006321 - 0.2912666188 - 0.3431801739 - 0.3742086172 - 0.4276935613*4) / 13 = -0.3317035785

This result is identical to the off-the-top EV, confirming that removing a random card from the shoe does not change the overall expected value.

This type of analysis can also be extended to the removal of multiple cards, following a similar probabilistic approach.

Hope this helps.

Sincerely,
Cac

[peterlee]

Hi peterlee,

I'd like to offer an example using CA that may help clarify this topic. For the purposes of this example, I’ll apply the following rules: 6D, S17, DOA, DAS, SPA1, SPL3, LS,
along with a fixed, total-dependent basic strategy. Under these conditions, the off-the-top expected value (EV) of the game is: EV = -0.3317035785

Now, consider the effect of removing a single, randomly selected card. What impact does this have on the expected value?
We know that the card removed could be any rank from Ace to Ten (where Ten also represents J, Q, and K).
Let’s examine the EV associated with removing each individual card, assuming we know in advance which one is removed:

• EV [A] = -0.4245165255
  
• EV [2] = -0.2619103255
  
• EV [3] = -0.2476875354
  
• EV [4] = -0.2170750840
  
• EV [5] = -0.1853267626
  
• EV [6] = -0.2562006321
  
• EV [7] = -0.2912666188
  
• EV [8] = -0.3431801739
  
• EV [9] = -0.3742086172
  
• EV [T] = -0.4276935613
  

Since we do not know in advance which card will be removed, and each rank appears 24 times in a 312-card shoe (6 decks), the probability of removing any given rank is 1/13.
To determine the average expected value, we compute the weighted mean across all possible ranks:

EV = (-0.4245165255 - 0.2619103255 - 0.2476875354 - 0.2170750840 - 0.1853267626 - 0.2562006321 - 0.2912666188 - 0.3431801739 - 0.3742086172 - 0.4276935613*4) / 13 = -0.3317035785

This result is identical to the off-the-top EV, confirming that removing a random card from the shoe does not change the overall expected value.

This type of analysis can also be extended to the removal of multiple cards, following a similar probabilistic approach.

Hope this helps.

Sincerely,
Cac

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.

[k_c]

There are some conditions are needed to fullfill the "same EV" results:
Enough cards to finish the hand, and the same rules for the two hands.

Throwing card(s) and blackjack are two different set of rules.
Two tables:
Table A, we play two hands, two hands are the same EV for long run. (No doubt about this)
Table B, throw away a picture(might need more than one card), then a blackjack game. Or..
Play one hand, throw away a picture, then play the second hand.
Are the two tables together four hands have the same EV? I don't know. But I think they are not all the same, because the rules are not the same.

[you read the red-card example, no?]
The red-card example fullfills the two conditions.
My thought experiment has two sets of rules.

[With the greatest respect for your considerable knowledge of the game, may I suggest that just because you don't understand the theory doesn't mean that it isn't true.]
I don't fully understand it, so I can only know the answer of the example in the paper. Therefor if a new example came in, I am not sure if I can apply the same theory to the new example.

In order to show the cut card effect I ran a series of sims. The purpose was not to get precise results but only to be able to see in general the effect of a cut card.

Sims were for 1 player versus dealer single deck. Cut card was placed after card 4,5,6,7,8,9,10,11,12,13,14,15. Player used basic strategy. In these sims composition dependent basic strategy was used. Deck was reshuffled upon encountering cut card.

http://www.bjstrat.net/simResults.html

Using a little common sense in conjunction with sim data leads to conclusions:

1) If probability of encountering cut card = 0 for a round, full shoe basic strategy EV applies
2) If probability of encountering cut card > 0 for a round, full shoe basic strategy EV applies but if cut card isn't encountered then EV
   for the following round deteriorates to a value less than full shoe basic strategy EV. This is where cut card effect is manifested.
3) Cut card effect can be entirely eliminated by making the 1st round with any possibility of encountering the cut card the last
   round played.

k_c

[peterlee]

Knock yourself out! People joining the table--whether card counters or not--doesn't matter either. We're not talking about reducing the number of rounds you play per hour; this isn't about hourly win or loss playing BS. It's about whether or not the per-hand EV for a BS player changes from round to round. The answer is that it doesn't, given the above-mentioned conditions we've already established and beaten to death.

It's a free country, so feel free to "study mappings" further. You seem intent on trying to reinvent the wheel, and that's fine. But when you come to the conclusion that we've all already told you, don't be surprised. There's NOTHING you can do to change the individual-round expectations.

Don

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?

[peterlee]

In order to show the cut card effect I ran a series of sims. The purpose was not to get precise results but only to be able to see in general the effect of a cut card.

Sims were for 1 player versus dealer single deck. Cut card was placed after card 4,5,6,7,8,9,10,11,12,13,14,15. Player used basic strategy. In these sims composition dependent basic strategy was used. Deck was reshuffled upon encountering cut card.

http://www.bjstrat.net/simResults.html

Using a little common sense in conjunction with sim data leads to conclusions:

1) If probability of encountering cut card = 0 for a round, full shoe basic strategy EV applies
2) If probability of encountering cut card > 0 for a round, full shoe basic strategy EV applies but if cut card isn't encountered then EV
   for the following round deteriorates to a value less than full shoe basic strategy EV. This is where cut card effect is manifested.
3) Cut card effect can be entirely eliminated by making the 1st round with any possibility of encountering the cut card the last
   round played.

k_c

Thanks for showing me the CCE results, I agree with that all the time.
I brought that up because CCE breaks the conditions for the "same EV round to round".
What I’m trying to say is that 'same EV at any point in the shoe' as lij45o6 said, is not something that can be applied 'no matter how'.
Something can affect the EV for the later rounds, that is why Thorp has to give quite several rules/restrictions in order to keep the one to one mapping.

[peterlee]

Show me what did I say wrong about cut card effect. Please.