Pvt John Winger, U.S. Army: ? re:sd pen

Pvt John Winger, U.S. Army · 01-17-2003, 08:48 PM

Was in Tunica last weekend talking to some ploppies about bj, and they raised a ? that I hadn't thought of before and that I can't think of the answer to after some reflection. Here goes: I was explaining to them the concept that the house advantage decreases as the number of decks in play decreases as there are more blackjacks dealt in single deck play. Then I showed them some simple math that demonstrates why this is so. For example, when your first card is an ace, you have a 16 out of 51 chance of getting a natural. This slightly decreases to 32 out of 103 for double deck and so forth. But what they questioned me on was the that they didn't see the difference between a single deck game dealt halfway through, and a half deck game dealt down to the last card. Over time, the 2 cards cut into play are going to approximate what you'd get if for example, you just used the red cards in a deck and not the black. so for computing the house ad on a game like this, you'd conclude that the player has an off the top advantage. for example, there are 26 cards in play; your first card is an ace. You know have on average, and 8 out of 25 chance of getting a natural, which is a greater chance than you would if you were playing a single deck game dealt to the last card. In effect, the non-counting basic strategist is helped by shallow peneteration. As for CSM games, only dealing out 1/4 deck would provide the player with a signifigant edge.
I feel as though I should have been able to come up with an easy, effortless refutation to this line of reasoning, but I still can't see it. And for all I know I'm either the 1st person to think of this or the one millionth. So if anyone can explain what I'm missing in simple crude English, I'd appreciate it. Thanks
Pvt Winger

Geoff Hall · 01-18-2003, 02:31 AM

> Was in Tunica last weekend talking to some
> ploppies about bj, and they raised a ? that
> I hadn't thought of before and that I can't
> think of the answer to after some
> reflection. Here goes: I was explaining to
> them the concept that the house advantage
> decreases as the number of decks in play
> decreases as there are more blackjacks dealt
> in single deck play. Then I showed them some
> simple math that demonstrates why this is
> so. For example, when your first card is an
> ace, you have a 16 out of 51 chance of
> getting a natural. This slightly decreases
> to 32 out of 103 for double deck and so
> forth. But what they questioned me on was
> the that they didn't see the difference
> between a single deck game dealt halfway
> through, and a half deck game dealt down to
> the last card. Over time, the 2 cards cut
> into play are going to approximate what
> you'd get if for example, you just used the
> red cards in a deck and not the black. so
> for computing the house ad on a game like
> this, you'd conclude that the player has an
> off the top advantage. for example, there
> are 26 cards in play; your first card is an
> ace. You know have on average, and 8 out of
> 25 chance of getting a natural, which is a
> greater chance than you would if you were
> playing a single deck game dealt to the last
> card. In effect, the non-counting basic
> strategist is helped by shallow
> peneteration. As for CSM games, only dealing
> out 1/4 deck would provide the player with a
> signifigant edge.
> I feel as though I should have been able to
> come up with an easy, effortless refutation
> to this line of reasoning, but I still can't
> see it. And for all I know I'm either the
> 1st person to think of this or the one
> millionth. So if anyone can explain what I'm
> missing in simple crude English, I'd
> appreciate it. Thanks
> Pvt Winger

The flaw in your logic comes from the composition of cards that make up your 1/2 or 1/4 deck.

You are right in saying that just the 26 red cards, taken from a single deck, would give you a better advantage, as you are now playing a 1/2 deck game and the less decks the better, as you previously stated.

However, if you take 1/2 deck from a set of 6 decks (as with a CSM for example) then you have to assume that the composition of the cards are the same as a 6 deck game NOT the composition of a normal 1/2 deck.

For example, I shuffle 6 decks and cut 1/2 deck off the top. Your first card is an Ace, so what is the probability of you now getting a 'Blackjack'?

Well, there are 25 cards left BUT they have come from a 'population' of 312 cards of which 24 are face cards and 288 are not. So the probability of the next card being a face card is calculated by taking into account that the first card is an Ace and equals 24/311.

To reiterate, you are assuming that the 1/2 deck that has been cut off retains the exact characteristics as the red cards in a single deck, which is incorrect, although possible.

Some casinos have a '2 deck' game whereby the 2 decks have come from cutting off the cards from a 6 or 8 deck stack of shuffled cards.

THIS IS NOT A 2 DECK GAME although some players are fooled into thinking that it is. Basically it is a 6 or 8 deck game with lousy penetration (33% or 25% respectively).

Finally, a puzzle that when answered correctly will lead you to the theory of sampling from a large population.

I have 3 envelopes of which one contains $100. If you can pick the envelope that contains the $100 then you keep it. I know which envelope contains the money but you do not. I allow you to choose an envelope which leaves me with the other 2. I then tear up one of my 2 envelopes to show you that it is empty (as I know which one has the money in). We now have 1 envelope each. I now offer to swap my envelope with yours.

The question is are you better off :-

1. Keeping the envelope that you have already.
2. Swapping with my envelope.
3. Dosen't make any difference.

I will post the answer, with explanation, at a later stage, but the solution, as I said earlier, touches on the topic of sampling from a large population.

I hope this helps.

Best regards

Geoff Hall

Red Baron · 01-18-2003, 06:21 AM

The cards are dealt from a random shuffle. You are using a hypothetical example of a perfectly stacked deck...something that dont exist.

> Was in Tunica last weekend talking to some
> ploppies about bj, and they raised a ? that
> I hadn't thought of before and that I can't
> think of the answer to after some
> reflection. Here goes: I was explaining to
> them the concept that the house advantage
> decreases as the number of decks in play
> decreases as there are more blackjacks dealt
> in single deck play. Then I showed them some
> simple math that demonstrates why this is
> so. For example, when your first card is an
> ace, you have a 16 out of 51 chance of
> getting a natural. This slightly decreases
> to 32 out of 103 for double deck and so
> forth. But what they questioned me on was
> the that they didn't see the difference
> between a single deck game dealt halfway
> through, and a half deck game dealt down to
> the last card. Over time, the 2 cards cut
> into play are going to approximate what
> you'd get if for example, you just used the
> red cards in a deck and not the black. so
> for computing the house ad on a game like
> this, you'd conclude that the player has an
> off the top advantage. for example, there
> are 26 cards in play; your first card is an
> ace. You know have on average, and 8 out of
> 25 chance of getting a natural, which is a
> greater chance than you would if you were
> playing a single deck game dealt to the last
> card. In effect, the non-counting basic
> strategist is helped by shallow
> peneteration. As for CSM games, only dealing
> out 1/4 deck would provide the player with a
> signifigant edge.
> I feel as though I should have been able to
> come up with an easy, effortless refutation
> to this line of reasoning, but I still can't
> see it. And for all I know I'm either the
> 1st person to think of this or the one
> millionth. So if anyone can explain what I'm
> missing in simple crude English, I'd
> appreciate it. Thanks
> Pvt Winger

humble · 01-18-2003, 12:44 PM

As forever settled by the movie "Trading places": swap and your odds of losing become your odds of winning.

suicyco maniac · 01-18-2003, 03:48 PM

> The flaw in your logic comes from the
> composition of cards that make up your 1/2
> or 1/4 deck.

> You are right in saying that just the 26 red
> cards, taken from a single deck, would give
> you a better advantage, as you are now
> playing a 1/2 deck game and the less decks
> the better, as you previously stated.

> However, if you take 1/2 deck from a set of
> 6 decks (as with a CSM for example) then you
> have to assume that the composition of the
> cards are the same as a 6 deck game NOT the
> composition of a normal 1/2 deck.

> For example, I shuffle 6 decks and cut 1/2
> deck off the top. Your first card is an Ace,
> so what is the probability of you now
> getting a 'Blackjack'?

> Well, there are 25 cards left BUT they have
> come from a 'population' of 312 cards of
> which 24 are face cards and 288 are not. So
> the probability of the next card being a
> face card is calculated by taking into
> account that the first card is an Ace and
> equals 24/311.

> To reiterate, you are assuming that the 1/2
> deck that has been cut off retains the exact
> characteristics as the red cards in a single
> deck, which is incorrect, although possible.

> Some casinos have a '2 deck' game whereby
> the 2 decks have come from cutting off the
> cards from a 6 or 8 deck stack of shuffled
> cards.

> THIS IS NOT A 2 DECK GAME although some
> players are fooled into thinking that it is.
> Basically it is a 6 or 8 deck game with
> lousy penetration (33% or 25% respectively).

> Finally, a puzzle that when answered
> correctly will lead you to the theory of
> sampling from a large population.

> I have 3 envelopes of which one contains
> $100. If you can pick the envelope that
> contains the $100 then you keep it. I know
> which envelope contains the money but you do
> not. I allow you to choose an envelope which
> leaves me with the other 2. I then tear up
> one of my 2 envelopes to show you that it is
> empty (as I know which one has the money
> in). We now have 1 envelope each. I now
> offer to swap my envelope with yours.

> The question is are you better off :-

> 1. Keeping the envelope that you have
> already.
> 2. Swapping with my envelope.
> 3. Dosen't make any difference.

> I will post the answer, with explanation, at
> a later stage, but the solution, as I said
> earlier, touches on the topic of sampling
> from a large population.

SIGN ME UP I WANT TO PLAY YOUR GAME!!!!!!!!!!!!!!!!!!!!!!!

Geoff Hall · 01-19-2003, 04:16 AM

> SIGN ME UP I WANT TO PLAY YOUR
> GAME!!!!!!!!!!!!!!!!!!!!!!!

Which one ? 'Blackjack Switch', The 3 envelopes or the 2 deck cut from 6 ?

Incidentally, the 3 envelopes answer is to 'switch' envelopes which will give you a 2/3 chance of winning.
Suicyo Maniac had the correct assumption which is to turn your odds into losing into your odds of winning, by switching. (I like that - I may be able to use that on some promotional literature).
The easiest way to see that is to take a larger sample, say 52 cards, of which if you pick the Ace of Spades then you win. After picking a card I then take the other 51 cards and tear up 50 cards which are not The Ace of Spades. We are left with 1 card each, of which either yours or mine is the Ace. It is obvious that you are better off switching with my card.
So, despite being down to a '1 card or the other' situation, the fact that the cards originally started from a much larger population, makes the decision more obvious, which is my roundabout way of using a comparison with the '2 decks from 6' scenario.

Best regards

Geoff

Don Schlesinger · 01-19-2003, 10:16 AM

Geoff,

Nothing wrong with trotting out the Monty Hall problem from time to time and even giving it a fresh coat of paint. But, somewhere along the line, you should probably acknowledge that this is decades old and has been the object of thousands of pages of discussion, lest someone think you just mnade it up.

Don

humble · 01-19-2003, 10:47 AM

> Suicyo Maniac had the correct assumption
> which is to turn your odds into losing into
> your odds of winning, by switching. (I like
> that - I may be able to use that on some
> promotional literature).

And I actually thought it was me that posted that :=).
Come to think of it, I still think I came up with that.

Geoff Hall · 01-19-2003, 02:44 PM

Thanks Humble - apologies for the oversight.

Still OK to use it in my promotional leaflets ?

Bset regards

Geoff

Geoff Hall · 01-19-2003, 03:03 PM

> Geoff,

> Nothing wrong with trotting out the Monty
> Hall problem from time to time and even
> giving it a fresh coat of paint. But,
> somewhere along the line, you should
> probably acknowledge that this is decades
> old and has been the object of thousands of
> pages of discussion, lest someone think you
> just mnade it up.

> Don

I think that pretty much all of my mathematical problems stem from previous puzzles in the past.
I didn't know the history of the '3 card' problem, in fact, I generally only know the questions and solutions for most of my puzzles.

Similarly, the 'minimum number of riffles' problem, presented by yourself, contained a question followed by the answer. There was no reference made to the studies made on this topic or to the people involved in providing the original solutions.

IMHO most people, when hearing a puzzle, or joke, will generally assume that it originated elsewhere unless the person stating it says otherwise.

Best regards

Geoff

Don Schlesinger · 01-19-2003, 08:23 PM

> I didn't know the history of the '3 card'
> problem, in fact, I generally only know the
> questions and solutions for most of my
> puzzles.

Maybe it was just an American thing, although I thought it had received worldwide attention.

> Similarly, the 'minimum number of riffles'
> problem, presented by yourself, contained a
> question followed by the answer. There was
> no reference made to the studies made on
> this topic or to the people involved in
> providing the original solutions.

Not true. The contest was introduced by mentioning Diaconis. There was no other mention, because the question that followed stemmed from original research by the Masters and wasn't treated elsewhere in the literature, to my knowledge. I'm never shy to give proper credit where it is due.

Don