newbie: European no-hole-card game

[newbie]

I have the same question as appeared on page57 of BJA2.

It seems to me Don?s explanation only explained that an unseen card is an unseen card no matter when it is dealt (which I agree and understand); but the answer failed to explain why the third base player under European no-hole-card game doesn?t have any additional/exploitable information.

For example of the case of player 16 Vs dealer 10 :

Under normal game, the player should hit if the next card is A,2,3,4,5 and stand if the next card is 6,7,8,9,10. Obviously the player cannot know what the next card is, so he would hit if the benefits/probably of improving his hand out weights the probably that the player will bust before dealer does.

Under no-hole-game, the third-base-player has already lost the hand if the next hand is 7,8,9,10. The player only needs to consider cases for A,2,3,4,5,6.

If the player hits, there are 6 (equal) possibilities:

Player 17 Vs Dealer 10

Player 18 Vs Dealer 10

Player 19 Vs Dealer 10

Player 20 Vs Dealer 10

Player 21 Vs Dealer 10

Player 22 Vs Dealer 10
If the player stands, there are 6 (equal) possibilities:

Player 16 Vs Dealer BJ

Player 16 Vs Dealer 12

Player 16 Vs Dealer 13

Player 16 Vs Dealer 14

Player 16 Vs Dealer 15

Player 16 Vs Dealer 16
The player would choose to hit/stand depend on which one has the high expected value. Unfortunately I couldn?t calculate the probably of different dealer final hand starting from 12,13,14,15.

Hence it seems to me that Don?s answer was incorrect; there is extra information. I am not sure if the extra information is exploitable though, the playing decision might be same doesn?t matter what type of the game.

comments anyone ?

[Don Schlesinger]

> Hence it seems to me that Don?s answer was
> incorrect; there is extra information. I am
> not sure if the extra information is
> exploitable though, the playing decision
> might be same doesn?t matter what type of
> the game.

> comments anyone ?

Yes, I'll comment. Unfortunately, your reasoning is incorrect, but I can't add much more than is already in the book. Whether the dealer places his hole card physically on the table before you play your hand or waits until after you've completed it can't possibly affect any of the odds in any way whatsoever.

Don

[ET Fan]

As usual, Don is right. (Annoying habit you have there, Don ;-) ).

Assume you're playing the last hand in the shoe. Even if you knew all the cards in the deck right after third base gets his second card, your decision would be unaffected by the ENHC rule. Here's why:

I. Suppose you are going to STAND. The ENHC rule can't make any difference, because the same card(s) go to the dealer either way.

II. Standing can't tie with 16 v T.

III. So with any combination of cards, standing is going to either WIN or LOSE whether or not there's a hole card.
...A. If standing WINS either way, you have nothing to lose by standing.
...B. If standing LOSES either way, you have nothing to lose by hitting.

Make sense?

The only problem comes when your "partners" at the table complain you've taken the dealer's bust card. They're wrong, but that requires a longer explanation.

ETF

> I have the same question as appeared on
> page57 of BJA2.

> It seems to me Don?s explanation only
> explained that an unseen card is an unseen
> card no matter when it is dealt (which I
> agree and understand); but the answer failed
> to explain why the third base player under
> European no-hole-card game doesn?t have any
> additional/exploitable information.

> For example of the case of player 16 Vs
> dealer 10 :

> Under normal game, the player should hit if
> the next card is A,2,3,4,5 and stand if the
> next card is 6,7,8,9,10. Obviously the
> player cannot know what the next card is, so
> he would hit if the benefits/probably of
> improving his hand out weights the probably
> that the player will bust before dealer
> does.

> Under no-hole-game, the third-base-player
> has already lost the hand if the next hand
> is 7,8,9,10. The player only needs to
> consider cases for A,2,3,4,5,6.

> If the player hits, there are 6 (equal)
> possibilities:

> Player 17 Vs Dealer 10

> Player 18 Vs Dealer 10

> Player 19 Vs Dealer 10

> Player 20 Vs Dealer 10

> Player 21 Vs Dealer 10

> Player 22 Vs Dealer 10
> If the player stands, there are 6 (equal)
> possibilities:

> Player 16 Vs Dealer BJ

> Player 16 Vs Dealer 12

> Player 16 Vs Dealer 13

> Player 16 Vs Dealer 14

> Player 16 Vs Dealer 15

> Player 16 Vs Dealer 16
> The player would choose to hit/stand depend
> on which one has the high expected value.
> Unfortunately I couldn?t calculate the
> probably of different dealer final hand
> starting from 12,13,14,15.

> Hence it seems to me that Don?s answer was
> incorrect; there is extra information. I am
> not sure if the extra information is
> exploitable though, the playing decision
> might be same doesn?t matter what type of
> the game.

> comments anyone ?

[newbie]

I don't think I understood your post. Suppose the next cards in the shoe is :
3,T,X,X,X,X,X,X

For third base European player 16 Vs dealer T:
If he stands -> 16 Vs T,3,T -> Win
If he hits -> 19 Vs T,T -> Lose

For first base player (where 2nd/3rd base player will buy cards ), then the first player should hit and improve his hand to 19 instead of 16.

[Don Schlesinger]

> I don't think I understood your post.
> Suppose the next cards in the shoe is :
> 3,T,X,X,X,X,X,X

Suppose they aren't!! You don't seem to understand that your job, in playuing the hand, is to maximize your EV. Unless you're psychic, you don't know what the order of the cards is going to be. You play to maximize the EV of ALL eventualities, not just the one you've concocted above.

> For third base European player 16 Vs dealer
> T:
> If he stands -> 16 Vs T,3,T -> Win
> If he hits -> 19 Vs T,T -> Lose

> For first base player (where 2nd/3rd base
> player will buy cards ), then the first
> player should hit and improve his hand to 19
> instead of 16.

Alas, I have to bow out, quoting the words of the immortal Peter Griffin, quoting from Samuel Johnson:

"I've provided you a reason; I'm not required to provide you an understanding."

If I were convinced that you truly wanted to understand this, I might continue, but I get the feeling that you seem more intent on trying to demonstrate why we're wrong, and you aren't going to learn anything that way.

Don

[gpap]

Newbie,

you must remember that when you play your hand you are playing it based on what cards remain at THAT particular moment and not what other players are going to do AFTER you have played. For one you do not know whether thay will take cards or not.

You should also note that the books that you read are based on extensive computer simulations (read Don's book to get an idea of many simulations he ran).

If you are challenging the simulations then I can tell you that aircraft are designed according to simulations so it is a safe bet that all the BJ simulations are extremely accurate.

[C]

"If I were convinced that you truly wanted to understand this, I might continue, but I get the feeling that you seem more intent on trying to demonstrate why we're wrong, and you aren't going to learn anything that way."

I read I differently. This must be indeed a self-confessed newbie who doubts the experts' position about a "newbie axiom". And him being a newbie it takes more than one go to turn his preconceptions around. The third-base mirage in ENHC is perhaps the strongest mirage in that game.

Diplomacy must go the extra mile...

[Don Schlesinger]

> Diplomacy must go the extra mile...

I don't see you going the extra mile to help explain. :-)

There are dozens of people here capable of picking up where I left off. I'm happy to help people who say things like, "I still don't grasp the concept; can you help me to understand." I'm less patient with people who start out, "you seem to have done something wrong; there really must be a difference." To me, that's a poor opening remark for a newbie.

Don

[ET Fan]

> I don't think I understood your post.

My post was an attempt to prove the premise precisely as stated, namely: "Assume you're playing the last hand in the shoe. Even if you knew all the cards in the deck right after third base gets his second card, your decision would be unaffected by the ENHC rule." From your first post, I had the impression you thought this premise wouldn't fly.

> Suppose the next cards in the shoe is :
> 3,T,X,X,X,X,X,X

> For third base European player 16 Vs dealer
> T:
> If he stands -> 16 Vs T,3,T -> Win
> If he hits -> 19 Vs T,T -> Lose

> For first base player (where 2nd/3rd base
> player will buy cards ), then the first
> player should hit and improve his hand to 19
> instead of 16.

If you open it up to more than one spot on the table, the explanation is much more complicated. The principle is that every possible permutation (ordering) of cards in the undealt stock is as likely as any other to appear. It's true that if you KNOW the exact order of cards before they come out, your strategy may depend on table position, and will often vary from basic. Basic is derived from CA (combinatorial analysis) which assumes the density of the undealt cards is known, but the exact order is not known.

You have to either write your own CA program, or trust that the programmers know what they're doing, and accept the results. There are endless discussions about CA over on www.bjmath.com. The programs literally examine every possible combination of cards remaining. They don't just stop with "first player should hit and improve his hand to 19;" they thrash it out all the way to a win/lose/draw conclusion.

Try it this way...

Suppose you know all the probabilities for the dealer's hole card. You have actual numbers for P(A), P(2), P(3) ... all the way up to P(T). Now suppose you decide you're going to hit your hand once. Assume there's enough cards remaining for you to take the hit, and remember, you don't know the order of cards to come. What effect do you suppose your one hit has on P(A) - P(T)? None at all. Nada.

Now suppose you decide to take two hits, or three, or any number you choose. What effect do you suppose your decision will have on P(A) - P(T)? Zilch.

Switch to ENHC. Guess what the probabily distribution is for the dealer's second card, if you take 0, 1, 2 ... n hits? You guessed it. Exactly the same P(A) - P(T) as we had for the the dealer's hole card. All these probabilities are based on what we KNOW -- the original composition of the shoe, and what we have seen removed from the shoe -- not on what we DON'T know -- the identity of any possible hit cards.

These statements can be proven mathematically, and have been known for well over a century. Thorp had to know this in order to write his program to compute basic. If you're interested, there's a very simple proof of something quite similar in Smart Casino Gambling by Vancura. In fact, the above follows as a quick consequence.

ETF

[Nick]

I agree with Don that if the dealer's card is already dealt or waiting to be dealt, the outcome is the same. But I think we are all overlooking an important aspect of the NH game.
In the case of third base having 16 against dealer's ten. Let's basic strategy or count strategy dictates that we hit. The difference here is that we have to make the decision whether the next card should be ours or the dealer's, and there lies the difference, it is the same card, and I have not heard anyone taking that into consideration in their analysis. It's ONE card, and it's either ours or the dealer's. I still don't know if this can be exploited, but I think we are disregarding this important fact in our conclusions without properly making a computer simulation, and I don't know how to make one. Maybe it's been done? If not, I think it should be.
In this case hitting a 16 in the hope of catching A,2,3,4 or 5, which may still lose in all like likelyhood, why not let the dealer get that small card we are after? (hoping it will be 2,3, 4 or 5 and not the Ace...)? Indeed why not? A dealer with 12,13,14,15,or 16 against 16 is better for us.
If the next card is anything else, we lose in any case. Sure the dealer can get a small card and then another and perhaps another and still not bust....But the majority of the cases he will bust with a stiff. This in my opinion justifies standing 16 v 10 at slightly negative counts. Busting the dealer this way has more chances of beating the dealer, even if that next card is 5.
The next case to tackle would be 15 v 10. I think with 14 and lower there are so many small card combinations that it is advisable to play the same way as if the dealer was dealt two cards.
Comments?

[newbie]

>>> "Assume you're playing the last hand in the shoe. Even if you knew all the cards in the deck right after third base gets his second card, your decision would be unaffected by the ENHC rule."

I thought you meant [if you know all the cards and their order in the deck ... you decision would be unaffected by the ENHC.], which was clearly wrong; so I made an artificial deck [3,T,X,X,X] to demonstrated ONE case where the above statement is wrong.

Now I realise you meant : knowing the deck composition only, but not the order.

>>> My post was an attempt to prove the premise precisely as stated, namely: "Assume you're playing the last hand in the shoe. Even if you knew all the cards in the deck right after third base gets his second card, your decision would be unaffected by the ENHC rule." From your first post, I had the impression you thought this premise wouldn't fly.

Yes, I wasn?t sure whether the premise would fly.

1, After reading your first post I now realise that if the decision was to stand, there is no difference between hole-card and no-hole card game.

2, After reading your second post I now realise that if the player hits, there is:
no change in the probably of different player final hand, and
no change in the probably of different dealer final hand between hole or no-hole game.

3, Therefore there is no difference between hole or no-hole games in this regard.
Unfortunately I still need time to convince myself that 3 is the logical conclusion of 1 and 2.

Last night I was writing a computer simulation in VBA to calculate the EV of 16 V 10 under hole/no-hole game for hitting/standing under infinite deck model. I was hoping to show different EV under hole/no-hole game if the player decides to hit. Well ... halfway through coding I realised that the code for hole game and no-hole game would be the same !!!! Thus both simulation would show same output, thus same EV; I didn?t finish the coding?

From now on I will hit/stand on my 15/16 vs T with the confidence knowing the basic strategy (and its variations) are correct for my type of game.

... Not quite finished yet. I still believe what I said in my first post is correct regarding my method of deciding whether to hit/stand based on the EV of those 2 sets of 6 hands; however I expect it to yield the same result as usual hole-card game.

ET-Fan: Can you look through my reasoning if you have the time, and point out the flaw in my way if you believe it would yield incorrect result. It?s a trivial exercise just to see if my intuition is correct.

[Don Schlesinger]

> But I think we are all
> overlooking an important aspect of the NH
> game.
No, we're not! :-)

> In the case of third base having 16 against
> dealer's ten. Let's basic strategy or count
> strategy dictates that we hit. The
> difference here is that we have to make the
> decision whether the next card should be
> ours or the dealer's, and there lies the
> difference, it is the same card, and I have
> not heard anyone taking that into
> consideration in their analysis.

You don't want to hear. READ MY LIPS: I-T D-O-E-S-N'-T M-A-T-T-E-R!!!

> It's ONE
> card, and it's either ours or the dealer's.
> I still don't know if this can be exploited,

I already told you here, and in BJA, that it cannot.

> but I think we are disregarding this
> important fact in our conclusions without
> properly making a computer simulation, and I
> don't know how to make one. Maybe it's been
> done?

Done by computer, done by combinatorial analysis, and done by pure logic, which screams out that ... altogether now ... IT DOESN'T MATTER!

>Comments?

I'd like to be kind, but the only comment is: you're mistaken.

Don

[ET Fan]

> I thought you meant [if you know all the
> cards and their order in the deck ... you
> decision would be unaffected by the ENHC.],
> which was clearly wrong; so I made an
> artificial deck [3,T,X,X,X] to demonstrated
> ONE case where the above statement is wrong.

> Now I realise you meant : knowing the deck
> composition only, but not the order.

No, I meant the order. But only for third base, and specifically only for hard 16 v T. It just happens to work out that way.

... Not quite finished yet. I still believe what I said in my first post is correct regarding my method of deciding whether to hit/stand based on the EV of those 2 sets of 6 hands; however I expect it to yield the same result as usual hole-card game.

ET-Fan: Can you look through my reasoning if you have the time, and point out the flaw in my way if you believe it would yield incorrect result. It?s a trivial exercise just to see if my intuition is correct.

... From your first post ...

If the player hits, there are 6 (equal) possibilities:

Player 17 Vs Dealer 10

Player 18 Vs Dealer 10

Player 19 Vs Dealer 10

Player 20 Vs Dealer 10

Player 21 Vs Dealer 10

Player 22 Vs Dealer 10
If the player stands, there are 6 (equal) possibilities:

Player 16 Vs Dealer BJ

Player 16 Vs Dealer 12

Player 16 Vs Dealer 13

Player 16 Vs Dealer 14

Player 16 Vs Dealer 15

Player 16 Vs Dealer 16

I see two problems:
1) There are more possibilities to consider if the player hits. 23 v T, 24 v T, etc. In particular, 26 v T will be much more likely than the other bust probabilities.
2) The six hands you list for stand are not equally likely.

Also, since 16 v T is a close decision, you really need to take the removal of the player's hand and the T upcard into consideration. And you need to weigh them correctly. T-6 v T is much more probable than 9-7 v T. The exact weighting depends on the number of decks.

If you can do all that, you're about 2% down the road to writing a complete CA program. If you go down that road, be prepared to spend months, if not years, working on the logic for split hands. :-Q

ETF