8 replies to this topic

[TimeSpaceLightForce]

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Place one or more chips on the square marks
and pay one to the dealer. He will nod if a bet
agrees with the hidden card then takes all chips
on the board even if he shook head.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
[ C ]                   [ K ]                   [ D ]

           [ 2 ]         [ 6 ]        [ 3 ]

[ J ]      [ 9 ]        [ A ]        [ 7 ]     [ 10 ]

           [ 5 ]         [ 8 ]        [ 4 ]

[ H ]                   [ Q ]                   [ S ]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

    (x)))))                   
 (x))))))))
      (x)))

How many chips is necessary to guess his card?

 

 

 

 

Happy Three Kings !

[bonanova]

Spoiler for For starters

I can do it using 21 chips with a method that is so straightforward it likely is not the best result.

[TimeSpaceLightForce]

Spoiler for For starters

I can do it using 21 chips with a method that is so straightforward it likely is not the best result.

Spoiler for

hi bonanova, actually this is a help solve problem ,i figuring the most efficient way. thanks!

[k-man]

Clarification... If I bet on both a suit and a rank will the dealer nod if either of them matches the card or only if both match? For example, if I bet on K and D, will he nod

1) only if he has a King of Diamonds or

2) if he has any King or any Diamond?

[CaptainEd]

Nice puzzle! We are pretty good at weighing coins here, but when you have to pay per card and pay per round, it's a different story. I started with one more than Bonanova found, but now I've caught up with him.

[TimeSpaceLightForce]

Clarification... If I bet on both a suit and a rank will the dealer nod if either of them matches the card or only if both match? For example, if I bet on K and D, will he nod

1) only if he has a King of Diamonds or

2) if he has any King or any Diamond?

His priority is shake head,   1) only if he has a King of Diamonds

[TimeSpaceLightForce]

Nice puzzle! We are pretty good at weighing coins here, but when you have to pay per card and pay per round, it's a different story. I started with one more than Bonanova found, but now I've caught up with him.

Hi CaptainEd

it is supposed a game we used to play with both opponent to guess first to win..asking any questions answerable by yes or no.

Like : is that a letter or is it a prime..

Unfotunately  the solution to puzzle is just straight forward. Iwould be happy with 20 but failed

[CaptainEd]

Spoiler for Proof that Bonanova solution is optimal

There are four suits. In our worst case, we'll need to put a chip on 3 of them to discover that it's really the fourth.

Similarly, there are 13 cards, In the worst case, we'll need to put a chip on 12 of them.

So we'll have to put out at least 15 chips. THen our task is to minimize rounds (one chip per deal). I don't see how to improve on two rounds for the suit and four rounds for the card. 15+6=21.

If we combine suits and denominations, I think we'll pay more chips per card, and not save enough in deals.

So if the rounds are (suits only--2,1) (cards only--6,3,2,1), we have 21 chips paid.

[TimeSpaceLightForce]

Spoiler for Proof that Bonanova solution is optimal

There are four suits. In our worst case, we'll need to put a chip on 3 of them to discover that it's really the fourth.

Similarly, there are 13 cards, In the worst case, we'll need to put a chip on 12 of them.

So we'll have to put out at least 15 chips. THen our task is to minimize rounds (one chip per deal). I don't see how to improve on two rounds for the suit and four rounds for the card. 15+6=21.

If we combine suits and denominations, I think we'll pay more chips per card, and not save enough in deals.

So if the rounds are (suits only--2,1) (cards only--6,3,2,1), we have 21 chips paid.

Aye CaptainEd
Clear one.Thank you.
Suppose you also held a hidden card and the dealer will guess it too.
Using Bonanova strategy (suits only--2,1) (ranks only--6,3,2,1) Vs.
Dealer using CaptEd strategy (suits only--2,1) (ranks only--5,4,2,1)
Who has the advantage?

Spoiler for

Suit : 2-1 trials worth 5 chips
1?   2?
C    C
S
D    D
H
--------------------
PLAYER

Rank: 6-3-2-1 trials worth 16 chips
3?   4?    5?    6?
A    A      A     A
K    K      K
Q    Q       
J             J      J
10         10           
9           

8     8      8    8
7     7      7
6     6

5            5      5
4            4
3                    3
2

---------------------------------
DEALER

Rank: 5-4-2-1 trials worth 15 or 16 chips
3?     4?   5?   6?   
A      A     A     A
K      K     K
Q     Q       
J             J
10                     

9     9    9    9
8     8    8
7     7          7
6     6

 

5          5     5  
4            4
3                    3  
2

 

..i dont know much statistic but i guess other strategies  are less effective.