Author |
Topic: Buy Or Fold (Read 1337 times) |
|
ThudnBlunder
wu::riddles Moderator
Uberpuzzler
The dewdrop slides into the shining Sea
Gender: 
Posts: 4489
|
 |
Buy Or Fold
« on: Jan 24th, 2011, 7:14am » |
 Quote  Modify
|
In this game for two players, thirteen clubs are shuffled and after betting one dollar each player receives one card face up. The player with the lower card can fold and lose the pot or buy another card for a dollar. He may continue to do this until he receives a card higher than his opponent. When a lower player buys a card higher than his opponent's their roles are reversed and now the other player may buy or fold. Given that a player loses everything if he folds, when should the lower man fold?
|
|
 IP Logged |
THE MEEK SHALL INHERIT THE EARTH.....................................................................er, if that's all right with the rest of you.
|
|
|
towr
wu::riddles Moderator
Uberpuzzler
Some people are average, some are just mean.
Gender:
Posts: 13730
|
|
Re: Buy Or Fold
« Reply #1 on: Jan 26th, 2011, 12:32pm » |
Quote Modify
|
Assuming the ace is highest, he should fold if his opponent has an ace (duh), or if his opponent has a Jack or Queen with 11 other cards in play, or a Jack with ten cards in play (meaning you either had the highest card, lower than a Jack, a turn ago, or should have folded then).
But I might have to double-check my recursion...
|
| « Last Edit: Jan 26th, 2011, 12:34pm by towr » |
IP Logged |
Wikipedia, Google, Mathworld, Integer sequence DB
|
|
|
Grimbal
wu::riddles Moderator
Uberpuzzler
Gender:
Posts: 7527
|
|
Re: Buy Or Fold
« Reply #2 on: Jan 28th, 2011, 1:17am » |
Quote Modify
|
Are the cards returned to the deck or discarded?
|
|
IP Logged |
|
|
|
ThudnBlunder
wu::riddles Moderator
Uberpuzzler
The dewdrop slides into the shining Sea
Gender:
Posts: 4489
|
|
Re: Buy Or Fold
« Reply #3 on: Jan 30th, 2011, 2:26pm » |
Quote Modify
|
on Jan 28th, 2011, 1:17am, Grimbal wrote:| Are the cards returned to the deck or discarded? |
|
Sorry, my omission. They are discarded face-up and not subsequently used.
|
|
IP Logged |
THE MEEK SHALL INHERIT THE EARTH.....................................................................er, if that's all right with the rest of you.
|
|
|
Grimbal
wu::riddles Moderator
Uberpuzzler
Gender:
Posts: 7527
|
|
Re: Buy Or Fold
« Reply #4 on: Jan 31st, 2011, 10:12am » |
Quote Modify
|
Some thoughts.
Let's call A the playing player and B the opponent.
What matters is the number of remaining cards, A's rank among the remaining cards and B's rank.
If B has the highest available card, A can't win. A folds and B wins the pot.
If B has the second-highest available card, A can draw until he gets the highest card and win the pot. A will have to pay for the cards but eventually gets that money back, so whenever B gets the 2nd best card, A's net earning is the value of the pot at that moment.
If B has the 3rd card, A can buy cards, if he gets a better card, A or B will win the pot with equal chances.
Not sure yet what the value of the situation is for A.
|
|
IP Logged |
|
|
|
towr
wu::riddles Moderator
Uberpuzzler
Some people are average, some are just mean.
Gender:
Posts: 13730
|
|
Re: Buy Or Fold
« Reply #5 on: Jan 31st, 2011, 11:40am » |
Quote Modify
|
For 2 high cards and l low cards I get a value of (15 - 2l)/3
For 3 high cards and l low cards I get a value of (56 - 7l)/12
[edit]
The following seems to cover all the values except where h+l=11, where the value is slightly lower.
h
1: (24 - 2*l) / (h*(h+1))
2: (30 - 4*l) / (h*(h+1))
3: (56 - 7*l) / (h*(h+1))
4: (85 - 11*l) / (h*(h+1))
5: (114 - 16*l) / (h*(h+1))
6: (140 - 22*l) / (h*(h+1))
7: (160 - 29*l) / (h*(h+1))
8: (171 - 37*l) / (h*(h+1))
9: (170 - 46*l) / (h*(h+1))
2,4,7,11 .. etc seems to be the sequence h(h+1)/2 + 1 But I can't find anything to fit 24,30,56 .. etc
Maybe something can be found by looking at decks with more or less than 13 cards.
[/edit]
|
| « Last Edit: Jan 31st, 2011, 1:42pm by towr » |
IP Logged |
Wikipedia, Google, Mathworld, Integer sequence DB
|
|
|
ThudnBlunder
wu::riddles Moderator
Uberpuzzler
The dewdrop slides into the shining Sea
Gender:
Posts: 4489
|
|
Re: Buy Or Fold
« Reply #6 on: Feb 1st, 2011, 3:13pm » |
Quote Modify
|
on Jan 31st, 2011, 10:12am, Grimbal wrote:
If B has the 3rd card, A can buy cards, if he gets a better card, A or B will win the pot with equal chances.
Not sure yet what the value of the situation is for A.
|
|
I think assuming B turns over Queen (3rd card), A should fold - as he has equal chance of getting Ace (winning 1 dollar) and getting King (losing initial stake plus all money paid for it).
|
|
IP Logged |
THE MEEK SHALL INHERIT THE EARTH.....................................................................er, if that's all right with the rest of you.
|
|
|
Grimbal
wu::riddles Moderator
Uberpuzzler
Gender:
Posts: 7527
|
|
Re: Buy Or Fold
« Reply #7 on: Feb 2nd, 2011, 6:12am » |
Quote Modify
|
on Jan 31st, 2011, 10:12am, Grimbal wrote:| What matters is the number of remaining cards, A's rank among the remaining cards and B's rank. |
|
You are wrong! 
A's rank doesn't matter. We know A's rank is higher (worse) than B and that is all that matters.
So what matters is B's rank (i.e. which card he has) and how many cards remain in the deck.
|
| « Last Edit: Feb 2nd, 2011, 6:14am by Grimbal » |
IP Logged |
|
|
|
|
RIDDLES SITE
WRITE MATH!
Home 
Help 
Search 
Members 
Login 
Register
Reply
Notify of replies
Send Topic
Print