Thursday, July 27, 2017

Cube Cards: 4 of 5

Diagrams

A diagram is a set of lines, possibly intersecting. Here are the eight possible diagrams within a hand of seven cards:

I  =  Line:   one line in hand.
Probability  =  33.20 %
K2R   Q2P            J2S

Trash = no lines in hand.
Probability  =  26.56%

V = Angle:  Two lines, linked at a card.
Probability  =  22.61%
K2R                              J1S
Q2P            J3S
J2S

II = Pair:  Two separate lines.
Probability = 6.32%
K2R    Q2P   J2S
Q1R     Q1P   Q1S

D = Triangle: Three lines linked at three cards.
Probability = 5.69%
K2R
Q2P            Q3P
J2S             J2S             J1S

Z  =  Chain:  Three lines linked at two cards.
Probability  =  4.74%
K2R      Q2P        J2S
J3S
J1S        J1R    J1P

Y  = Tripod:  Three lines linked at one card.
Probability  =  0.71%
K3P                             J1S
Q1R            J3S
J2S
Q2P
K2R

X  = Butterfly: Two lines pivoting through a card.
Probability = 0.16%
K2R                              K3R
Q2P            Q1P            Q3P
J2S                                J3S

Diagram Games

Andiron
Deal out 7 cards each to two players. They arrange their hands into a diagram: trash, I, V, II, D, Z, Y or X. Do a round of betting; call, raise or fold. Each player may then replace a card. Do a second round of betting, a second replacement option, a third round of betting, then compare diagrams:
I   <   Trash   <   V   <   II   <   D   <   Z   <   Y   <   X

Berkeley Take ’Em
Deal out 3 “Hole” cards each to three players. Do a round of betting; call, raise or fold. Dealer then lays out 2 “Flop” cards face-up. Another round of betting. Dealer then lays out 1 “Turn” card face up. Players may now exchange 1 card. Another round of betting. Dealer then lays out 1 “The Bay” card to each player. Another round of betting. Players then lay out their cards, and compare what diagrams their cards make with the face-up cards. Rank diagrams as in Andiron:
I   <   Trash   <   V   <   II   <   D   <   Z   <   Y   <   X

Seven Card Mare
Like Berkeley Take ’Em, with this sequence of deals: each player gets 3 hole cards, face down, plus one face up; 1 card face up; 1 card face up plus option to exchange; 1 card face down. Do betting between each deal. Rank diagrams as in Andiron:
I   <   Trash   <   V   <   II   <   D   <   Z   <   Y   <   X

Tonic
Deal 7 cards each to two or three players. Each arranges their cards into a diagram: I, V, II, D, Z, Y, X. Any card not in a diagram is “deadwood”. Trash is all deadwood. The value of a hand is the sum of the numbers on the deadwood cards.
Do several rounds of replacing cards. Discard face up. You may replace from discard piles. You may knock if your hand is worth less than 4. You must knock if your hand is worth zero. Once someone knocks, then record hand values.
Repeat deals, summing values. Players who reach 13 lose.