Raise your hand if you are ready for micropoker, which minimalistically resembles 5-card poker.
- The deck has just 8 cards with 2 suits of 4 cards each.
- A hand is dealt as 3 cards that are final, with no further play.
- The two suits —“b” (bitties) and “i” (itties) — have different sets of consecutive integers to be determined. The bitties are ‘ (b0)b (b0+1)b (b0+2)b (b0+3)b ’ while the itties are ‘ (i0)i (i0+1)i (i0+2)i (i0+3)i ’ with -∞ < b0 < i0 < ∞ .
Six types of hands are possible.
- Dud – Three cards that do not qualify as any other type of hand.
- Plain flush – Three non-consecutively numbered cards from one suit.
- Straight flush – Three consecutively numbered cards from one suit.
- Mixed straight – Three consecutively numbered cards
with at least one from each suit.
- Mixed pair – Two cards have the same number from different suits.
- Flush pair – Two cards have the same number from the same suit.
A flush pair seems impossible as each card is unique in its suit.
Here is a break from tradition.
Two cards may be combined to form one new card in their place. The new card’s number is the sum of the original two cards. The resulting suit is inherited from the original cards if their suits match. The resulting suit is “o” (other) if the original suits differ.
A flush pair can derive from a straight flush or a plain flush, suppose ‘1b 3b 4b’, which may become the flush pair ‘4b 4b’ by combining 1b+3b = 4b.
A mixed pair can derive from a mixed straight or a dud, suppose ‘1b 3i 4b’, which may become the mixed pair ‘4o 4b’ by combining 1b+3i = 4o.
Q. How to number the suits
so that a dud hand is the third-likeliest type of hand to be dealt?
(Two types of hands would be more likely than a dud hand while three types would be less likely. In a game with such a deck, duds would outrank two more-glamorous-sounding types of hands.)