Mid-Autumn Festival gambling game

Question

Tomorrow is the Mid-Autumn festival, and in the spirit of that holiday, I will introduce a gambling game that we (people from Xiamen) play during the holiday!

Rules

The game is played with six 6-sided dice. Different combinations of numbers have different ranks, with a special emphasis on fours and ones. Your job is to write a program/function that will rank the hand, given a roll of 6 dice. Here are the ranks (I've modified/simplified the rules a bit):

I guess only Chinese people can do this challenge! Okay, fine, here are some English explanations.

• 0: 4 fours and 2 ones.
• 1: 6 fours.
• 2: 6 ones.
• 3: 6 of any kind except fours and ones.
• 4: 5 fours.
• 5: 5 of any kind except for fours.
• 6: 4 fours.
• 7: Straight. (1-6)
• 8: 3 fours.
• 9: 4 of any kind except 4.
• 10: 2 fours.
• 11: 1 four.
• 12: Nothing.

Input

6 numbers, an array of 6 numbers, or a string of 6 numbers that represent the values of the 6 dice rolls from 1-6

Output

Your program/function may return/output anything to indicate the rank, as long as each rank is indicated by one output and vice versa. Ex. Using the numbers 0-12, 1-13, etc.

Examples(Using 0-12 as the outputs)

[1,1,1,1,1,1]->2
[1,4,4,4,1,4]->0
[3,6,5,1,4,2]->7
[1,2,3,5,6,6]->12
[3,6,3,3,3,3]->5
[4,5,5,5,5,5]->5

This is code-golf, so shortest byte count wins!

Answer 1

JavaScript (ES6), 88 bytes

a=>a.map(o=n=>[x=o[n]=-~o[n],6,,,21,9,8^o[1]][a=x<a?a:x])[5]|[,1,4,5,o[1]&2|8,2,4][o[4]]

Try it online! or Test all possible rolls!

Outputs an integer according to the following mapping:

 Rank | Output       Rank | Output
------+--------     ------+--------
   0  |  31            7  |   7
   1  |  12            8  |   5
   2  |  14            9  |  21
   3  |   8           10  |   4
   4  |  11           11  |   1
   5  |   9           12  |   0
   6  |  29

How?

Method

The output is computed by performing a bitwise OR between:

• a bitmask based on \$F\$: the number of 4's
• a bitmask based on \$M\$: the maximum number of occurrences of the same dice

Exceptions:

• When \$F=4\$: we use a special bitmask \$4b\$ when the two other dice are 1's, or a default bitmask \$4a\$ otherwise.
• When \$M=6\$: we use a special bitmask \$6b\$ when we have a six-of-a-kind of 1's, or a default bitmask \$6a\$ otherwise.

Table

Valid combinations of \$F\$ and \$M\$ are highlighted in bold and blue in the following table.

$$\begin{array}{c|c|cccccccc} &F&0&1&2&3&4a&4b&5&6\\ \hline M&\text{OR}&0&1&4&5&8&10&2&4\\ \hline 1&6&\color{grey}{6}&\color{blue}{\textbf{7}}&\color{grey}{6}&\color{grey}{7}&\color{grey}{14}&\color{grey}{14}&\color{grey}{6}&\color{grey}{6}\\ 2&0&\color{blue}{\textbf{0}}&\color{blue}{\textbf{1}}&\color{blue}{\textbf{4}}&\color{grey}{5}&\color{grey}{8}&\color{grey}{10}&\color{grey}{2}&\color{grey}{4}\\ 3&0&\color{blue}{\textbf{0}}&\color{blue}{\textbf{1}}&\color{blue}{\textbf{4}}&\color{blue}{\textbf{5}}&\color{grey}{8}&\color{grey}{10}&\color{grey}{2}&\color{grey}{4}\\ 4&21&\color{blue}{\textbf{21}}&\color{blue}{\textbf{21}}&\color{blue}{\textbf{21}}&\color{grey}{21}&\color{blue}{\textbf{29}}&\color{blue}{\textbf{31}}&\color{grey}{23}&\color{grey}{21}\\ 5&9&\color{blue}{\textbf{9}}&\color{blue}{\textbf{9}}&\color{grey}{13}&\color{grey}{13}&\color{grey}{9}&\color{grey}{11}&\color{blue}{\textbf{11}}&\color{grey}{13}\\ 6a&8&\color{blue}{\textbf{8}}&\color{grey}{9}&\color{grey}{12}&\color{grey}{13}&\color{grey}{8}&\color{grey}{10}&\color{grey}{10}&\color{blue}{\textbf{12}}\\ 6b&14&\color{blue}{\textbf{14}}&\color{grey}{15}&\color{grey}{14}&\color{grey}{15}&\color{grey}{14}&\color{grey}{14}&\color{grey}{14}&\color{grey}{14}\\ \end{array}$$

All other combinations (in gray) can't possibly happen. For instance, if we have three 4's, we must have \$M\ge3\$. But because there are only 3 other remaining dice in such a roll, we also have \$M\le3\$. So, there's only one possible value of \$M\$ for \$F=3\$.

Example

If we have a straight, each dice appears exactly once. So we have \$M=1\$ and \$F=1\$. Using the bitmasks described in the above table, this leads to:

$$6 \text{ OR } 1 = 7$$

There is another \$7\$ in the table, but it's invalid. Therefore, a straight is uniquely identified by \$7\$.

Commented

a =>                   // a[] = input array, reused as an integer to keep track of the
  a.map(               //       maximum number of occurrences of the same dice (M)
    o =                // o = object used to count the number of occurrences of each dice
    n =>               // for each dice n in a[]:
    [                  //   this is the lookup array for M-bitmasks:
      x =              //     x = o[n] = number of occurrences of the current dice
        o[n] = -~o[n], //     increment o[n] (we can't have M = 0, so this slot is not used)
      6,               //     M = 1 -> bitmask = 6
      ,                //     M = 2 -> bitmask = 0
      ,                //     M = 3 -> bitmask = 0
      21,              //     M = 4 -> bitmask = 21
      9,               //     M = 5 -> bitmask = 9
      8 ^ o[1]         //     M = 6 -> bitmask = 14 for six 1's, or 8 otherwise
    ][a =              //   take the entry corresponding to M (stored in a)
        x < a ? a : x] //   update a to max(a, x)
  )[5]                 // end of map(); keep the last value
  |                    // do a bitwise OR with the second bitmask
  [                    // this is the lookup array for F-bitmasks:
    ,                  //   F = 0 -> bitmask = 0
    1,                 //   F = 1 -> bitmask = 1
    4,                 //   F = 2 -> bitmask = 4
    5,                 //   F = 3 -> bitmask = 5
    o[1] & 2 | 8,      //   F = 4 -> bitmask = 10 if we also have two 1's, 8 otherwise
    2,                 //   F = 5 -> bitmask = 2
    4                  //   F = 6 -> bitmask = 4
  ][o[4]]              // take the entry corresponding to F (the number of 4's)

Answer 2

R, 100 bytes

Encode the score as a bunch of indexed conditionals. Simpler than my first stringy-regex approach.

Edit- fixed bug and now rank all rolls.

function(d,s=sum(d<2))min(2[s>5],c(11,10,8,6-6*!s-2,4,1)[sum(d==4)],c(7,12,12,9,5,3)[max(table(d))])

Try it online!

Answer 3

Charcoal, 55 bytes

≡⌈Ｅθ№θι⁶Ｉ⁻²⌕14§θχ⁵Ｉ⁻⁵⁼⁵№θ4⁴⎇⁼№θ4⁴§60⁼№θ1²9¹7Ｉ⁻¹²⌊⊘Ｘ²№θ4

Try it online! Link is to verbose version of code. Does not skip 10. Explanation:

≡⌈Ｅθ№θι

Calculate the highest frequency of any digit.

⁶Ｉ⁻²⌕14§θχ

If there is a 6 of a kind, then subtract the position of the digit in the string 14 from 2. This results in 1 for 6 4s, 2 for 6 1s, and 3 for 6 of anything else.

⁵Ｉ⁻⁵⁼⁵№θ4

If there is a 5 of a kind, then the result is 5 unless there are 5 4s, in which case 1 is subtracted.

⁴⎇⁼№θ4⁴§60⁼№θ1²9

If there is a 4 of a kind, then if there are 4 4s then the result is 6 unless there are 2 1s in which case the result is 0, otherwise the result is 9.

¹7

If all the digits are different then the result is 7.

Ｉ⁻¹²⌊⊘Ｘ²№θ4

Otherwise the result is 12 - (4 >> (3 - # of 4s)).

Answer 4

JavaScript (Node.js), 169 bytes

a=>-~"114444|123456".search(w=a.sort().join``,[l,t]=/(.)\1{3,}/.exec(w)||[0],l=l.length)||(l>5?3-"14".search(t):l>3?4+(5.5-l)*(t-4?4:2):[,13,12,11,9][w.split`4`.length])

Try it online!

Returns 1..13

Answer 5

Python 2,  148  119 bytes

-27 bytes thanks to ovs's (1. use of .count allowing a map to be used; 2. removal of redundant 0 in slice; 3. use of an in rather than a max; 4. shortened (F==4)*O==2 to F==4>O==2 [since golfed to F>3>O>1])

C=map(input().count,range(1,7))
O,F=C[::3]
print[F>3>O>1,F>5,O>5,6in C,F>4,5in C,F>3,all(C),F>2,4in C,F>1,F,1].index(1)

Try it online!

Answer 6

Pyth, 60 bytes

eS[@[ZhZ2 4*6hq2hJuXtHG1Qm0Q8hT)@J3*5hSJ*Tq6hJ*<3KeSJ@j937TK

Maps to reversed rank, 0-12. Try it online here, or verify all the test cases at once here.

The full mapping used is as follows:

12: 4 fours and 2 ones.
11: 6 fours.
10: 6 ones.
 9: 6 of any kind except fours and ones.
 8: 5 fours.
 7: 5 of any kind except for fours.
 6: 4 fours.
 5: Straight. (1-6)
 4: 3 fours.
 3: 4 of any kind except 4.
 2: 2 fours.
 1: 1 four.
 0: Nothing.

This works by mapping the dice values to frequencies, then calculating the value of several rules, and taking the maximum of the set.

Implicit: Q=eval(input()), Z=0, T=10

JuXtHG1Qm0Q   Input mapping
 u     Q      Reduce each element of the input, as H, ...
        m0Q   ...with initial value, G, as an array of 6 zeroes (map each roll to 0)
   tH           Decrement the dice roll
  X  G1         Add 1 to the frequency at that point
J             Store the result in J

@[ZhZ2 4*6hq2hJuXtHG1Qm0Q8hT)@J3   Rule 1 - Values for sets including 4
  Z                               *0
   hZ                             *1 (increment 0)
     2                            *2
       4                          *4
              JuXtHG1Qm0Q          Input mapping (as above)
             h                     First value of the above - i.e. number of 1's
           q2                      1 if the above is equal to 2, 0 otherwise
        *6h                       *Increment and multiply by 6
                                   Maps to 12 if there are 2 1's, 6 otherwise
                         8        *8
                          hT      *11 (increment 10)
 [                          )      Wrap the 7 starred results in an array
                             @J3   Get the 4th value of the input mapping - i.e. number of 4's
@                                  Get the value at that position in the array

*5hSJ   Rule 2 - Straight
  hSJ   Smallest frequency in input mapping (first, sort, J)
        For a straight, smallest value will be 1, 0 otherwise
*5      Multiply by 5

*Tq6hJ   Rule 3 - 6 1's
    hJ   Frequency of 1's (first value from input mapping)
  q6     1 if the above == 6, 0 otherwise
*T       Multiply by 10

*<3KeSJ@j937TK   Rule 4 - 4,5,6 of a kind, other than 4's
   KeSJ          Get the max frequency from input mapping, store in K
        j937T    [9,3,7]
       @     K   Get the element at K'th position in the above (modular indexing)
 <3K             1 if 3<K, 0 otherwise
*                Multiply the previous 2 results

eS[   Wrapping it all up!
  [   Wrap all the above rules in an array
eS    Take the max value of the above, implicit print

Answer 7

Retina, 137 126 bytes

4
A
O`.
^11A+
0
1+$
2
^A+
1
(.)\1{5}
3
^.A+
4
.?(.)\1{4}.?
5
^..A+
6
12356A
7
.+AAA$
8
.*(.)\1{3}.*
9
.+AA$
10
.+A$
11
.{6}
12

-11 bytes thanks to @Neil.

Output is 0-indexed (0..12).

Try it online or verify all test cases.

Explanation:

Replace every 4 with an 'A':

4
A

Sort all the input-digits (the A's will be at the back):

O`.

Every other two lines replaces the input with the expected output:

Regex         Replacement  Explanation

^11A+         0            starts with "11", followed by any amount of A's
1+$           2            ends with any amount of 1s
^A+           1            starts with any amount of A's
(.)\1{5}      3            six of the same characters
^.A+          4            starts with any character, followed by any amount of A's
.?(.)\1{4}.?  5            five of the same characters,
                           with optionally a leading or trailing character
^..A+         6            starts with any two characters, followed by any amount of A's
12356A        7            literal "12356A" match
.+AAA$        8            any amount of leading characters, ending with three A's
.*(.)\1{3}.*  9            four of the same characters,
                           with optionally any amount of leading/trailing chars
.+AA$         10           any amount of leading characters, ending with two A's
.+A$          11           any amount of leading characters, ending with a A
.{6}          12           any six characters

Answer 8

05AB1E, 57 55 bytes

4¢4@U.M¢©5-Di14¹нk2αë>Di5X-ë>i9X3*-¹1¢2Ê*ë®i7ë¹4¢o;ï12α

Port of @Neil's Charcoal answer, because my initial approach was already at 60 bytes and I wasn't done yet. My current answer can probably be golfed some more, though.

Input as a list of digits.

Try it online or verify all test cases.

Explanation:

4¢              # Count the amount of 4s in the (implicit) input-list
  4@            # Check if it's larger than or equal to 4
                # (results in 1 for truthy; 0 for falsey)
    U           # Pop and store that result in variable `X`
.M              # Push the most frequent number in the (implicit) input-list
  ¢             # Pop and push the count of that number in the (implicit) input-list
   ©            # Store it in the register (without popping)
5-Di            # If the maximum count - 5 is exactly 1 (so the maximum count is 6):
    14          #  Push 14
      ¹н        #  Push the first digit of the input-list
        k       #  Get its index in 14, resulting in -1, 0, or 1
         2α     #  Take the absolute difference with 2
                #  (This covers cases 1, 2, and 3)
ë>Di            # Else-if the maximum count - 5 + 1 is exactly 1 (so the maximum count is 5):
    5           #  Push 5
     X-         #  And subtract variable `X`
                #  (This covers cases 4 and 5)
ë>i             # Else-if the maximum count - 5 + 2 is exactly 1 (so the maximum count is 4):
   9            #  Push 9
    X3*         #  Multiply variable `X` by 3
       -        #  And subtract it from the 9
        ¹1¢     #  Count the amount of 1s in the input-list
           2Ê   #  Check if it's NOT equal to 2 (1 if truthy; 0 if falsey)
             *  #  Multiply it with the 9 or 6
                #  (This covers cases 0, 6, and 9)
ë®i             # Else-if the maximum count is 1:
   7            #  Push a 7
                #  (This covers case 7)
ë               # Else (maximum count is 2 or 3):
 ¹4¢            #  Count the amount of 4s in the input-list
    o           #  Take 2 to the power this count
     ;ï         #  Halve and floor it
       12α      #  And take the absolute difference with 12
                #  (This covers cases 8, 10, 11, and 12)
                # (Output the top of the stack implicitly as result)

Answer 9

Ruby, 100 bytes

->a{%w(^2.*4$ 6$ ^6 6 5$ 5 4$ ^1*$ 3$ 4 2$ 1$ .).index{|b|/#{b}/=~([1,*a,4].map{|c|a.count(c)}*'')}}

Try it online!

How it works:

Count occurrences of every number in the array, prepend number of 1s and append number of 4s.

After that, try to match with different regex patterns.