Dice game probabilities: Difference between revisions

Line 156:

=={{header|J}}==

'''Solution:'''

⚫

gen_dict =: (({. , #)/.~@:,@:(+/&>)@:{@:(# <@:>:@:i.)~ ; ^)&x:

<lang J>gen_dict =: (({. , #)/.~@:,@:(+/&>)@:{@:(# <@:>:@:i.)~ ; ^)&x:

beating_probability =: ~~4 :~~ 0

beating_probability =: dyad define

'C0 P0' =. gen_dict/ x

'C1 P1' =. gen_dict/ y

(C0 +/@:,@:(>/&:({."1) * */&:({:"1)) C1) % (P0 * P1)

⚫

)</lang>

)

'''Example Usage:'''

10 5 (;x:inv)@:beating_probability 7 6

<lang J> 10 5 (;x:inv)@:beating_probability 7 6

┌─────────────────────┬────────┐

│3781171969r5882450000│0.642789│

Line 172:

┌─────────────────┬────────┐

│48679795r84934656│0.573144│

└─────────────────┴────────┘

└─────────────────┴────────┘</lang>

</lang>

gen_dict explanation:

gen_dict is akin to gen_dict in the python solution and

<code>gen_dict</code> is akin to <code>gen_dict</code> in the python solution and

returns a table and total number of combinations, order matters.

The table has 2 columns. The first column is the pip count on all dice,

the second column is the number of ways this many pips can occur.

({. , #)/.~ make a vector having items head and tally of each group of like items in this case pip count and occurrences

<code>({. , #)/.~</code> make a vector having items head and tally of each group of like items in this case pip count and occurrences operating on

⚫

<code>,</code> raveled data (a vector) made of

operating on

⚫

<code>+/&></code> the sum of each of the

⚫

, raveled data (a vector)

~~made~~ of the

<code>{</code> Cartesian products of the

⚫

<code>(# <@:>:@:i.)</code> equi-probable die values

⚫

+/&> the sum of each

⚫

<code>&x:</code> but first use extended integers

of the

⚫

<code>; ^</code> links the total possibilities to the result.

{ Cartesian products

of the

⚫

(# <@:>:@:i.) equi-probable die values

⚫

&x: but first use extended integers

⚫

<~~nowiki~~>; ^</~~nowiki~~> links the total possibilities to the result.

The verb beating_probability is akin to the python solution function having same name.

The verb <code>beating_probability</code> is akin to the python solution function having same name.

C0 >/&:({."1) C1 is a binary table where the pips of first player exceed pips of second player. "Make a greater than table but first take the head of each item."

<code>C0 >/&:({."1) C1</code> is a binary table where the pips of first player exceed pips of second player. "Make a greater than table but first take the head of each item."

C0 */&:({:"1) C1 is the corresponding table of occurrences

<code>C0 */&:({:"1) C1</code> is the corresponding table of occurrences

* naturally we multiply the two tables (atom by atom, not a matrix product)

<code>*</code> naturally we multiply the two tables (atom by atom, not a matrix product)

+/@:,@: sum the raveled table

<code>+/@:,@:</code> sum the raveled table

% (P0 * P1) after which divide by the all possible rolls.

<code>% (P0 * P1)</code> after which divide by the all possible rolls.

=={{header|Java}}==