Closed Doppelkopf question from StackExchange

[HighDiceRoller]

The question.

from icepool import Deck, multiset_function

# https://math.stackexchange.com/questions/5048259/number-of-card-decks-in-doppelkopf-and-probability-of-specific-events

deck = Deck(range(20), times=2)

print('Specific player draws both of a specific card')
print(deck.deal(10) >= [0, 0])

all_deal = deck.deal((10, 10, 10, 10))

# given ace of clubs

@multiset_function
def i_have_ace_of_clubs(hands):
    a, b, c, d = hands
    return (a.keep_outcomes([0]).size(),
            (b & [0, 1, 4]).any(),
            (c & [0, 1, 4]).any(),
            (d & [0, 1, 4]).any())

for me, result in i_have_ace_of_clubs(all_deal).group_by[0].items():
    print(f'Given that I have {me} aces of clubs, other players each have A or 10 or K of clubs')
    print(result.marginals[1:].map(all))

# queen counts
print('How many queens do I have')
print(deck.deal(10).keep_outcomes([0, 5, 10, 15]).size())

# partner

two_deal = deck.deal((10, 10))

@multiset_function
def partner_match(hands):
    a, b = hands
    return (a & [10]).any(), (b & [10]).any()

print('Given I have specific card, does partner have its double')
print(partner_match(two_deal).group_by[0][0].marginals[1])

i_have_ace_of_clubs is easily the most time-consuming of these. There is certainly some redundant state in the anys, but is there a clean way of allowing to remove the redundancy without a custom MultisetEvaluator?

[HighDiceRoller]

Result

Specific player draws both of a specific card
Die with denominator 847660528

Outcome	Quantity	Probability
False	798757036	94.230769%
True	48903492	5.769231%

Given that I have 0 aces of clubs, other players each have A or 10 or K of clubs
Die with denominator 2624143562714106473040

Outcome	Quantity	Probability
False	920028863048844875040	35.060157%
True	1704114699665261598000	64.939843%

Given that I have 1 aces of clubs, other players each have A or 10 or K of clubs
Die with denominator 1809754181182142395200

Outcome	Quantity	Probability
False	928965466707191971200	51.331030%
True	880788714474950424000	48.668970%

Given that I have 2 aces of clubs, other players each have A or 10 or K of clubs
Die with denominator 271463127177321359280

Outcome	Quantity	Probability
False	192394411681657751280	70.873129%
True	79068715495663608000	29.126871%

How many queens do I have
Die with denominator 847660528

Outcome	Quantity	Probability
0	64512240	7.610622%
1	224390400	26.471729%
2	294512400	34.744145%
3	188487936	22.236253%
4	63433440	7.483354%
5	11277056	1.330374%
6	1006880	0.118783%
7	39680	0.004681%
8	496	0.000059%

Given I have specific card, does partner have its double
Die with denominator 14203292790026340

Outcome	Quantity	Probability
False	6203737080701160	43.678161%
True	7999555709325180	56.321839%