¿Cuántas veces un jugador (J1, J2, J3 o J4) recibe exactamente la misma mano en diferentes simulaciones?

Escenario

¿Cuántas veces un jugador (J1, J2, J3 o J4) recibe exactamente la misma mano en diferentes simulaciones?, (la vez anterior (https://simulacion168.acostasite.com/2026/04/en-16800-simulaciones-cuantas-veces-se.html) solo se analizó al jugador uno. 

Este nuevo escenario analizar la manos de todos los jugadores en todas las simulaciones y nuevamente buscamos por manos duplicadas

Resultados

Esta vez fuimos directo a correr 16800 simulaciones. Obtuvimos 1750 resultados lo que representa un 10,41%

Mi opinión: En lo personal lo veo alto, ¿qué te parece a tí?

Código python en caso de que veas algo malo

import numpy as np

from collections import Counter

num_simulations = 16800

num_players = 4

pieces_per_player = 7

all_simulations_player_hands = []

# Re-run simulations to populate all_simulations_player_hands

for simulation_num in range(num_simulations):

# Re-initialize the full set of 28 domino pieces

domino_pieces_full = []

for i in range(7):

for j in range(i, 7):

domino_pieces_full.append((i, j))

# Shuffle the domino pieces

np.random.shuffle(domino_pieces_full)

current_simulation_hands = []

start_index = 0

# Distribute pieces to players

for _ in range(num_players):

player_hand = domino_pieces_full[start_index : start_index + pieces_per_player]

current_simulation_hands.append(player_hand)

start_index += pieces_per_player

# Store the hands for the current simulation

all_simulations_player_hands.append(current_simulation_hands)

print(f"Simulaciones completadas: {num_simulations}.")

print(f"Total de simulaciones almacenadas: {len(all_simulations_player_hands)}\n")

all_players_hands_canonical = []

# Convert all players' hands from all simulations to a canonical (sortable and hashable) form

for simulation_hands in all_simulations_player_hands:

for player_hand in simulation_hands:

# Sort pieces within the hand, then sort the hand itself

# This ensures that hands with the same pieces, regardless of original order, are identical

canonical_hand = tuple(sorted(tuple(sorted(piece)) for piece in player_hand))

all_players_hands_canonical.append(canonical_hand)

# Count the occurrences of each unique canonical hand

hand_counts = Counter(all_players_hands_canonical)

# Filter for hands that appeared more than once

duplicate_hands = {hand: count for hand, count in hand_counts.items() if count > 1}

# The total number of duplicate occurrences is the sum of (count - 1) for each duplicate hand,

# as each count already includes the first occurrence.

total_duplicate_occurrences = sum(count - 1 for count in duplicate_hands.values())

print(f"De {num_simulations * num_players} manos distribuidas (en {num_simulations} simulaciones a {num_players} jugadores),")

print(f"la misma mano fue recibida por cualquier jugador (J1, J2, J3 o J4) en diferentes corridas un total de {total_duplicate_occurrences} ocasiones.")

print(f"Manos únicas que se repitieron: {len(duplicate_hands)}.")

print("Ejemplos de manos que se repitieron:")

for hand, count in list(duplicate_hands.items())[:5]: # Mostrar hasta 5 ejemplos

print(f" Mano: {list(hand)}, Cantidad: {count}")