12.2.08

Poleana - Poliana. Consideraciones técnicas.

Está por demás decir que utilizando dos dados se pueden obtener doce números diferentes, ya sea de manera directa o por suma. En los siguientes renglones se estudiará la probabilidad de obtener cada uno de ellos.

La probabilidad se define como el número de eventos favorables entre la totalidad de los eventos posibles. Sea P(i) la probabilidad de ocurrencia del número i, donde i = 1, 2,...,12. Entre más cercano sea este valor a uno, mayor factibilidad tiene de ocurrir.


Para obtener el número 1 se tienen dos eventos favorables (uno por dado) entre doce posibles (seis por dado). Entonces,

P(1)= (1+1)/(6+6)= 1/6

Sucede algo similar con el número 2; pero, además, existe la posibilidad de que salga doble 1, cuya suma es igual a dos. Esto remite a un evento condicional y se define como el producto de las dos probabilidades por seperado:

P(1|1) = 1/6*1/6 = 1/36 y se lee
"La probabilidad de 1 dado 1 es igual a...".

P(2')= P(2) + P(1|1) = 1/6 + 1/36 = 7/36

La apóstrofe se utiliza para diferenciarla de la probabilidad de obtener el número directo. A partir de ahora se omitirán los detalles y únicamente se expondrán las sumas.

P(3')= P(3) + P(1|2) + P(2|1) = 1/6 + 2*(1/36) = 2/9

P(4')= P(4) + P(1|3) + P(2|2) + P(3|1) = 1/6 + 3*(1/36) = 1/4

P(5')= P(5) + P(1|4) + P(2|3) + P(3|2) + P(4|1) = 1/6 + 4*(1/36) = 5/18

P(6')= P(6) + P(1|5) + P(2|4) + P(3|3) + P(4|2) + P(5|1) =
1/6 + 5*(1/36) = 11/36

No se necesita ser muy perspicaz para darse cuenta que, después del 6, el resto de los números no pueden salir de manera directa:

P(7)= P(1|6) + P(2|5) + P(3|4) + P(4|3) + P(5|2) + P(6|1) =
6*(1/36) =1/6

P(8)= P(2|6) + P(3|5) + P(4|4) + P(5|3) + P(6|2) = 5*(1/36) = 5/36

P(9)= P(3|6) + P(4|5) + P(5|4) + P(6|3)= 4*(1/36) = 1/9

P(10)= P(4|6) + P(5|5) + P(6|4) = 3*(1/36) = 1/12

P(11)= P(5|6) + P(6|5) = 2*(1/36) = 1/18

P(12)= P(6|6) = 1*(1/36) = 1/36

Para hacer todo lo anterior más representativo, se ordenerán los resultados de mayor a menor:

P(6')= 30.5556%

P(5')= 27.7778%

P(4')= 25.0000%

P(3')= 22.2222%

P(2')= 19.4444%

P(1')= 16.6667%

P(7)= 16.6667%

P(8)= 13.8889%

P(9)= 11.1111%

P(10)= 8.3333%

P(11)= 5.5556%

P(12)= 2.7778%

La diferencia entre cada valor precedente y procedente es siempre igual a 2.7778%.


Para nuestros fines, aterrizar las ideas estadísticas al juego de azar, resulta claro que el número seis tiene mayores probabilidades de ocurrir y ésta va decayendo, en estricto orden inverso, hasta el número 1. La probabilidad del uno y del siete son iguales; a partir de éste sigue disminuyendo, en estricto orden progresivo, hasta el último posible, 12.


Para hacer más explícito el análisis, y sin olvidar jamás que el estudio se aplica al juego de azar denominado "poleana" (o "poliana"), habría que indagar la probabilidad de habilitar una ficha para empezar a jugar, para "salir" en términos simples. Recordemos que esto sucede cuando los dados expresan de manera exacta múltiplos de 6 además del número 6 y 3. Las combinaciones son, entonces, 1 y 5, 2 y 4, 3 y 3, 6 y 3, 6 y 6 y viceversa. En términos matemáticos:

P(salir)= P(1|5) + P(2|4) + P(3|3) + P(4|2) + P(1|5) + P(6|6) +
P(3|6) + P(6|3) = 8*(1/36) = 2/9, o 22.2222%. Aproximadamente 1 de cada 5 tiros.

Si usted, fino y esporádico lector, no tiene ni la más remota idea de qué es la poleana (o poliana) y cómo se juega, sírvase desplazar unas líneas hacia abajao y encontrará una guía, superficial, de carácter genérico.

41 comentarios:

Sergio dijo...

Una excelente apreciación del juego, no podía haberse interpretado d mejor forma.

Ahora comienzo a entender la simetria y equidad de los números en el juego por eso es tan adictiva y entretenida...

Anónimo dijo...

acabo de llegar a u.s.a vivo en temple texas yo jugaba en toluca edo mex.

Anónimo dijo...

acabo de llegar a u.s.a en temple texas y pues boy a construir una poleana para ilustrar alos gabachitos de aqui un poco de la cultura del d.f o mostrarles un juego nuevo y diferente y asi quitarles sus dolares de las manos ja ja ja yo vivia en toluca edo mex. si aqui donde vivo ahora hay alguien de toluca escriba para tener un compa de aya ya que equi no hay . el ranas.

ivan bb leche dijo...

estas son unas pocas de las muchas reglas que tiene este juego por eso es tan bueno y estricto..

aqui en TOCUMBO Michoacan lo juegan la mayoria de los jovenes y quisiera saber mas..
iva_ronaldo10@hotmail.com

aqui hay reta para quien sea.

aRkHAm AsyLUm dijo...

no creí que este interesante pasatiempo fuera conocido en otros estados. La verdad es que es un poco sorprendente porque la poleana es bastante subterránea..

iremos pues a Tocumbo a ver qué tan buenos son por allá

DIABLO dijo...

La `poleana`, el juego socorrido de la cárcel .

Para algunos internos proviene de Lecumberri, para otros, de Santa Martha

La "poleana" es un juego de mesa 100 por ciento canero , es decir, se inventó en una cárcel, de ahí su característica contienda: policías contra ladrones.
Su origen a ciencia cierta no se sabe, para algunos internos proviene del palacio negro de Lecumberri, mientras que otros aseguran que fue en la penitenciaría de Santa Martha Acatitla, ubicada en Iztapalapa, en donde fue creado.

En las calles poco o nada se sabe de este juego, sólo a través de aquellos ex convictos que la han introducido en sus comunidades, pero en los reclusorios varoniles capitalinos, todos los internos la conocen y la juegan y es uno de sus pasatiempos favoritos.

Incluso, detrás de las rejas se hacen competencia, torneos o se cruzan apuestas.


Su tablero asemeja una cárcel y son los dados los que indican el número de casillas que avanza el jugador, quién debe de cuidarse para no caer en una de ellas, que es donde se encuentra la policía, quien hace retroceder totalmente al ladrón.
miles de presos, literalmente, matan el tiempo encerrados.cuando gusten que nos hechemos una polianita, los espero en las esquinas de florida y costa rica, en el barrio de tepito...eso si de milpa para arriba.

arkham asylvm dijo...

mil varos por juego es algo elevado para mí, pero de cualquier manera me da curiosidad saber cómo es la dinámica de la apuesta..
¿Cada perdedor paga mil al que gana o la ficha tiene un valor específico??

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