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El papel de las matemáticas en el poke

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Cualquiera que tenga intención de vivir del poker o al menos hacer dinero con él, debería tener una idea más o menos general de qué papel tienen las matemáticas en la teoría del poker y cuál es su importancia específica; si es absolutamente fundamental dominar bien ciertas técnicas matemáticas o si es algo que se puede suplir gracias a conocimiento adquirido por parte de otros jugadores o la experiencia.

Siguiendo el artículo de Bryce Paradis que tenéis traducido en NoticiasPoker, podemos dividir el juego del poker en dos aspectos fundamentales e independientes entre sí: 1) determinar cuál es la estrategia más probable del oponente. 2) Una vez que hemos determinado esa estrategia, jugar nosotros con la estrategia con mayor valor esperado a largo plazo contra la estrategia del oponente.
Conviene llamar la atención sobre el hecho de que, sólo con la mera ayuda de las matemáticas, podemos resolver el punto 2 a la perfección. Si un oponente con 20bb sube tantas manos pre-flop y abandona tantas manos ante una resubida, se puede determinar matemáticamente con precisión absoluta cuál es el rango con el que debemos jugar contra ese jugador. (Si el oponente tiene 100bb también se puede, pero los cálculos se complican enormemente incluso para un bot).
¿Quiere decir esto que un conocimiento matemático de primera mano es imprescindible para poder elegir correctamente nuestros movimientos contra la estrategia del rival? Bueno, en principio no tendría por qué ser exactamente así. Podría resultar que deducir los movimientos con más EV fuese tan sencillo e intuitivo que cualquier humano en condiciones psicofísicas normales podría verlo claramente casi sin necesidad de pensar: es lo que pasa en el piedra-papel-tijera, donde si pudiésemos adivinar qué va a sacar nuestro oponente, no habría que romperse la cabeza para responder con el mejor movimiento. Otro ejemplo es el juego del tres-en-raya, un poco más complicado pero que aún así cualquier humano lo puede resolver con un poco de esfuerzo. Por contra, juegos como el go, el ajedrez o el backgammon no son nada intuitivos, y deducir la jugada perfecta, incluso teniendo a mano toda la información relevante en juego, es de todo menos fácil o intuitivo, hasta el punto de que actualmente ningún ordenador, por potente que sea, es capaz de jugar perfecto al go o al ajedrez. El poker, afortunadamente para todos nosotros, se parece más al ajedrez que al tres-en-raya, lo que hace que calcular la mejor jugada no sea instintivo ni obvio.
Aún así, esto no nos fuerza, de algún modo, a hacer los cálculos por nuestra cuenta para tener un juego decente. Siempre podemos tener una buena idea de cuál es la jugada correcta gracias al trabajo de otros jugadores, que nos transmitan ese conocimiento, o gracias a la experiencia.
La experiencia por supuesto es fundamental, pero no nos sirve de mucho para determinar qué jugada es mejor si el asunto es relativamente dudoso. Si no tenemos muy claro si elegir entre resubir un proyecto de color o hacer sólo call, es casi imposible que a base de jugar muchas manos vayamos a aclararnos. Otra cosa es determinar la estrategia de los oponentes, en cuyo caso la experiencia es mucho más importante.
El conocimiento adquirido puede sustituir muchos cálculos propios. Cualquier grinder de NL100 puede obtener nociones relativamente avanzadas de juego pre-flop, de situaciones de cbet, de manos con las que hacer call o resubir en el flop… sólo a base de conocer las opiniones de los jugadores más expertos. Aún así, las situaciones son demasiadas como para poder adaptarnos a todas si no conocemos el por qué de esos movimientos: que por supuesto descansa en el cálculo. Es decir, conviene atender al hecho de que casi nadie es capaz de realizar cálculos mientras juega una mano de poker, especialmente online donde se juega en muchas mesas a la vez: la mayoría de los cálculos se hacen offline, y nos dan suficiente clarividencia como para ajustarnos a muchas situaciones. P.E. si sé que tal tipo de oponente farolea en un river en el que hay un proyecto fallido un 33% de las veces, eso me dice que puedo llegar a hacer call a una apuesta del bote con cualquier mano hecha. Sabiendo eso, y habiendo estudiado casos similares con otras frecuencias de faroleo, y siempre teniendo en cuenta que cada tipo de board ayuda más o menos a farolear o no, puedo tener una noción relativamente correcta de cuándo igualar, aunque no sea capaz de realizar efectivamente el cálculo en los pocos segundos que tengo para decidir. Es decir, si bien tener estrategias prefijadas (nunca re-subir en el flop con TPTK, hacer siempre una apuesta de continuación con TPTK en el turn si hay proyectos en el board, no hacer nunca la apuesta de continuación sin mano contra dos o más oponentes en el flop… etc. etc.) ayuda a compensar la falta de conocimiento matemático, es casi imposible convertirnos en buenos jugadores si no sabemos plantear los cálculos por nuestra cuenta, al menos no a partir de niveles ya con cierta dificultad de juego, como Nl100 o 200.
Esto, en lo que respecta al punto 2. El punto 1, dada su complejidad, se tendrá que tratar en otro artículo. Sin bien el orden parece invertido a cómo se juega una mano, tiene bastante sentido hacerlo así, puesto que es más complicado poner al oponente en una mano que jugar correctamente una vez que hemos determinado cuál es su rango

 

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