I recently did a bit of reading about paradoxes, and it got me thinking about where there might be paradoxes in my strategic approach to poker. This was inspired by watching Vsauce2’s video on the subject:

I have a couple of ideas but I’ll start by summarizing 3 types of paradoxes. Hopefully that will generate more discussion than me starting off with my own convoluted and half-formed ideas about where they might exist in poker thought.

1) Falsidical Paradoxes

These are questions which lead to an incorrect (often nonsensical) answer which we are unable to disprove. The key component of Falsidical paradoxes is that they are demonstrably false when thoroughly investigated, but may require new knowledge or ways of thinking about the question before they can be disproved.

For example, the video highlights a paradox involving a fast runner and a tortoise first conceptualized in Ancient Greece. The paradox was clearly absurd to even a casual observer, but could not be proven false until the invention of calculus, some 2000 years later.

2) Veridical Paradoxes

These are solutions to problems that initially defy logic but can be proven categorically true upon further investigation. This often requires breaking down the presuppositions which frame the initial question, and approaching the problem from a new angle.

The video uses an example where a contestant picks 1 of 3 hidden prizes on a game show, with 1 of those prizes being clearly preferable. If the host reveals one of the other prizes, which will never be the most desirable prize (otherwise the drama of the moment falls apart), the contestant should always switch their choice if allowed to. This logically seems like a pointless 50/50 decision, but can be mathematically demonstrated to double he contestant’s odds from 33.3% to 66.6%.

3) Antinomy

This is the type of paradox which most readily comes to mind when we think of paradoxes. These are situations which can’t be true but also can’t be false. They create a ‘crisis in logic.’

The video gives two examples:

The grandfather paradox – if you time travel and kill your grandfather before the birth of your father, how could you ever be born? You can’t possibly go back in time if you never existed but you can’t possibly cease to exist if you’re unable to go back in time.

The liar’s paradox – the sentence “I am lying” can neither be true or false.

Many historical advancements in thought have been the result of discovering that an apparent Antimony is in fact Falsidical or Veridical. Considering how poker theory is still in the early stages of development, it must be the case that there are plenty of dilemmas which seem unsolvable (or which are falsely assumed to be solved) that are just waiting for the discovery of false or misleading premises.

Anyone care to venture some ideas, or share ‘aha!’ moments from your experiences that changed they way you think about poker?