I have been working on mathematical paradoxes.
I am looking for paradoxical situations in Poker for a deep study. I found things, like Morton's Theorem, Implicit Collusion or "all in" strategy, could you help me to find more?
Not sure if this is really a paradox, but...
In a heads-up game your opponent truthfully confides in you that he is playing a 100% range.
So you think to yourself, "Great, from now on I will play a 70% range and I will be profitable because I’m ahead of his range."
You are dealt a new hand and see that it is at the bottom of your range, but you no-longer want to play the hand because it is behind most of your opponents range.
Not sure if this is a paradox as much as counter-intuitive, but according to Phil Gordon, a rare case of over-cards being a slight favorite to a pocket pair is JTs vs. 55.
Ace high straight is highest but it is actually easier to make because there are no blockers above.
To me this is a Best hand versus AA as every way I look at it it seems like 67s should be better.
How almost all hands have at least a 33 percent chance of winning in a showdown against a pre-flop raiser. But yet they rarely actually win 33 percent of the time.