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?

  • 1
    I'm not certain this type of question is a good fit for this site, although it is interesting! It could be a good jumping off point for generating some extra questions on poker.se. For that reason I hope you get some good answers ;)
    – Toby Booth
    Oct 29 '15 at 0:20
  • A paradox is when one uses generally acceptable logic to, seemingly, soundly conclude something that is prima-facie illogical. Perhaps apply Zeno's paradox to pushing all in? Read out an equation that incorrectly subtracted, or divided as a story. Here is an example: en.wikipedia.org/wiki/Missing_dollar_riddle
    – Snipe
    Dec 17 '15 at 18:19
  • Probably a little bit late: Do situations where ICM advises you to fold aces in Holdem qualify?
    – Drunix
    Jul 19 '16 at 6:12
  • Would you make a distinction between a paradox and something which is just highly counter-intuitive?
    – 3N1GM4
    Jan 5 '17 at 15:11

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 seeing how 69% is behind a random hand (50%).
    – paparazzo
    May 4 '18 at 14:13
  • @paparazzo because 69 > 50. Isn't that the definition of being behind?
    – Buh Buh
    May 4 '18 at 14:25
  • Sure not my definition.
    – paparazzo
    May 4 '18 at 14:27
  • I think we might be looking at it from opposite ends. I meant 69th percentile as in a low quality hand. Not a high quality. Perhaps I should have written it as 31st percentile? Does that help?
    – Buh Buh
    May 4 '18 at 14:35
  • Playing the bottom of a 70% range is worse than playing the average of a 100% range
    – Buh Buh
    May 4 '18 at 14:36

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.

  • 4
    That's just one example of the not-really-a-paradox of the non-transitive value of starting hands. Another is 22 > AK > JTs > 22. Jun 9 '17 at 2:11
  • @LeeDanielCrocker :o could you send me a link regarding that? Sounds interesting. Apr 5 '18 at 15:54
  • (haha sorry for the late! this question was bumped and I read it just now) Apr 5 '18 at 15:55

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.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.