Poker Pros Debate Patrick Leonard's Game Theory Challenge

Poker players recently engaged in a lively debate sparked by Patrick Leonard's game theory problem on Twitter. The scenario involved five players writing a unique number between 1 and 10 to determine who gets a highly desired room. Patrick Leonard posed a game theory problem on Twitter, asking what number between 1 and 10 poker players would write to win a highly desired room.

Dan O'Brien asked Patrick Leonard to publish the names of those who would write 7 or 8. Josh Arie wrote that he would write the number 6. Jamie Staples wrote that he would write the number 9, as the mathematics suggests 10 and reason suggests 8. Jake Abdalla suggested flipping a coin among the five players to determine the room assignments. Patrick Leonard described a credit card roulette scheme in restaurants where losers flip again for double the bill.

Olivier Busquet wrote that he would choose 9 because poker players think they are the smartest and will consider it an obvious choice. Max Silver wrote that he would write 9 and show it to everyone. Henrik Heiklen suggested that the best exploit would be to write 9 and insist on not changing the choice. Niall Farrell wrote that he would write 1, as no one would expect it. M4LT wrote that he would be satisfied if he wrote 10 and lost, as long as no one else won with 10. Darrell Gooch wrote that he found a new favorite coin flip variation. Brian Rast wrote that the task is more about exploiting other players' strategies rather than solving it by GTO. ArtySmokesPS wrote that by Nash/GTO, one should mix frequencies, choosing 10 more often but also including numbers below 7.