Friday, April 18, 2014

GTO Brainteaser #3 -- Blind Man's Bluff

This weeks brainteaser involves solving a simplified, three card version of Blind Man's Bluff poker for two players. If you've never played Blind Man's Bluff before, you can play a full version of the 52 card game against our Arnold GTO bot below (note that his edge against sub-optimal play is very small).

The simplified version of the game game works as follows:

1. There is a 3 card deck with an Ace, a King, and a Queen.
2. Both players must ante \$50.
3. Each player is dealt a card from the deck, face down, and is not allowed to look at their own card.
4. Each player then gets to see the other player's card (you can imagine them putting their cards on their foreheads).
5. Player 1 may then either bet \$75 or check.
6. Player 2 can call or fold if Player 1 bets and can check or bet \$75 if Player 1 checks.
7. If the hand goes to showdown (a bet is called or both players check) then the player with the higher card wins the pot.
What is the optimal strategy in this game?

As usual, I'll post a solution next week, but I'm going to shift to posting the solutions on Tuesdays so that I'm not scrambling to write them up over the weekend as often :)  If you haven't already, be sure to check out last weeks solution to the Red or Black game.