In tournament poker, when the field goes from three players to two (or really, from any number down to two), the position of the dealer button and blinds can seem a little backwards.
Here’s the setup:
The player who most recently paid the big blind becomes the small blind, the other player becomes the big blind, and the button moves to the small blind.

The small blind (dealer) deals to the big blind first, and then has first action.

On following streets, the big blind is first to act.

Why is this correct?
Blinds and Button Placement
Throughout the tournament, the big blind moves consistently and determines placement of the small blind and button. Sometimes this results in a “dead” dealer button or multiple small blinds when players are eliminated or brought over from another table. The goal is to always move the big blind in a way that ensures all players pay the big blind an equal number of times and never multiple times in a rotation. Giving the small blind to the player who most recently paid the big blind prevents a player from having to pay the big blind in two consecutive hands.
Button placement is the least intuitive piece of the puzzle, in my opinion. The best thing I can say here, is that it sets up the correct pre/post-flop action.
Pre-Flop Action
Pre-flop, the small blind (dealer) has first action. This is consistent with the rest of the tournament, in that the player who paid the small blind must act before the big blind, and the player who paid the big blind has final action.
Post-Flop Action
Post-flop, the big blind is first to act. This is consistent with the rest of the tournament, in that the dealer has final action on all post-flop streets.
This transition always feels a bit weird, but it sets up play to remain as consistent as possible with all other stages of the tournament. For me, the easiest way to remember has always been this…
The player who paid the big blind most recently gets the small blind and the button.
