Does infect damage to a player cause them to lose the game when they reach 10 poison counters immediately or at end of turn?

A player loses the game the moment they have 10 or more poison counters. This is a state-based action checked continuously throughout the game, not a delayed trigger that waits until end of turn. As soon as the 10th poison counter is placed, the game checks state-based actions and that player loses.

Infect (CR 702.90) causes a source with infect to deal damage to players in the form of poison counters instead of loss of life — one poison counter per 1 damage dealt. The loss condition itself is governed by CR 104.3d and CR 122.1b, which state that a player with 10 or more poison counters loses the game as a state-based action (CR 704.5c).

State-based actions (CR 704) are checked at specific game moments — before each player gets priority — but this still means they are checked very frequently and take effect almost immediately after the triggering event. There is no 'wait until end of turn' delay involved.

Concrete example: Your opponent is at 9 poison counters. You attack with a 2/2 creature with infect. It deals 2 damage (placing 2 poison counters), bringing your opponent to 11 poison counters. Before anyone receives priority after combat damage resolves, state-based actions are checked and your opponent loses the game immediately — not at the end of the turn.

Note that poison counters, once placed, do not go away at end of turn; they remain on the player for the rest of the game unless a specific effect removes them.