I keep forgetting to click "Sort by Date" and when it sorts by rating I get confused. My question was different, let me rephrase: Assume there was no round before (A,B,C) = (4, 2, 5) with B and C active gets at the end of round 1 to (4, 4, 3). 1) Do we stop here even if the active players are not the ones equal? Bonanova's response does imply so i.e. Game ends at the end of the round if ANY 2 players are equal (different wording than OP though). So we count a minimum of 1 round before game with (4,2,5) ends. 2) If we let it go to the next round since the two active players (B and C) are not equal: 2A) assuming A and B could be active AND if we don't check the condition before we subtract, then one of them gets 0, and that may cause infinite rounds. 2B) If we do check the condition A=B since they are the active, then we call the game ending in Round 2. What I meant is that different wording makes either N=1 or N=2. In any case, I'm assuming and counting using rule "Game ends at the end of the round if ANY 2 players are equal". And another submission from me: