Zndrsplt, Eye of Wisdom

If an effect has a player flip a coin and refers to winning or losing a flip, only the player who flipped the coin wins or loses the flip. If that player loses the flip, nobody wins the flip.

The second ability represented by the "partner with [name]" keyword modifies the rules for deck construction in the Commander variant and has no function outside of that variant. If a legendary creature card with "partner with [name]" is designated as your commander, the named legendary creature card can also be designated as your commander. For more information on the Commander variant, please visit Wizards.com/Commander.

"Partner with [name]" represents two abilities. The first is a triggered ability: "When this permanent enters the battlefield, target player may search their library for a card named [name], reveal it, put it into their hand, then shuffle their library."

The triggered ability of the "partner with" keyword still triggers in a Commander game. If your other commander has somehow ended up in your library, you can find it. You can also target another player who might have that card in their library.

If an effect has a player flip a coin but refers to whether the flip came up heads or tails, that flip has no winner or loser.

Once the game begins, your two commanders are tracked separately. If you cast one, you won't have to pay an additional {2} the first time you cast the other. A player loses the game after having been dealt 21 damage from one of them, not from both of them combined. Command Beacon's effect puts one into your hand from the command zone, not both.