Update tic-tac-toe.md

tic-tac-toe.md

@@ -10,7 +10,7 @@ In the non-cooperative case older transactions are replaced by newer transaction
 <img src=tictactoe.png >
 
 Before the game starts, each player traverses the tree of game states and signs every possible move of their opponent. The player subtracts his signature by his signature of the parent transaction that leads to this particular game state.
-These so-called *adapter signatures* form a tree which is exchanged upfront. This ensures a player can execute a transaction exactly if the opponent executed the preceding move, that lead to that particular game situation.
+These so-called *adapter signatures* form a tree which is exchanged upfront. This ensures a player can execute a transaction exactly if the opponent executed the preceding move, that lead to that particular game situation. The set of transactions that a player can complete at a point in time represents the set of valid moves they can choose from.
 
 Note that the index of a move is actually represented by the nonce of the signature. The message is always simply one of three possibilities: "Player A takes the money", "Player B takes the money", or "Both players are refunded." 
 
@@ -29,3 +29,4 @@ Only one last transaction hits the chain and spends the output.
 - The game must end before an intermediate game state hits the chain. 
 - Using RBF as consensus mechanism is risky. This update mechanism depends on the mempool of bitcoin miners. We assume no player cooperates with a miner. 
 - The players have to sign and exchange the whole game tree upfront, which is about 25000 signatures per game.
+