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Working backwards: before the second game, Brendan must have had £90 and so Adam had £270.

Before the first game, Adam must have had £135, so Brendan had £225.

Extension

After the next game, one player will have all the money and no more games can be played. Hence £135 and £225 lead to a finite number of games being played.

If the player with the most money always loses, which starting values £\(A\) and £\(B\) will lead to finite and infinite numbers of games?