Alice and Bazza are playing the inekoalaty game, a two‑player game whose rules depend on a positive real number \lambda which is known to both players. On the $n$th turn of the game (starting with n=1) the following happens:
If n is odd, Alice chooses a nonnegative real number x_n such that
x_1 + x_2 + \cdots + x_n \le \lambda n.
If n is even, Bazza chooses a nonnegative real number x_n such that
x_1^2 + x_2^2 + \cdots + x_n^2 \le n.
If a player cannot choose a suitable x_n, the game ends and the other player wins. If the game goes on forever, neither player wins. All chosen numbers are known to both players.
Determine all values of \lambda for which Alice has a winning strategy and all those for which Bazza has a winning strategy.
Proposed by Massimiliano Foschi and Leonardo Franchi, Italy