Cupcake Bayesian Payout

Ten cupcakes are visually indistinguishable and each is either lemon (L) or vanilla (V). You are told that the true composition is equally likely to be either (1 L, 9 V) or (9 L, 1 V). You may eat as many cupcakes as you want, one by one, observing only the flavors you ate. After you stop, you must guess a flavor (L or V). You then receive $1 for each remaining cupcake of the flavor you guessed (e.g., if you guess V and there are 7 vanilla cupcakes left, you win $7). What is the maximum expected payout under optimal play, and what strategy achieves it?

Answer format: round to 1 decimal place.