JSFiddle - React, Tailwind, and code Playground

JavaScript

const findWinner = (n) => (!n || n <= 0) ? null : whoWins(n - 1, true) ? 'A' : 'B';
const whoWins = (n, player) => (n <= 0) ? !player : whoWins(n - (player ? 2 : 1), !player);

/** Test cases **/
console.log(findWinner(1)); // B
console.log(findWinner(2)); // A
console.log(findWinner(3)); // A
console.log(findWinner(4)); // B
console.log(findWinner(0)); // null
console.log(findWinner(null)); // null