A solution to the game of googol (Q1345610)

For every \(n > 2\) exchangeable random variables \(X_ 1,\dots,X_ n\) are constructed for which, among all stopping rules \(\tau\) based on the \(X_ i\), \(\text{sup}_ \tau P(X_ \tau = \max(X_ 1,\dots,X_ n))\) is attained by a rule based only on the relative ranks of the \(X_ i\). The underlying distribution serves as a minimax rule for one of the players in the ``game of googol''.