When the possible offers are $1 and $5, the best strategy is to take the first 50 offers no matter what and then take only $5 offers. If the ticket exchanger offers $1 for each of your tickets and then halts the trading, your regret ratio would be 1.8 ($90 divided by $50). If the exchanger initially offers $1 but then switches to $5, the regret ratio would still be 1.8 ($450 divided by $250). If the possible offers are $1 and $1 million, take the first 45 offers no matter what and then wait for $1-million offers. This strategy yields a regret ratio of 2.
The basic strategy is to take the first x offers no matter what they are and then take only $5 offers after that. We are told that the number of tickets is 90, but let¿s solve this symbolically for a number T and then specialize to T = 90. If all offers are $1, the oracle will get $T, so the regret ratio will be T/x. If there are at least T $5 offers, but they come after the first x have been given out, then the oracle will get $5T, making the regret ratio 5T/(x + 5(T ¿ x)).