From a row of integers 0,1,2,…1023,1024 A erases 512 numbers of his choice, - following this B erases 256 numbers of B’s choice.
Step 3: A erases 128 numbers, etc…
So at Step 10 player B chooses one of the 3 remaining numbers and erases it to define the amount of (dollars, pounds, euros, marbles) to be paid by A i.e. the difference between the two remaining numbers.
Clearly, A chooses a strategy to minimize this amount while
his opponent wants to maximize the outcome.
Assuming both follow the best strategy (Which?),
what will be the outcome of the game?