This is a problem about poker players. Let's make some assump- tions: (i) Every professional poker player uses an identical strategy and will make the same play in every situation. (ii) Every poker tournament has n players and each player plays with d dollars, so that there are two outcomes for an individual player in a tournament: either they lose d dollars or they win (n 1)d dollars (that is, they walk away with nd dollars, but they had to put in d dollars to play, so their winnings are (n 1)d dollars). (iii) No matter the outcome of the tournament, a player must pay a fee to the casino of f dollars to play. Under these circumstances, explain (using probability theory) why it would be for a professional poker player to make money only playing tournaments consisting of other professional poker players. (And hence why they need to play against amateurs!) This is a problem about poker players. Let's make some assump- tions: (i) Every professional poker player uses an identical strategy and will make the same play in every situation. (ii) Every poker tournament has n players and each player plays with d dollars, so that there are two outcomes for an individual player in a tournament: either they lose d dollars or they win (n 1)d dollars (that is, they walk away with nd dollars, but they had to put in d dollars to play, so their winnings are (n 1)d dollars). (iii) No matter the outcome of the tournament, a player must pay a fee to the casino of f dollars to play. Under these circumstances, explain (using probability theory) why it would be for a professional poker player to make money only playing tournaments consisting of other professional poker players. (And hence why they need to play against amateurs!)