Jim Holtzhauer Is Playing the Tables at Vegas

Essay

Jim Holtzhauer is playing the tables at Vegas. He currently has $10,000, which I will denote as 10K in order to keep things simple. He is looking at a bet where with ½ chance he can win 6K while with ½ chance he will lose 2K. Jim's utility of wealth function is given by U(W) = (W)^2. (U(W) is equal to the W Squared). Should Jim accept this gamble? If yes, why? If not, then why not? Does Jim have a certainty equivalent in this case? If yes, then what is this amount? Briefly explain whether this will imply Jim actually giving up money or Jim having to be given extra money in order to forego the gamble.