Assume all twos are made with probability, p and all threes regardless of situation are made with probability, q.

Now assume that you are down 3 points with under 20 seconds left and again ignoring offensive rebounds, and assuming one wins in overtime 50 percent of the time and is risk neutral. There is only time for you to have at most two possessions. Assume that the opposing teams shoots foul shots at a rate of 0.75. If you take and miss the two the game is over.

To win if one shoots a two, you must: make the two then foul, the opposing team gets two foul shots, then make a three or two to send the game into overtime or win in regulation (depending on how many free throws were made).

If you miss the three the game is over. If you make the three, the other team scores on the next possession and wins with probability .

How much more frequently does a 2 point shot have to be made than a 3 point shot for the 2 point shot to be the right shot to take?