text: You will encounter a series of gambling problems where you have to select between two options.
  You can select an option by pressing the corresponding key.
  For some problems, you are told the points you received and missed out on after each selection, while for others this information is suppressed.
  In cases where the probabilities are unknown, they sum up to one and remain constant within a problem.
  
  Option Y delivers 48.0 points with 75.0% chance, or -40.0 points with 25.0% chance.
  Option Z delivers 27.0 points with 99.0% chance, 54.5 points with 0.5% chance, or 55.5 points with 0.5% chance.
  You press <<Z>>. You receive 27.0 points by selecting this option. You would have received 48.0 points had you chosen the other option.
  You press <<Y>>. You receive 48.0 points by selecting this option. You would have received 27.0 points had you chosen the other option.
  You press <<Y>>. You receive 48.0 points by selecting this option. You would have received 27.0 points had you chosen the other option.
  You press <<Z>>. You receive 27.0 points by selecting this option. You would have received -40.0 points had you chosen the other option.
  You press <<Z>>. You receive 27.0 points by selecting this option. You would have received 48.0 points had you chosen the other option.
  
  Option Y delivers either 23.0 points with 10.0% chance, or 23.0 points with 90.0% chance.
  Option Z delivers either -22.0 points with unknown chance, or 83.0 points with unknown chance.
  You press <<Z>>. You receive -22.0 points by selecting this option. You would have received 23.0 points had you chosen the other option.
  You press <<Y>>. You receive 23.0 points by selecting this option. You would have received -22.0 points had you chosen the other option.
  You press <<Y>>. You receive 23.0 points by selecting this option. You would have received 83.0 points had you chosen the other option.
  You press <<Z>>. You receive 83.0 points by selecting this option. You would have received 23.0 points had you chosen the other option.
  You press <<Z>>. You receive -22.0 points by selecting this option. You would have received 23.0 points had you chosen the other option.
  
  Option Y delivers 72.0 points with 20.0% chance, or -18.0 points with 80.0% chance.
  Option Z delivers -25.0 points with 60.0% chance, or 30.0 points with 40.0% chance.
  You press <<Y>>. You receive 72.0 points by selecting this option. You would have received -25.0 points had you chosen the other option.
  You press <<Y>>. You receive -18.0 points by selecting this option. You would have received 30.0 points had you chosen the other option.
  You press <<Z>>. You receive -25.0 points by selecting this option. You would have received -18.0 points had you chosen the other option.
  You press <<Z>>. You receive -25.0 points by selecting this option. You would have received -18.0 points had you chosen the other option.
  You press <<Y>>. You receive -18.0 points by selecting this option. You would have received -25.0 points had you chosen the other option.
  
  Option Y delivers 17.0 points with 95.0% chance, or 8.0 points with 5.0% chance.
  Option Z delivers 17.0 points with 99.0% chance, 37.5 points with 0.0078% chance, 38.5 points with 0.0547% chance, 39.5 points with 0.1641% chance, 40.5 points with 0.2734% chance, 41.5 points with 0.2734% chance, 42.5 points with 0.1641% chance, 43.5 points with 0.0547% chance, or 44.5 points with 0.0078% chance.
  You press <<Y>>. You receive 17.0 points by selecting this option. You would have received 17.0 points had you chosen the other option.
  You press <<Z>>. You receive 17.0 points by selecting this option. You would have received 17.0 points had you chosen the other option.
  You press <<Y>>. You receive 17.0 points by selecting this option. You would have received 17.0 points had you chosen the other option.
  You press <<Y>>. You receive 17.0 points by selecting this option. You would have received 17.0 points had you chosen the other option.
  You press <<Z>>. You receive 17.0 points by selecting this option. You would have received 17.0 points had you chosen the other option.
  
  Option Y delivers 25.0 points with 20.0% chance, or 18.0 points with 80.0% chance.
  Option Z delivers 29.0 points with 75.0% chance, or 38.0 points with 25.0% chance.
  You press <<Z>>. You receive 29.0 points by selecting this option. You would have received 18.0 points had you chosen the other option.
  You press <<Y>>. You receive 18.0 points by selecting this option. You would have received 29.0 points had you chosen the other option.
  You press <<Z>>. You receive 38.0 points by selecting this option. You would have received 18.0 points had you chosen the other option.
  You press <<Z>>. You receive 38.0 points by selecting this option. You would have received 18.0 points had you chosen the other option.
  You press <<Z>>. You receive 29.0 points by selecting this option. You would have received 18.0 points had you chosen the other option.
  
  Option Y delivers -10.0 points with 100.0% chance, or -10.0 points with 0.0% chance.
  Option Z delivers -19.0 points with 75.0% chance, or -17.0 points with 25.0% chance.
  You press <<Z>>. You receive -17.0 points by selecting this option. You would have received -10.0 points had you chosen the other option.
  You press <<Y>>. You receive -10.0 points by selecting this option. You would have received -19.0 points had you chosen the other option.
  You press <<Y>>. You receive -10.0 points by selecting this option. You would have received -19.0 points had you chosen the other option.
  You press <<Y>>. You receive -10.0 points by selecting this option. You would have received -19.0 points had you chosen the other option.
  You press <<Y>>. You receive -10.0 points by selecting this option. You would have received -19.0 points had you chosen the other option.
  
  Option Y delivers 28.0 points with 100.0% chance, or 28.0 points with 0.0% chance.
  Option Z delivers 27.0 points with 10.0% chance, or 32.0 points with 90.0% chance.
  You press <<Y>>.
  You press <<Z>>.
  You press <<Z>>.
  You press <<Y>>.
  You press <<Y>>.
  
  Option Y delivers -3.0 points with 100.0% chance, or -3.0 points with 0.0% chance.
  Option Z delivers 1.0 points with 99.0% chance, 60.0 points with 0.5% chance, 62.0 points with 0.25% chance, 66.0 points with 0.125% chance, 74.0 points with 0.0625% chance, 90.0 points with 0.0312% chance, 122.0 points with 0.0156% chance, or 186.0 points with 0.0156% chance.
  You press <<Z>>.
  You press <<Z>>.
  You press <<Y>>.
  You press <<Z>>.
  You press <<Y>>.
  
  Option Y delivers 10.0 points with 100.0% chance, or 10.0 points with 0.0% chance.
  Option Z delivers -4.0 points with 75.0% chance, or 33.0 points with 25.0% chance.
  You press <<Z>>. You receive -4.0 points by selecting this option. You would have received 10.0 points had you chosen the other option.
  You press <<Y>>. You receive 10.0 points by selecting this option. You would have received -4.0 points had you chosen the other option.
  You press <<Y>>. You receive 10.0 points by selecting this option. You would have received -4.0 points had you chosen the other option.
  You press <<Y>>. You receive 10.0 points by selecting this option. You would have received -4.0 points had you chosen the other option.
  You press <<Y>>. You receive 10.0 points by selecting this option. You would have received -4.0 points had you chosen the other option.
  
  Option Y delivers 51.0 points with 25.0% chance, or -21.0 points with 75.0% chance.
  Option Z delivers -28.0 points with 40.0% chance, 11.0 points with 30.0% chance, 9.0 points with 15.0% chance, 5.0 points with 7.5% chance, -3.0 points with 3.75% chance, or -19.0 points with 3.75% chance.
  You press <<Y>>. You receive -21.0 points by selecting this option. You would have received 11.0 points had you chosen the other option.
  You press <<Z>>. You receive -28.0 points by selecting this option. You would have received -21.0 points had you chosen the other option.
  You press <<Y>>. You receive -21.0 points by selecting this option. You would have received 5.0 points had you chosen the other option.
  You press <<Z>>. You receive -28.0 points by selecting this option. You would have received -21.0 points had you chosen the other option.
  You press <<Z>>. You receive 5.0 points by selecting this option. You would have received -21.0 points had you chosen the other option.
  
  Option Y delivers 34.0 points with 40.0% chance, or -6.0 points with 60.0% chance.
  Option Z delivers 10.0 points with 95.0% chance, 76.0 points with 2.5% chance, or 78.0 points with 2.5% chance.
  You press <<Z>>. You receive 10.0 points by selecting this option. You would have received -6.0 points had you chosen the other option.
  You press <<Z>>. You receive 10.0 points by selecting this option. You would have received -6.0 points had you chosen the other option.
  You press <<Z>>. You receive 10.0 points by selecting this option. You would have received -6.0 points had you chosen the other option.
  You press <<Z>>. You receive 10.0 points by selecting this option. You would have received -6.0 points had you chosen the other option.
  You press <<Z>>. You receive 10.0 points by selecting this option. You would have received 34.0 points had you chosen the other option.
  
  Option Y delivers either 2.0 points with 10.0% chance, or -8.0 points with 90.0% chance.
  Option Z delivers either -34.0 points with unknown chance, 15.0 points with unknown chance, 13.0 points with unknown chance, 9.0 points with unknown chance, 1.0 points with unknown chance, or -15.0 points with unknown chance.
  You press <<Z>>. You receive -34.0 points by selecting this option. You would have received -8.0 points had you chosen the other option.
  You press <<Y>>. You receive -8.0 points by selecting this option. You would have received -34.0 points had you chosen the other option.
  You press <<Y>>. You receive -8.0 points by selecting this option. You would have received -34.0 points had you chosen the other option.
  You press <<Y>>. You receive -8.0 points by selecting this option. You would have received 13.0 points had you chosen the other option.
  You press <<Y>>. You receive -8.0 points by selecting this option. You would have received 15.0 points had you chosen the other option.
  
  Option Y delivers -6.0 points with 100.0% chance, or -6.0 points with 0.0% chance.
  Option Z delivers -5.0 points with 90.0% chance, or 3.0 points with 10.0% chance.
  You press <<Y>>.
  You press <<Z>>.
  You press <<Y>>.
  You press <<Y>>.
  You press <<Y>>.
  
  Option Y delivers 30.0 points with 60.0% chance, or 23.0 points with 40.0% chance.
  Option Z delivers 31.0 points with 5.0% chance, or 42.0 points with 95.0% chance.
  You press <<Z>>.
  You press <<Z>>.
  You press <<Z>>.
  You press <<Y>>.
  You press <<Y>>.
  
  Option Y delivers 24.0 points with 100.0% chance, or 24.0 points with 0.0% chance.
  Option Z delivers 18.0 points with 75.0% chance, 84.5 points with 0.1953% chance, 85.5 points with 1.3672% chance, 86.5 points with 4.1016% chance, 87.5 points with 6.8359% chance, 88.5 points with 6.8359% chance, 89.5 points with 4.1016% chance, 90.5 points with 1.3672% chance, or 91.5 points with 0.1953% chance.
  You press <<Z>>. You receive 18.0 points by selecting this option. You would have received 24.0 points had you chosen the other option.
  You press <<Y>>. You receive 24.0 points by selecting this option. You would have received 18.0 points had you chosen the other option.
  You press <<Y>>. You receive 24.0 points by selecting this option. You would have received 18.0 points had you chosen the other option.
  You press <<Y>>. You receive 24.0 points by selecting this option. You would have received 88.5 points had you chosen the other option.
  You press <<Z>>. You receive 85.5 points by selecting this option. You would have received 24.0 points had you chosen the other option.
  
  Option Y delivers either 17.0 points with 100.0% chance, or 17.0 points with 0.0% chance.
  Option Z delivers either 17.0 points with unknown chance, 46.0 points with unknown chance, 44.0 points with unknown chance, 40.0 points with unknown chance, 32.0 points with unknown chance, 16.0 points with unknown chance, or -16.0 points with unknown chance.
  You press <<Z>>. You receive 17.0 points by selecting this option. You would have received 17.0 points had you chosen the other option.
  You press <<Y>>. You receive 17.0 points by selecting this option. You would have received 17.0 points had you chosen the other option.
  You press <<Z>>. You receive 17.0 points by selecting this option. You would have received 17.0 points had you chosen the other option.
  You press <<Y>>. You receive 17.0 points by selecting this option. You would have received 17.0 points had you chosen the other option.
  You press <<Z>>. You receive 17.0 points by selecting this option. You would have received 17.0 points had you chosen the other option.
  
  Option Y delivers either -4.0 points with 100.0% chance, or -4.0 points with 0.0% chance.
  Option Z delivers either -26.0 points with unknown chance, or 82.0 points with unknown chance.
  You press <<Y>>. You receive -4.0 points by selecting this option. You would have received -26.0 points had you chosen the other option.
  You press <<Y>>. You receive -4.0 points by selecting this option. You would have received -26.0 points had you chosen the other option.
  You press <<Y>>. You receive -4.0 points by selecting this option. You would have received -26.0 points had you chosen the other option.
  You press <<Y>>. You receive -4.0 points by selecting this option. You would have received -26.0 points had you chosen the other option.
  You press <<Y>>. You receive -4.0 points by selecting this option. You would have received -26.0 points had you chosen the other option.
  
  Option Y delivers either 28.0 points with 100.0% chance, or 28.0 points with 0.0% chance.
  Option Z delivers either 34.0 points with unknown chance, 40.5 points with unknown chance, 41.5 points with unknown chance, 42.5 points with unknown chance, 43.5 points with unknown chance, 44.5 points with unknown chance, or 45.5 points with unknown chance.
  You press <<Y>>. You receive 28.0 points by selecting this option. You would have received 34.0 points had you chosen the other option.
  You press <<Z>>. You receive 34.0 points by selecting this option. You would have received 28.0 points had you chosen the other option.
  You press <<Z>>. You receive 34.0 points by selecting this option. You would have received 28.0 points had you chosen the other option.
  You press <<Z>>. You receive 34.0 points by selecting this option. You would have received 28.0 points had you chosen the other option.
  You press <<Z>>. You receive 34.0 points by selecting this option. You would have received 28.0 points had you chosen the other option.
  
  Option Y delivers 4.0 points with 5.0% chance, or -2.0 points with 95.0% chance.
  Option Z delivers -28.0 points with 10.0% chance, or 5.0 points with 90.0% chance.
  You press <<Y>>. You receive -2.0 points by selecting this option. You would have received 5.0 points had you chosen the other option.
  You press <<Z>>. You receive 5.0 points by selecting this option. You would have received -2.0 points had you chosen the other option.
  You press <<Z>>. You receive 5.0 points by selecting this option. You would have received -2.0 points had you chosen the other option.
  You press <<Z>>. You receive 5.0 points by selecting this option. You would have received -2.0 points had you chosen the other option.
  You press <<Z>>. You receive -28.0 points by selecting this option. You would have received -2.0 points had you chosen the other option.
  
  Option Y delivers 40.0 points with 50.0% chance, or -42.0 points with 50.0% chance.
  Option Z delivers -20.0 points with 75.0% chance, or 14.0 points with 25.0% chance.
  You press <<Z>>. You receive -20.0 points by selecting this option. You would have received -42.0 points had you chosen the other option.
  You press <<Z>>. You receive -20.0 points by selecting this option. You would have received 40.0 points had you chosen the other option.
  You press <<Y>>. You receive -42.0 points by selecting this option. You would have received -20.0 points had you chosen the other option.
  You press <<Z>>. You receive 14.0 points by selecting this option. You would have received 40.0 points had you chosen the other option.
  You press <<Y>>. You receive -42.0 points by selecting this option. You would have received -20.0 points had you chosen the other option.