One day, NAME_1 walks into a lottery shop. She noticed that the shop offers a special kind of scratch-and-win lottery game: there is only one grand prize among all the 4 lottery tickets. By paying 1 dollar for each trial, she gets to scratch a piece of lottery ticket to try out her luck. Say, if she gets the prize on the first trial, she may collect it, if not, she may proceed the trials with the same cost but with 3 choices left, and this is repeated until she gets the prize (assuming that she desperately wants the prize so that she won’t quit midway). The problem is, she has to evaluate: how much must the grand prize be, at least, for her to expect a break-even (no net gain nor loss) throughout the game? Note that she is allowed to play the game herself, andtry out all the possible tickets by paying 1 dollar for each trial; the ”net gain” can be interpreted as the difference in grand prize and the expected trials. Wrap the entire output in JSON format.
user