This game has taught me something. I get more enjoyment than I should out of watching a random variable go up and down, and probably should avoid gambling. :)
Nice work, congrats! Looks fun and useful, better than the calibration apps I've seen so far (including one I made, that used confidence intervals - I had a proper scoring rule too!)
My score:
Current score: 3.544 after 10 plays, for an average score per play of 0.354.
If it's worth saying, but not worth its own post (even in Discussion), then it goes here.