Personally, from experience, I think it runs like the NBA draft lottery:
View attachment 19079
There are a total of 9 prizes on a fresh board but 27 opportunities. If each opportunity is a ping pong ball, the following number of ping pong balls would be dropped into a bowl:
1 - Guard Post Selection Kit
2 - Goods From A Previous Age
2 - SoK Fragment
2 - Mass Self-Aid Kit
4 - Palm Tree
4 - 10% Supply Boost
4 - Large Supplies
4 - Medium Supplies
4 - Medals
You now draw a ping pong ball and have a 1:27 chance at the grand prize. On the board above, a Medals ball was drawn so the remaining balls are now:
1 - Guard Post Selection Kit
2 - Goods From A Previous Age
2 - SoK Fragment
2 - Mass Self-Aid Kit
4 - Palm Tree
4 - 10% Supply Boost
4 - Large Supplies
4 - Medium Supplies
3 - Medals
Which gives you a 1:26 chance at the grand prize.