UNDERDOG

The UNDERDOG adds the total number of foreign colonies (other than their own) to their attack total BUT only for aliens that have more foreign colonies than the UNDERDOG. For example, take aliens A, B, C, U (underdog). A has 1 foreign colon...y, B has 3 foreign colonies, C has 4 foreign colonies, U has 2 foreign colonies. Hence, U could add 7 (B + C) to his/her attack total.

SQUABBLER

The SQUABBLER. If invited to ally - if both players negotiate then the SQUABBLER may use his/her power to quash the deal. If only one player negotiates and the SQUABBLER has allied with them, the SQUABBLER may use his/her power to cancel the negotiating players compensation.

HERMIT (or PRIDE) - not sure on name

You have the power of one. Use at reveal stage. If you have not invited allies, roll a die and add the value to your attack total. If you HAVE invited allies, subtract the die roll from your attack total. (Yes this introduces a new device called a die into the game - radical).

MATHEMATICIAN.

During the Planning phase the Mathematician may use his/her power by calling one of "add", subtract", "mutiply", "divide". For example, if Mathematician calls "add" then the digits on the encounter cards are added (e.g. 09 = 0+ 9 = 9. 12 = 1 + 2 = 3 etc.). If "subtract" then 40 becomes 4 - 0 = 4. 11 becomes 1 - 1 = 0 etc. If "multiply" then 06 becomes 0 x 6 = 0. 23 becomes 2 x 3 = 6 etc. If "divide" (round up), 23 becomes 2 / 3 = 1 (after round up), 0 / 9 = 0, 4 / 0 = negotiate, 1 / 0 = negotiate. (Alterntive rule is that diveide by 0 becomes infinity in which case if both encounter cards result in infinity then defender wins becaus of same result irrespective of number of ships because any operation on infinity is still infinity).

This power applies to both main players' encounter cards.

Edit to Mathematicican - for those who don't like "divide" - leave it out (or as a variant) - it could be problematic and confusing. So, that reduces Mathematician to "add", "subtract", "multiply". All of those are fairly simple operations.

Kill Hermit/Pride (use of die is too radical).

So that leaves us with UNDERDOG, SQUABBLER, MATHEMATICIAN (add, subract, multiply).