So I spent a bit of time along with Amazing Ampharos on the whole algorithm thing for game one (basically both players rank their stages from most to least preferred and we figure out the best stage)

He suggested a very simple formula:

P1Rank + P2Rank + abs(P1Rank -P2Rank)

Both players only need to rank half of the stages plus 1 (or plus 0.5 if odd), since anything after that has a 0% chance of winning mathematically. Any stage that isn't present in both lists is immediately discarded. If two or more stages are tied, choose randomly.

This seems to work pretty well, although there are some possibly problematic scenarios, for example:

Our stages are: A B C D E F G H I

P1: ABCDE(IHGF)
P2: EFGHA(IDCB)

In this case, the result is a tie between A and E. Choosing randomly would give one player a pretty sizeable advantage. So is I the better pick here?

However! I decided to compare this to regular striking, and simply assumed that the players would strike starting from the absolute bottom of their lists (which makes sense).

P1 strikes F, P2 strikes B&C, P1 strikes G&H, P2 strikes D&I, P1 strikes E, and the winning stage is A.

Essentially though it comes down to a gamble depending on who goes first and the order of the last four stages. Basically even with regular striking, the result is still a toss-up between A and E. The only way you could get a stage in the last four spots was if one of the players changed their mind during the striking process and decided to strike something higher up.

This all leads me to believe that the algorithm is essentially equivalent to 1-2-1 striking, with the important distinction of being completely double-blind. This means that no information is exchanged during the process, so there's less room for strategy.

So going back to the formula, if we decide that this isn't the most preferable outcome, and a stage such as I is a better pick, then we can modify the formula to give more 'weight' to the second part (the 'distance' part), thus giving I a higher score.

Wether this is a good decision or not I don't really know, but we should keep in mind that we'd potentially be looking at a system which is actually *more* effective than regular striking (if the changes are actually beneficial).

Anyways, the formula can actually be simplified down to a degree. A stage's 'score' is essentially its lowest rank between the two lists, multiplied by 2. This means that all you need to do to figure out the winning stage, is look at the stage with the highest 'lowest ranking'.

So to recap:

1) Both players rank their preferred stages (until they've covered > half of the stagelist)
2) Remove stages that aren't present in both lists
3) Pick the stage with the highest 'lowest ranking' (and random if there's a tie)

This would definitely require pen & paper if done without an app, but it has the added benefit of being additive rather than subtractive (compared to regular striking).