Part 1:

Rewrite “Training Skirmishes” as follows:

As a Daily Action, the Allfather may announce that a Skirmish has taken place in perperation for the Final Battle.

A Skirmish is announced by first rolling DICEX in the GNDT, where “X” is the number of numerical Einherjar Statistics, and where the roll has a comment of “Skirmish Check”. The number rolled shall be used to determine which of the numerical Einherjar Statistics is relevant to the Skirmish, by counting down from the top of the list in the “Statistics” rule - this Statistic is the “Challenged” Statistic.

Each Einherjar who has a Challenged Statistic that is not equal to zero will have their Skirmish Rating for the Skirmish calculated by the Allfather.  Each Einherjar’s Skirmish Rating is calculated as follows:
*  If the Einherjar’s Challenged Statistic is a positive number (X), then the Einherjar’s Skirmish Rating for the Skirmish is equal to XDICE10.
*  If the Einherjar’s Challenged Statistic is a negative number -(X), then the Einherjar’s Skirmish Rating for the Skirmish is equal to ((XDICE10) minus (*** times X).
By way of example, if an Einherjar’s Challenged Statistic is +6, then the Einherjar’s Skirmish Rating for the Skirmish is 6DICE10; and if an Einherjar’s Challenged Statistic is (-6), then the Einherjar’s Skirmish Rating for the Skirmish is (6DICE10) - (6 times ***).

The Skirmish Rating of each Einherjar who belongs to Fólkvangr who does not have a Challenged Statistic equal to 0 shall be calculated in the same manner.

Einherjar who have a Challenged Statistic of 0 are deemed not to have participated in the Skirmish.

If an Einherjar belonging to Fólkvangr has the highest Skirmish Rating among all Einherjar who participated in the Skirmish, then the Skirmish is lost, all Valkyries lose 20 Acorns, and the single Einherjar currently in Fólkvangr with the lowest Skirmish Rating who participated in the Skirmish (if one exists) has fallen, and is transferred to the “Unrecruited Einherjar” list to ensure fairness in future training exercises.

If an Einherjar belonging to an Active Valkyrie has the highest Skirmish Rating among all Einherjar who participated in the Skirmish, then that Valkyrie is triumphant in that Skirmish and receives 10 Acorns, and the Einherjar belonging to an Active Valkyrie who had the lowest Skirmish Rating among all Einherjar who participated in the Skirmish has fallen, and is transferred to Fólkvangr’s section of the Einherjar page to ensure fairness in future training exercises.

If two or more Einherjar tie for the highest or for the lowest Skirmish Rating among Einherjar who participated in the Skirmish, those two Einherjar are deemed to be “Locked in Single Combat”.  The Allfather shall re-calculate the Skirmish Ratings of the Einherjar who are Locked in Single Combat, and the Einherjar with the highest re-calculated Skirmish Rating is deemed to have the highest Skirmish Rating (if before the re-calculation they were tied for highest) or to not have the lowest Skirmish Rating (if before the re-calculation they were tied for lowest), and the Einherjar with the lowest re-calculated Skirmish Rating is deemed (or also deemed, in the case of an Einherjar who was tied for the highest Skirmish Rating before the re-calculation) to have fallen and shall be transferred to Fólkvangr’s section of the Einherjar page to ensure fairness in future training exercises.

After having calculated these results and made the changes required, the Allfather should post a blog entry summarising them.

The statistic “Tinkering” is ignored for purposes of Skirmishes.

Part 2:
If Hix votes in favor of this Proposal, then replace *** with whatever numerical value Hix includes in his vote.  If Hix does not vote in favor of this Proposal, then replace *** with 6.

Explanatory notes:
- Under the current ruleset, the Valkyrie whose Einherjar sum to the highest Challenged Statistic wins, without any element of chance.  This adds the element of chance—in theory, an Einherjar with a very low (or even negative) Challenged Statistic could sometimes win.
- Under this proposal, Skirmish Ratings are calculated for each _Einherjar_ who participates in the Skirmish, not for each _Valkyrie_.  Owning more Einherjar can give a Valkyrie a higher chance that an Einherjar owned by that Valkyrie will win, but having a bigger team is not an absolute advantage. 
- Einherjar who have a Challenged Statistic of zero do not participate inn the Skirmish—this cuts down on the number of dice that Hix has to roll.
- An Einherjar who ties for first can still lose the “Single Combat” and become Fallen in the skirmish.
- With respect to rolling the dice, I believe that the expected value of XDICE10-6X is a negative number (I left a placeholder so that Hix can tweak this).  The idea is that with respect to an Einherjar with a low negative Challenged Statistic, rolling more dice should result in a lower number, but it should still be possible in theory for an Einherjar with a Challenged Statistic of (-10) to have a Skirmish Value of as high as (10DICE10 -10 times (six?)), or 40, which could possibly be enough to win.