In the final major calculation of my Math Hulk series, we look at the broodlord verses the powersword sergeant. This is a complicated calculation to do exactly and to develop a decision tree for especially when both parry and guard are active. To review the rules, the broodlord has mighty blow which allows him to roll 3 dice and add his high and low to get his combat value. Parry allows the powersword sergeant to force the broodlord to reroll his highest die while guard allows the sergeant to reroll his own attack die. The order is to roll the dice then decide whether to parry see that result and then decide to guard or not.
The reason this gets complicated is that fact that having the broodlord reroll an attack die depends on what all three of his dice currently are. The former high die being rerolled can now become either the high die, rejected die or the low die. For example if the broodlord currently has 7 with a 6, 6, and 1 rerolling the high die does nothing since he cannot roll higher than 6 or lower than 1 so this die just becomes the rejected one. If he has a 7 with a 5, 5, 2 then 1/6 of the time he will get to 8 (6, 5, 2), 4/6 he will stay at 7 (5, 5-2, 2) and 1/6 he will go down to 6 (5, 2, 1). Since when to reroll also depends on what the sergeant has (never reroll wins and sometimes reroll ties) just using parry of the Broodlord involves about 330 possible combinations.
To make determining whether to parry easier on myself I tried to optimize the ratio of wins to loses for the sergeant. Of course without Guard you parry every time you lose regardless of whether it can help. This just leaves determining whether to parry in ties. If you always hold a tie as the baseline you get 18.85% win, 18.90% tie, and 62.24% lose. While this seems pretty bad remember that the normal powerfist terminator is at win 5.56%, tie 5.25 %, and die 88.19%. So you are doing 3 times better. Since you are at pretty low survival chances for each successive combat using parry in some ties might give you a better chance of killing the broodlord now compared to another attack. Being aggressive in trying to kill the broodlord from ties yields win 23.97%, tie 11.93, and lose 64.09%. The first rule is never reroll a double high die with a 1 like 6, 6, 1 or 3, 3, 1 since you can gain nothing and just increase the chances of dying. Other than that reroll all ties on 7 and 6. For ties on 5 do not reroll a 3,3,2 tie or a 2,2,2 for 4. Never rerolls ties on 3 or 2 with parry. These little things get very complicated but make small changes to the ratios. The basic rule to fight by with just parry is look at his results if 2 of the 6 outcomes on the rerolled die gets you a win have him reroll less than that probably hold the tie.
Now on to parry and guard, if you take the simplest approach which starts with holding all ties and then rerolling all loses with parry and then if you are still losing use guard the numbers are 26.35% win, 25.82% tie, and 47.83% loss. While this is even better than just using parry it is far from optimal from a killing the broodlord point of view. Fighting for ultimate survival where you reroll no ties and do not use parry in cases of the Broodlord starting with a pretty low score yields 29.08% win, 23.67% tie, and 47.27% loss. Going for the highest win to loss ratio gets 34.29% wins, 16.20% ties, and 49.51% loss. You are losing about 2% more but also winning 5% more. This result is from not parrying broodlord total results of 4 or less, essential only parrying results of 5 if he has a 1, and not parrying totals less than seven with a double high and a 1. There are a couple of more little adjustments but they are all in the margins. On the guard side it is rerolling 2-4 results on a tie but holding 5-7. You can get a better kill percent by rerolling on the 5 but the death percent goes up enough that the ratio is worse.
These results make the power sword sergeant on guard essentially as good at fighting the broodlord as the thunderhammer sergeant so about as good as you could expect as the broodlord is the stealers big buy and should not go down easy to anyone in close combat.
Now that the main series is done I will try to get all the results plotted up in a final summary post. Might go back and add some additional little things to earlier posts also.