tirsdag 24. oktober 2023

Going first advantage of 57%: The math

The results from WTC show that the first player has a 57% chance to win the game. On average any player will win the game 50% of the time, since ties are close to impossible. If it's possible to get a tie, I am ignoring it for this calculation.

The math

The chance that this result happened by chance can be computed using the Binominal Test - you can try it here for yourself: Easy Binomial Test Calculator (socscistatistics.com)

There were 292 games played (n), 166 (or 167) games were won by the first player (K), and the chance of winning a game (p) is 0.5. Inserting the numbers show that the chance of the first player getting at least this many wins by chance is .011, or 1.1%. So we can conclude that it is almost certain that the first player win rate is due to going first being better, and not due to random chance.

I am not a professional statistician, but this seems rather straight forward - feel free to inform me if the calculation is wrong.

Went second against Lucant, pushed off scenario


Every single player I have talked to during the WTC agrees that going first is a huge advantage. One just said "don't even look at the table or matchup, always go first". The problem is as follows:

Most armies can run units (almost) to the middle of the table turn 1, leaving the opponent the choice of not grabbing much - if any - table space, or getting alphaed top of 2. Both are bad. 

Many armies can run, then defensive / control feat plus run, scoring zones on their side while leaving the second player scrambling to not lose on points top of 3.

I had several matches at the WTC where I knew that if I won the die roll I had good chances, and if I lost I was already in trouble. And that was exactly what happened, if I went first I had a fairly good time (even if I lost - I am not all that good), but going second was brutally hard.

Going first against Borka

I even had one game where I had to move AD units backwards bottom of 1 to not get charged. It’s ridiculous, Steamroller has to be fixed for Mk4. Mk4 is otherwise amazing though, best edition ever, miniatures are awesome, keep it coming.

Just fix Steamroller, please!


onsdag 1. februar 2023

Kraye, Pincushion, and Trencher Express Teams: The math

I did a little math to see whether Pincushion helps to land Express Team critical knockdowns. I was expecting it to be slightly better, but was a bit surprised to see how much better!

AnyDice code below. It will check if the 3 highest dice hit the target number, and then whether any of these 3 dice show the same face.

function: crit ROLL:s drop lowest at least TARGET:n {
  result: {1,2,3}@ROLL >= TARGET &
          (1@ROLL = 2@ROLL | 1@ROLL = 3@ROLL | 2@ROLL = 3@ROLL)

output [crit 4d6 drop lowest at least 12]

This gives the following chances of hitting the KD on boosted shots using Pincushion (4D6-DL-C), and without Pincushion (3D6-C):

Target  4D6-DL-C  3D6
 4      53.63%    43.98%
 5      53.32%    42.59%
 6      52.55%    39.81%
 7      51.85%    37.96%
 8      49.85%    33.80%
 9      46.91%    29.63%
10      44.52%    26.39%
11      39.74%    22.22%
12      34.80%    18.06%
13      30.25%    14.81%
14      24.38%    10.65%
15      16.67%     6.48%
16      13.04%     4.63%
17       5.79%     1.85%
18       1.62%     0.46%