Saturday, 3 November 2012

The Theory of Lucky Dice Rolls

What happens when you roll dice. You get a random result. Actually no. It's fractal.

 Everyone knows that for shooting by Imperial Guard with ballistic skill of 3 requiring a 4, 5 or 6 to means that 50% of shots should hit target. Why then can Imperial Guard shooting be so much worse than that? Perhaps you don't find that. Perhaps for you IG shooting is better than that 50-50 chance to hit. But dice rolls average out over 30 - 50 rolls so bad or good turns occur, unless the IG units are massed up.

Here is an experiment. Take 12 GW dice and roll them. As each number has an equal chance of occurring there should be 2x 1, 2x 2, 2x 3, 2x 4, 2x 5 and 2 x6. Six shots out of twelve should hit with for the IG. What did you get. Repeat the dice rolls and see what occurs.

Here is a set of genuine dice rolls done here, nothing has been made up:

Dice Value Roll 1 Roll 2 Roll 3
1 - - 1
2 3 5 4
3 3 2 2
4 4 2 4
5 - 2 -
6 2 1 1

It looks reasonably OK for IG shooting with 6 hits  for roll 1, 5 for rolls 2 and 3. But if these were saving throws with an expectation of 4 saves for 12 dice rolls it does not look so good with only 2 and 1 saves for rolls 1 and 3, and 3 saves for roll 2. Why is this.

The thing is that these rolls are not "random". Dice rolls are a self organising system. This means that the number of dice in the cup or hand, the force with which they are rolled, the surface they roll across, including anything they bounce off, the material the dice are made of, any wear and tear on the dice, the number of times they are shaken etc all go to make the result. Self organising systems make for a fractal pattern of numbers. Yes, numbers will trend to the expected over a large number of rolls but for rolling a small number of dice the fractal patterns of a self organising system predominate making for those "lucky" dice rolls. Its not luck, its not random its just unpredictable because the factors involved in rolling the dice are difficult to control.

What this means for the game is that units with small numbers of dice to roll are less dependable in the game. And if you can, roll as many dice as you can simultaneously to try to reduce fractal results and get close to the expected result.

If you like to gamble for a "lucky result" roll as few dice simultaneously as you can. Lady luck has no memory so the probability of getting any particular result depends completely on the circumstances each time - number of dice, amount of energy in the rolling, wear on the dice and surface rolled every time a dice is rolled 

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