I am not actually.

You are talking about the idea that if you flip a coin. No matter how many times you flip a coin, you always have a fifty-fifty chance of heads or tails.

This concept, like all statistics, requires a large sample to be true. When you have at most 5 or 6 dice when all are rolled, it is not a large enough sample for what you are saying to apply.

Depending on which side of 4+ the save falls, the probability will change. If you make a 6+, it is a 1 in 6 chance. If you have to re-roll it, you still have a 1 in 6 chance. If you are only rolling 4 dice, odds are not in you favor.

However, this is not about statistics, it is about rules and when rules apply. You can houserules it to say you only roll one dice, but that is not what the rules say. When eldar and swarmlord meet, you always roll a second dice depending on which rule is invoked and only one reroll happens as of the rule book.

Eldar only applies if you fail. Swarmlord only applies if you pass. One re-roll.

I'm actually quite qualified to rebute your assumption.

I'm a math tutor at the college I attend, with a special interest in statistics.

(It's why my friends say I play mathammer, not warhammer!)

Since you said statistics, I will elaborate in said language.

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What your describing is true, but only if your accepting the first rolls have value.

But since the first roll has no elements in any set related to the outcome, and only the second roll has elements in either the PASS set, or the FAIL set, the first roll is discounted completely.

The probabilities related to what you roll in the first rolling, are not related to what you roll in the second set.

I see what your trying to say, that you should have a minimum number of rolls and that if you roll more dice, the mean should hit 3.5, but in fact, it allready does, its just that its not easily recognizable when your rolling less then 30 or 40 dice.

Your assumption that by rolling the first set it will improve the mean of the second set is flawed in this way. The mean already exists, rolling more dice will not cause it to change, only become more visable to us humans.

Fin