Expected value = 3.50
Die roll variance = 2.92
Standard deviation = 1.71

Your opponent's average = 4.22
Sample = 50
Sqrt(Sample) = 7.07
z = (4.22-3.5)/(1.71/7.07) = 2.97

Your average = 2.2
Sample = 38
Sqrt(Sample) = 6.16
z = (2.2-3.5)/(1.71/6.16) = -4.68

Given that 99% of the samples are supposed to give values between -2.58 and +2.58, the data you quote is indeed unexpected assuming you collected all the data impartially, and not choosing the start date and end date so as to maximise the difference.

However.

If you had found normal data, you wouldn't have put a message on the forum, would you?

1) You decided to post THIS sample and not another one AFTER noticing an "unsual streak". That is, you did not pick a random sample. You purposefully picked one that looked weird.



2) If a streak like this one never happened, it wouldn't be a random number generator. A random number generator is in fact supposed to produce these numbers infrequently.



3) If 100 people check their numbers impartially, 1 in 100 will get a "weird" result and will post it in the forum. The other 99 won't.

So, if you want, we can repeat the experiment this way: Let us use all the games you will complete between June 1st and June 31st, inclusive. This is guaranteed to be an impartial sample. You collect the data, I will do the maths.



Let's see what happens, ok?