[narkee]

The call for larger sample sizes isn't always appropriate. It can often lead to spurious inferences.

As Jacob Cohen (famous statistician) has said, "all null hypotheses, at least in the two tailed forms, are false".

That is, with nearly any hypothesis about differences between groups, given a large enough sample size, you're likely to find a significant difference.

[mingfu]

i think the difference here is between the two different experiments (one with three rolls of the dice and one with a single roll) and not a difference between the groups. You could choose to use the exact same group of participants for both experiments.