This looks like an interesting aspect of the general concept of Moral Luck, which I'm sure you would find worth investigating. The most commonly cited first paper on this stuff is Thomas Nagel's Moral Luck, where he discussed the idea of the Control condition:
Without being able to explain exactly why, we feel that the appropriateness of moral assessment is easily undermined by the discovery that the act or attribute, no matter how good or bad, is not under the person's control.
Nagel wanted to argue that the role of luck in assessment threatened to undermine not just individual apportionings of blame but the whole project of making moral judgements. That's because there are some cases where we do and some where we don't want to think that control over the outcome is important - for instance, you don't lose responsibility for your actions just by being under the influence of hallucinogenic drugs.
One worthwhile response is to consider that "luck" may play much less of a factor in assessments of responsibility, and I think this is generally the case in your example. A Kantian would say that you're responsible not because of how your actions have brought about consequences increasing or decreasing the likelihood of the correct outcome, but because of your intentions when acting. Regardless of the question of whether I win the roll or not, you are responsible for the choice you made to pass the 8-sided dice rather than the 6-sided one. This in a harmful action for which you bear responsibility, with no sense of there being a "degree" of responsibility lessened by appeal to luck since the actual outcome of the roll didn't impact whether what you did was morally correct or not.
But there are different kinds of moral luck that Nagel discusses, and all of these need addressing in order to get over the suggestion that our concept of holding people responsible might be in trouble.
