When I edited the question to be readable there was no indication that the system had any significant relation to an RPG at all. The OP said in the post at that point:
OK working on a dice game as part of an in game system where players can play a dice Game that requires a players roll specific results in order to gain a card,
Ok its a game within a game
This plus the content of the game made it appear that the game mechanics asked about had no bearing on the RPG they were being played in at all. The question, as it appeared, was "How can I get probabilities for this card game I'm developing?" with the only RPG context being that the OP was planning on having the people playing an RPG with them play this card game, too. The question did not and does not invite commentary on how to integrate such a game or anything like that, it is and was solidly about the probabilities of a card game.
This differentiated it from arbitrary questions about statistics, in my mind. Were the mechanics intended for use in an RPG (as the OP's answer here indicates) our expertise would be applicable, and we could talk about the stochastic characteristics of this method in the context of its use in RPG conflict resolution (well, somebody could. I have trouble doing that with non-math terms).
When we ask a question about arbitrary statistics on this site, it is understood that we are asking about those statistics in an RPG context. That context is necessary for the questions to be on-topic, and the principle of good faith tells us we should assume that's the context the question is in unless there is strong evidence to the contrary. If somebody asks "Are sequential coin flips good random bytestring generators?" here, it's appropriate to respond with "No, because that takes way too much table time", because we're answering from an RPG context.
Now, questions about using tools primarily used for RPGs are, in my opinion, also on-topic here. We have the experts to be able to answer such questions to a high standard, because the experts in those tools have that expertise as an extension of their RPG expertise. Dice are a tool we use extensively, but dice are also used extensively outside RPGs. Asking about dice in general should be on-topic, I think, since they are ubiquitous and quintessential RPG tools, but asking about dice in the specific context of a non-RPG (like, 'what are the odds of me being able to take this space in Risk') is not on topic. This is kinda weird because the underlying question of 'what are the odds that A beats B with this weird dice pool mechanic?' would be on-topic, but somehow because that pool is called 'playing the board game Risk' it becomes off topic. I'm not sure that this division is fair but it is the division that seems most appropriate to me.
Questions about a Board or Card game with no significant RPG context shouldn't be on topic here, even if they are just a question of statistics, even though general questions about statistics with no context are on topic.
That said, the OP made it clear here that these mechanics are intended to be used in the actual game system as well, so I'll edit the question to mention that (since the OP still hasn't), and it should be open.