Are you up for a DIY Monte Carlo simulation?
I don't know of any specific applications, but if you're comfortable with coding I suggest you gin up a little Monte Carlo simulation.
In case you're not familiar with how that would work I'll explain (and can elaborate later if necessary):
- Populate some sort of database or data structure with your cards.
- Write a function that draws from this list at random and marks the card as drawn so it couldn't be re-sampled.
- Write another function to evaluate the built-out sequence to evaluate win or loss
- Wrap this core program with a loop that would play the game a huge number of times and
generate statistics on the results (e.g. number of wins and losses, longest streak of consecutive wins and losses, etc.)
The first three steps are a simple computer implementation of your card game. The trick is to model everything that's important to the mechanic and nothing that's not (easier said than done right?)
That last part is the Monte Carlo simulation where you use brute force computation (yea for cheap comp cycles) to get a result instead of trying to calculate probabilities closed-form, which for even simple card and dice games is more math (and more error-prone math) than most people are comfortable with.