A solitaire was played on normal cards such that there are four suits and 13 numbers for each suit. Rules are the following:
You put four cards to front of you. If there are at least two same suits, you remove the cards with same suit and put new cards from the deck to front of you such that there are four cards front of you. If you can't fill the board, you may have 1 to 3 cards at the final round. You lose if the cards in the board are all of different suits at the end. What is the probability that you can remove all the cards in this solitaire? Can this be counted exactly or are there any decent approximation?
I was looking for something else and come up to your question. I did a small macro in Excel and my results are:
Success rate: 131 out of 1000. , so the probability is ca. 1/7 - 1/8.
You can try to build a decision tree to calculate the real probability. This should be not very complex as we talk about only 4 colours (cards values don't care).
You can try it in some calculation sheet.