I have a question about a weird, unknown (and possibly impossible) game a friend of mine has taught me. It is a solitaire game that's played with a regular deck of 52 cards but it is suspiciously difficult to beat. What's more, neither my friend nor I were able to find ANY reference to it in all the Internets.
I am aware that the question is not necessarily interesting to anyone but my friend and I, but I was wondering if someone would be willing to help me calculate the odds of beating this game? I think it would help us decide if this is a real game or if it's just a weird multi-generational prank my friend's father (who taught him the game) is pulling. My current grasp of math and probability does not allow me to undertake the project alone.
Here are the rules:
Nine columns of three overlapping face up cards are laid on the table. The face value of each card is used to calculate a sum with the two closest cards (either on top or on bottom) on the column and the last card can "wrap" with the bottom card (the first one played on the column) to achieve a certain sum if needed. Face cards all are worth 10 points.
Each turn you go to the "next" column (cyclically), place a card from the deck on the top of that column, and then, in the same column, look for potentially three cards one after another (two at the top and one at the bottom, and one at the top and two at the bottom, are also valid) which make up 9, 19 or 29, then, if found, remove those cards and put them at the bottom of the deck, in the same order.
If any other valid combinations are revealed after the removal of a triplet of cards from a column, they are also removed and placed back at the bottom of the deck.
If all the cards of a column are thus picked up, the column is eliminated.
The theoretical goal is to pick up all nine columns before the deck runs out. If the deck does run out, it's game over.
Now... my friend has played thousands of games and has never beat the game even once. He holds on to it only because his own father boasts that he finished it twice in thirty years of playing it... But it really sounds fishy.
Can anyone help?