Mike sat down and started shuffling the cards. "What stakes?" he asked.

"Let's make it a gamble," Steve replied, putting a few bills and some coins on the table. "The first game, the loser pays 1 cent, the second 2 cents, and so on. Double up each time."

"OK", laughed Mike. "I've only got $6.01 and I'm not playing any more than ten games anyway."

They played, and game followed game until at last Mike stood up. "That's my last cent I've just paid you", he declared, "but I'll have my revenge next week."

How many games had they played, and which did Mike win?