Jake dropped by the Happy Valley Card Club to see what was happening on a snowy winter’s Friday evening in December. Jake enjoyed the conviviality and high-spirited discussions about the probabilities of card games in the lounge by the bar.
Jake saw a large gathering around a large rectangular table, where Charlie was dealing cards on the luxurious green felt cover, Christmas music sounding enchantingly in the background.
“What’s the game this evening, Charlie?” asked Jake.
“It’s a variation of the game of the other day. It is called the ‘Four Card Deal’,” said Charlie. Half of your winnings will go to our university scholarship Christmas charity.
“Sounds fine to me. How does this ‘Four Card Deal’ work,” said Jake.
“Well, my man, you pay me 10 dollars and I shuffle and deal four cards face up. I also pull a card from the top of a stationary deck I don’t shuffle,” explained Charlie.
“Very interesting, but what’s the idea?” said Jake.
“If the four cards all have a different suit and no two the same value, you win. But if I pull an ace from the other deck, you lose,” explained Charlie.
“What’s the prize?” asked Jake.
“You win twenty dollars, but if you don’t win and I pull no ace, I repeat the procedure,” said Charlie.
“Ok, Charlie, let’s give it a go,” said Jake.
How long would you say this game continued on average until Jake won or lost, and what could be any amount Jake paid to charity after playing ‘Four Card Deal’ ten times?