Three Dice Cups

Jackson was concentrating on the three cups filled with dice placed in front of him on the table covered with green felt, wondering which to choose.

“Some say that the result of any of the cups will be the same, just a fifty percent chance,” said Snipes the slick gambler. “Which of the cups do you say has the best chance?”

Jackson had bet Snipes a thousand dollars that he could pick the right cup and prove his point with a hundred throws of each cup.

Respectively, the cups – colored red, green and blue – contained six, twelve and eighteen dice. The issue was regarding the event probability of a throw of the cup with six dice giving at least one six, of the cup with twelve dice giving at least two sixes, and of the cup with eighteen dice giving at least three sixes. The question was which cup had the greatest event probability.

“Well, what do you say, Jackson,” said Snipes with a sly grin, a golden tooth glinting. “Which cup do you choose, the red, green or blue one?”

“Hard to say,” mumbled Jackson, thoughtfully stroking his bearded chin.

“Could be close, indeed. Snipes, would you mind if I check my runes?” Jackson pulled out a decorative brown leather bag containing rune stones and placed it on the table.

“No problem, Jackson. Take your time,” grinned Snipes, whose mental equipment did not believe in mumbo-jumbo.

Jackson rummaged in the rune bag with a pensive expression on his face and picked out three rune stones, which he carefully placed in a row on the green felt.

After a quick look at the runes he said, “Snipes, I’ll take that one,” indicating a certain cup on the table.

“Well, you picked the right one, Jackson. Just luck, I guess,” said Snipes with a mournful expression on his face and handed over the thousand dollars to Jackson.

“What about a game of Black Jack, eh?” Snipes placed a deck of cards on the table with a swift movement of his hand.

Jackson replaced his runes and walked away.

Which would you pick, the red, green or blue cup? And why?

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