[indio]

A video poker machine at ABC casino randomly deals you 5 cards at the rate of 55 hands a minute, and will pay out $200 for any 4 of a kind, $600 for any straight flush (non-royal), and $3000 for a royal flush.

You can play this game for a yet to be determined amount that will give you exactly 15 minutes of play (825 total hands). In intervals of $1 ($10,$11,$12,etc), what is the absolute lowest amount you can play this game for that still has an edge to the house?

To get the proper answer, you can try and do the math, you can take a wild stab, or you can look to the former stars of Las Vegas and the twinkling stars in China to get the answer.

I'll reveal the answer in a few days.

Good Luck.

[indio]

The correct answer is $51

There were 19 scenarios with a probability equal or greater than 1 million to 1 to factor into our payouts. The most common obviously was nothing at .809996, the most common paying result was 1 four of a kind at .160412 and the rarest paying results were 2 quad + 2 st flush and 3 quads + 1 royal at .000001 each. In all, 1 million results payed out $50,283,200 so the lowest entry fee with a house edge would be $51.

For those that didn't want to figure the math, there were 2 clues given in the last sentence. When you were told to look to the former stars of Las Vegas, that was a reference to the former Las Vegas Stars baseball team of the Pacific Coast League which changed it's name to the present day Las Vegas 51's (in reference to Area 51 which is nearby). The other clue told you to look to the twinkling stars of China which references the Hsikwangshan Twinkling Star Co. Ltd of Hunan which is an Antimony mining company (in fact the largest Antimony mining company in the world). Antimony is of course number 51 on the periodic table of elements.

[Optional]

Great brain teasers.

Those clues were pretty darn cryptic though!

At the risk of sounding like a dummy. I still don't get how the value of your bet affects the house edge from that. And are you saying that playing $52 per hand means the player now has the edge?

[indio]

Great brain teasers.

Those clues were pretty darn cryptic though!

At the risk of sounding like a dummy. I still don't get how the value of your bet affects the house edge from that. And are you saying that playing $52 per hand means the player now has the edge?

If you were a player and played this game at $50 a game, you'd (the player) have a slight edge over the house. Playing at $52 a game would increase the house edge. Keep in mind that if this game was played a million times, in theory, you'd have a payout of $50,283,200. So since we must find a number from intervals of a whole dollar, $51 x 1 million games would give us a total of $51,000,000 paid to the house, we'd get $50,283,200 (apx) returned to the player, so the house would have a 0.56% edge at $51 a game.