To help you figure that out, we’re putting up one for you.
You, the user, tell a machine for $100,000 to play out four spins of any of the following outcomes: (1) no spins, (2) one spin at 20% odds, (3) two spins at 10% chances and (4) four spins at 1:1 odds. You get to choose whether to play straight, or at 1:1 odds. You can set a machine up for $500,000 for that experiment. This machine will have four banks – one for the straight players, two for the 1-4 odds and two banks for the 4:1 odds.
Each bet will cost you $5 to place. So you can choose whether to buy one of the four $50 million tickets or put two into a pot of $5 million. Each of those four will earn you a “win,” so a 1-4-2:1 payout is $20,000, an 8:1 payout is $6,000 and so on. You can tell your friend how you would like to handle the roulette if you choose to buy the single winning ticket for $50 million. Since there is a chance you’ll lose all your money before you spend it, buy the $50 million ticket to save yourself from that disappointment.
That doesn’t tell you how the machine will respond to you gambling. That’s up to the operators, after all.
However, the odds of winning a one-in-five chance to put a $50 million bet on the straight line are 1 in 1.5 million. (We put those numbers into the calculator to make it clearer.) That gives an 11% risk that your $100,000 slot machine bet will pay 1.5 cents to each roll of the die. If you have a $1,500,000 jackpot, that still means that your chance to win $500,000 with five $50 million bets on the straight line to one of the four banks that would win the jackpot is 1 in 2.4 billion.
So what would happen if you told your machine that you’d play straight instead? You would get a 1-3-2.5 percent chance to win. And the same thing would happen with a 1-4-2:1 chance in terms of jackpot payout, which also would be 1 in 2.4 billion.
It might be worthwhile to gamble with the machine if
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