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# alternative to Pachinko

## Question

This is a simple game like Pachinko and in a similar vein as my "coin with a conscience" problem.

You insert money into the machine at one metal ball per 10cents. The balls drop one at a time onto discs. The first ball drops and lands on a disc and then rolls and lands on the next disc, and then falls on two more (for a total of 4 discs). If after landing on the fourth disc, the ball rolls off to the left, you get 20cents. if the ball rolls off to the right, you earn nothing. After inserting your money, you choose whether the 1st ball should aim for the left part of the first disc or the right part of the first disc (and the ball will always go down that particular side). Once a ball goes down a particular side, the rest of the discs are rigged to bias the odds the ball falls the other way by a change of 5%.

For example--with 1 ball

• aim for right side, disc 1--(goes down right side), disc2-- 52.5% (50% * 1.05 = 52.5) likely to fall down left, disc 3-- 52.5% likely to fall down left, disc 4-- 52.5% likely to fall down left
• ball reaches disc2 say it falls down the left side, 49.875% likely to fall down the right side of disc 3, 49.875% likely to fall down the right side of disc 4
• ball reaches disc3, say it falls down the left side of disc3, 52.36875% chance it will fall down the right of disc4
• say the ball rolls off the right side of disc4....darn, i lost 10cents.

Can you make money playing this game in the long run? If so, how should you play it? If not, why not?

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