Consider a three-reel single-line slot machine such as “Red White and Blue” Afte

Question

Consider a three-reel single-line slot machine such as “Red White and Blue”

After the player makes a bet and presses the spin button, the machine selects three random numbers (1 to 64), one for each reel

Each random number is mapped to a stop position (certain symbol)

The number of times each symbol appears on each reel is shown in a following figure above.

Calculate the odds of getting three sevens of any color (a seven on reel 1, another seven on reel 2, and another seven on reel 3)

Please show work in formula method.

1 Total Weights for Red White & Blue Stop Reel 1 Reel 2 Reel 3 2 Number 3 Red 7 4 White 7 5 Blue 7 6 3 bar 7 2 bar 8 1 bar 9 blank 10 Total 3 5 32 32 32

Explanation / Answer

P(7 on reel 1) = (1 + 6 + 6)/64 = 13/64

P(7 on reel 2) = (3 + 1 + 7)/64 = 11/64

P(7 on reel 3) = (1 + 7 + 1)/64 = 9/64

Since these three are independent of each other,

P(three sevens) = (13/64)*(11/64)*(9/64) = 1287/262144

Hence,

Odds in favor of getting three sevens = 1287 : 260857

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