Posted on April 3,
2017by jamesdmccaffrey

I love
old electro-mechanical devices. Years ago my college roommate Ed and I enjoyed
playing “bingo pinball machines” that were manufactured in the 1950s. The
machine’s top screen has a 5 by 5 bingo-like grid with the numbers 1-25 in a
scrambled order. You shoot five metal balls, one at a time, and try to get
three or four or five numbers in a row. If you did, the machine paid out
nickels like a slot machine.

These
old devices were complex mechanically and many were really beautiful works of
mechanical art. I discovered a fantastic simulation Web site (link below) and
was able to relive some of the fun Ed and I had with these machines. Here’s an
example session playing “Beach Time”, a typical bingo pinball game.

1. To
get started, I put in a bunch of (virtual) nickels. After each nickel, zero,
one, or more features would light up. After about 30 nickels I reached the
image below (you can click on it to enlarge). The two key items are the payout
tables at the bottom and the lighted letters, A through F. If I get 3, 4, or 5
in a row on a red line, my payoffs are 450, 240, 120 respectively. My payouts
for yellow (200, 96, 32) and green (300, 144, 64) lines are a bit less.

2. I
shot my first four balls and they landed in numbers 7, 13, 20, and 12 as shown
below in the image on the left. Now comes the cool part. Notice that “Press
Buttons Before Shooting 5th Ball” feature is lighted. I have the option of
pressing A B, C, D, or F because they’re all lighted. The D grid has the
numbers

16 13

5 21

I
pressed the D button three times. After each press the four numbers physically
rotate one step clockwise so I positioned the 13 under the 7, giving me two
chances to get three in a row (a 2 or a 16). Then I pressed the E button two
times to position the lighted 12 under the 13, giving me a chance to get four
in a row (if I got a 16). See the image below, on the right. Note that I didn’t
press the F button but I should have because the 20 in the F section cannot be
part of any three-in-a-row. I should have pressed F once to move the 20 down
one position, giving me a chance for 12-8-20 or 13-5-20.

3. I
shot my fifth and final ball and my faulty strategy worked because I got a 2,
completing a 2-7-13 three-in-a-row on a green line. I won 64 virtual nickels,
as shown in the counter in the upper left of the image below. Good fun!!

There
is some fascinating combinatorial mathematics going on here. The positions of
the 25 numbers on the display screen, combined with the positioning of the 25
holes on the playing surface are critically important with regards to the
probabilities of payouts.

I’ve
just touched on a tiny bit of these fascinating machines. If you want to learn
more about bingo pinball machines, I suggest starting with:

You can download the
excellent simulation program from:

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