## Bingo Pinball Machines

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:

https://bingo.cdyn.com/