In 1941, when I started my first job at The American Locomotive Company in Schenectady, New York, I met a numbers runner for the first time. An individual would come to the area where I worked and take bets from workers. There was a game the workers played. If I guessed what the number to come out the next day was going to be, I’d get $540 for every dollar that I bet. The number to guess could have three digits from 000 to 999. This was a marvelous reward, I thought, and I tried doing it for a while. I didn’t win anything so I reduced the amount bet to ten cents and made ten bets each day. My reasoning was that I had ten times as much chance to win. My bets were no more successful with this strategy than they had been before.
I thought about the problem and hit upon an idea that I thought might work. I asked the runner if he could give me a list of the winning numbers for the last several years. He was able to do this and did. I divided the numbers into 100 groups of ten numbers each. (There are 1000 possible numbers between the numbers 000 and 999.) I numbered each group from 1 to 100 and made a table that showed how many times a number had won in each group. Some groups had one or two winning numbers, some six or seven, some none. I felt that if there had been no winning number in a particular group for a long time that group was due! That is, if a group had not had a winning number within it, the chances of that group receiving a winning number was better than they were for the groups that had had a few or even many winning numbers. I restricted my bets to groups that had not had a winning number for the longest time.
As before, none of my bets won. This puzzled me greatly. Where had my logic gone wrong? I stopped betting feeling that the numbers knew me and didn’t want to give me any winners. It was long time before I finally learned that numbers have no memory. The chances that any one number would win on any particular day were 1000 to 1 against winning. These were the chances for every number every day. It did not matter how long a number or a number within a group had not come out.
The reward of 540 to 1 was not at all generous. The mathematics of what I had been doing showed me that for every thousand dollars I played in this game, I would lose $460.
This experience soured me against gambling in general. I do invest in stocks. Some people might deem this to be gambling.