The danger of gambling

Source 

I once heard a story about a young man who was propositioned by an old man on a long-distance train. It was not THAT sort of proposition, however. 

This one involved GAMBLING. Despite having been warned by his mother about the dangers of gambling with strangers on trains, the young man listened. The two men had a compartment to themselves, which had a small fold-down table positioned between them. 

The old man removed his jacket and hat, rolled up his shirt sleeves and produced three two-inch discs. On one, there were two identical, plain crosses – one on each side. The second was blank on both sides. And the third was blank on one side, with a cross on the other. 

He explained the methodology thusly. Each would take it in turn to place the three disks into the hat, give it a shake and hold it under the table – and then the OTHER would remove one disk, clench it in his fist and slap it down on the table. At which point, the first would have to guess whether the UNDERSIDE was blank, or had a cross on it. 

The old man pointed out that since the other was drawing the counter, cheating would be impossible. He further stipulated that either party could examine and re-examine the hat and/or the disks at any time – as many times as they liked. The young man examined the counters carefully. Without doubt, the crosses WERE identical – precisely centred and PRINTED onto the counters. All were perfectly flat, with clean edges. 

He then examined the hat, which proved to be mundane. He even checked the old man and determined he had no concealed mirrors or trick glasses – not even contact lenses. 

At which point, the young man said okay then, what was the point? If the cross was on top, the disk could not be the double-blank – thus it had to be either the cross-blank or the double-cross. 

The odds were fifty-fifty. And likewise, if the top was blank, it could not be the double-cross. Therefore it had to be either the cross-blank or the double-blank. Again, fifty-fifty. 

Plus, the discs had the same number of crosses and blanks, evenly distributed on their faces. Yet again, fifty-fifty. Precisely, said the old man. He went on to explain that since the train journey they were on was a long one, a fifty-fifty game would pass the time more quickly – without either of them being in danger of losing a significant amount of cash. 

Having established that both parties had fifty pounds on them which they could afford to lose, they decided on that sum as a ”ceiling”. And since their money was not in single pounds, they would keep score on a piece of paper, which would be placed on the table – in view of both at all times – and settle up when one of them reached the ceiling or they both reached their destination. 

And so they began to play. At first, the game proceeded pretty much as the young man had expected, with neither man moving ahead. However, after a while, the old man’s fortunes appeared to improve. 

The process was gradual – but slowly, the old man’s total began to approach the fifty pounds. Despite the young man having examined the discs and hat a number of times – with no anomalies detected – the old man finally hit the agreed sum, a few miles before the journey’s end. 

The young man paid up – and asked the old man for the secret. Their time together had been good-humoured, so the old man let him into the secret. He pointed out the young man had been INCORRECT when he had determined the game to be fifty-fifty. He said that in fact it was two-thirds/one-third. 

The trick was in the NUMBER OF COUNTERS. There were THREE – not two. Thus, if one bet on the hidden side being the same as the top side – one would be correct two times out of three. Therefore, if one said the hidden side was the SAME, MORE than fifty percent of the time – in the LONG TERM, one would have an EDGE. 

Obviously, if one ALWAYS said the underside was the same as the top side, the other person would realize what was going on and COPY them – and therefore, while they might not understand the principle, they would neutralise the first person’s advantage. 

The trick was to exploit the advantage enough to show a profit – without alerting the other player to the method used. The young man considered fifty pounds to be a fair price for having learned an interesting ploy – and having an equally interesting anecdote to tell his friends. They shook hands and went their separate ways.