One double in five throws? Who could do that?

The following little story happened at a backgammon tournament in Berlin in 1986. A bunch of the best players in Germany were gathered there. So good players, professional players and wannabes, but also admitted hobby players.

In the evening, Jürgen, a well-known gambler of many years’ standing, suddenly took a dice cup in his hand (oh, did he ever put it down?) and said, “Listen, guys. You know: Normally there is a double every 6 throws, I make a double in 5 throws, you can all put up, everything goes, it doesn’t matter now, I’m on fire” (that means: I lost a lot, of course he just said that, but Jürgen could really lose the overview sometimes and “burn”).

The tournament hall was still well filled even at night time and Jürgen’s organ and in general his whole appearance always caused a stir. So he succeeded in attracting attention and many people. He repeated his announcement a few more times: “I make a double in 5 throws. If it comes up to and including the 5th throw, I win, otherwise you win. Anything goes. You can bet as much as you want. Normally it comes in six throws, I’ll do it in five.”

The gamblers traditionally have their cash in their pockets, ready to hand. And the hundreds of notes flew onto the table in front of him. “Who else wants to join in? Anything goes. I’ll do doubles in five throws.” Everyone seemed to think that Jürgen had lost the plot again. With him, you had to expect a lot. But had he built up his image consciously?

So the bet was: He has five attempts to throw doubles. If he succeeds, he collects the money. If he doesn’t, he has to pay out everything. The bet was without odds, i.e. 100 DM against 100 DM, just like everyone used to bet, there was only so-called “equal money”. Odds 2.0, 100 DM against 100 DM (see chapter “How are odds created?”).

So, a lot of people were betting. The whole thing ran for half an hour. The hundreds flew across the table. Sometimes Jürgen won, sometimes he had to pay out everything.

I could have played too, but I didn’t. Would you have played along? Did I really just not do it out of fear? Or is there some mysterious mathematics behind it all? In any case, it sounds and obviously tempting: Normally you really need 6 throws for a double.

After half an hour, the game was over. Jürgen had earned a pile of dough, the lucky guy. One or the other may have had a somewhat shorter night’s rest afterwards. But whether he just cursed his bad luck or took out a calculator after all? Nothing has come down to me about that. I always have my calculator with me in the form of my light bulb. Is there a solution to this riddle? There is, please continue in the chapter “How many throws does it really take to make a double?” After all, we are in the biographical section here, there is no calculating!