Dominos first draw

Question

If one person always draws first,taking 7 dominos in a two person domino game does he stand a greater chance of getting doubles than the other player who always draws his seven after? Standard 28 domino set. Thanks

Answer 1

Only if either:

1. The dominoes are face up during the drawing, or
2. There is an element of extrasensory perception involved. ;) If you're playing against a psychic and he draws first, he can choose the best tiles; if you draw first, he can only choose the best tiles among those you didn't happen to draw.

Without some form of knowledge of which dominoes are being drawn (whether from direct observation, a hidden camera, a cheating partner under the glass table, or psychic abilities)—in other words, if the selection of dominoes is actually random—then your chances are not different whether you draw tiles first or second.

Of course, that is based on a mathematical model which assumes no knowledge on the part of those drawing tiles (rather than proving it), and doesn't take into account such immeasurable, non-concrete possibilities as some people being naturally "luckier" than others, even if they don't have ESP. There is some evidence to support this—but its relevance depends on whether you want to know the mathematical answer (which is "No difference in chances") or the practical answer (which is that you probably shouldn't gamble unless you're lucky.) ;)

Answer 2

Imagine that a domino shuffling machine brings the $28$ dominos into a random linear order. Why should we expect more doubles in the first quartile of seven dominos than in the second quartile?