From North Texas State Teachers College's 1924 yearbook.

From The Children's Newspaper, 1959.

From Arkansas Polytechnic College's 1925 yearbook.

From Arkansas Polytechnic College's 1925 yearbook.

"We go in circles."  From Toike Oike, 1937.

Here's a lottery-winning talisman from Witchcraft, Magic and Alchemy by Grillot De Givry, 1931.

From Michigan State Normal College's 1949 yearbook.

Here's a precursor to the three doors of the Let's Make a Deal gameshow (1963), from The Gateway, 1962.

As we noted back in 2016, we call hogwash where we find it.  There's a probability puzzle popularly called the "Monty Hall Problem."  Entire books have been written about it, but we feel compelled to establish that it is pure nonsense.  A contestant on Let's Make a Deal declares a choice from three doors (two hiding goats and one a new car).  Then the host reveals a goat behind a door not chosen and suggests the possibility of switching to the other remaining door.  On paper, this is a counterintuitive paradox in which the contestant is convinced of a 50/50 chance of success, when in fact switching doors offers demonstratively better odds.  However, theorizing about the puzzle is ludicrous, and the considerable debate over the years is meritless, for the simple reason that a game show is a piece of theatre tantamount to a magic trick.  The host of this purported gambling scenario obviously works for "the house" and knows where the car is hidden (presuming—which one cannot, in fact—that the car is not moved from door to door behind the scenes).  Based upon subtle facial expressions and tones of voice (neither of which can be tabulated mathematically), the contestant wonders about being manipulated (with good reason).  Creating truth tables or running simulations of possible outcomes is meaningless because there is no circumstance in the real world where any of the probability theory could possibly be relevant.  There's a reason why the game show does not allow the contestant to simply walk up to a door and open it to determine the outcome.  Just as a magician displays a deck to prove that it's well-shuffled (which it isn't, and that's why pains are taken to prove otherwise), the host opens a door with a goat as part of an elaborate psychological and theatrical presentation that "proves" the outcome is random.  The outcome is not random on a television show designed to entertain.  The contestant wins if the powers that be wish to give away a car during that episode, period.  There is no other conceivable consideration (sorry, mathematicians and statisticians!).  While we tip our hat to those who are capable of modeling possible scenarios ad nauseam, the "Monty Hall Problem" is no problem at all.

From Amusing Experiments (After Martin Gardner), by M. Stoliar and L. Formin.

If your math doesn't always come out right, it may be because you forgot that 10 became 9 back in 1957.  From Toike Oike, 1957.

From Amusing Experiments (After Martin Gardner), by M. Stoliar and L. Formin.

From the University of North Carolina at Chapel Hill's 1917 yearbook.

From Amusing Experiments (After Martin Gardner) by M. Stoliar and L. Formin.

INSTRUCTIONS: Click twice to cartoon the circles. From the Duluth Evening Herald, 1909.

From The Initiates of the Flame by Manly P. Hall, 1922.

From The Great Pyramid Jeezeh by Louis Philippe McCarty, 1907.

INSTRUCTIONS: Click twice to cartoon the circles. From the Duluth Evening Herald, 1910.

From Hampden-Sydney College's 1907 yearbook.

INSTRUCTIONS: Click twice to cartoon the circles. From the Duluth Herald, 1910.