1939 photo with Twenty One

Someone shared this old photo: 

1939 Birney Montana

Twenty One (by Groetchen, 1936)

Hello it's time for more mathematics!   Yes, I managed to get this lovely little restored trade stimulator from 1936:

Twenty One (21) by Groetchen circa 1936

These are devilish little machines designed to trick the player in to thinking it's a skill game.  Please be advised of a little operator secret:  these are NOT skill games.  The fix is in, and it's designed for you to lose, and to hopefully make you think it's your fault you lost.

We'll dive in to the mathematics of that a bit later, but first a gameplay overview:  place a nickel in, pull the handle down, and the reels spin.  The left-most windows (5, 4, 3) will all have a shutter close in front of them.  You have your two cards (windows labeled 2 & 1).  Want another card?  You can press the button under window 3 to reveal it.  Want another card?  Do the same for button 4.  When you are satisfied with your hand, press button 5 to reveal the dealer's hand.  You can't press button 4 until 3 is press, forcing an order.  Once you press button 5, the other 2 window buttons are disabled.  If you stand on 3 cards and reveal the dealer's hand, there is no way for the played to know what window 4 had.

When it arrived it was super sluggish and not really spinning at all.  I went inside: