The illustration is a detail from Pieter Brueghel's "Children's Games", painted in 1560. The child is holding a teetotum in her left hand. The Elliott Avedon Museum identifies this as a gambling game that dates back to ancient Rome. Each side is marked differently and players wager on which side will end up when the teetotum is spun. The model the child holds has a long spindle requiring two hands to spin it. Modern versions have short spindles which can be spun in the fingertips.
Brueghel would most likely have been familar with the French version of the game. Each player contributes a certain number of coins to the pot. The Oxford History of Board Games by David Parlett states the sides were marked as follows: 'P' for "pillar" or "plunder", the player wins the same number of coins he wagered; 'R' for "rein" or "nothing", the player loses his wager and his turn; 'J' for "jocque" or "game, the player loses his wager and must add the same amount of his wager to the pot again; and 'F' for "fors" or "out", the player wins the entire pot and the game ends. Players ante in again to continue playing.
In Traditional Games of England, Scotland and Ireland by Alice Gomm, the game is described as being played by English children at Christmas time. Readers may note the game is remarkable similar to Spinning the Dreidel, a game that's traditionally played by Jewish children during the Hebrew festival of Hannukah which takes place at approximately the same time of the year. The four sides are marked with the Hebrew letters 'Nun' which stands for "Nes" meaning "miracle"; 'Gimmel' which stands for "Gadol" meaning "great"; 'Heh' which stands for "haya" meaning "happened"; and 'Shin' which stands for "sham" which means "there", a reference to Isreal.
"A Great Miracle Happened There" refers to the miracle of Hannukkah, which occurred in 165 B.C. when a day's worth of lamp oil burned for eight days. While the game honors an event which occurred back in Biblical times, The Elliott Avedon Museum and Game Archive has been unable to trace the dreidel back any further than 18th century Germany.
Everyone starts the game with the same number of markers, generally ten to fifteen. Markers may be nearly anything; pennies, nuts, matchsticks, etc. Jewish children frequently play for small candies. Everyone puts one marker into the pot. On their turn, each player spins the dreidel once. When the dreidel stops, the face that's uppermost determines the player's pay-off.
'Nun' stands for "nisht" which means "nothing". The player wins nothing. 'Gimmel' stands for "gantz" which means "all". The player wins the entire pot. 'Heh' stands for "halb" which means "half". The player wins half the pot. If there is an odd number of tokens, the player takes the extra token. 'Shin' stands for "shtel" which means "put in". The player must put two of his own tokens in the pot.
When the pot is reduced to less than two tokens, all the players must add one token to the pot. When a player runs out of tokens, they are out of the game. The game ends when one player has collected everything.
I have also read multiple references that the letters stand for "Nefesh" meaning "Soul", "Guf" meaning "Body", "Sechel" meaning "Wisdom" and "Hakol" meaning "All" which is supposed to be a reference to the four ancient kingdoms which persecuted the Jews; Babylon, Persia, Greece and Rome respectively. However, I can't find anything to indicate this is anything except a modern interpretation.
Brueghel, Pieter "Children's Games" 1560. 46-1/2 x 63-3/8" (118x161cm) Kunsthistorisches Museum, Vienna.
The Elliott Avedon Games Museum -- http://www.ahs.uwaterloo.ca/~museum
Gomme, Alice Traditional Games of England, Scotland and Ireland (London, Eng.; Thames and Hudson; 1894; 2 vol.; ISBN 0-500-27316-2; $18.95)
Parlett, David The Oxford History of Board Games (Cary, N.Carolina; Oxford University Press; 1999; ISBN: 0192129988 )
Portman, Paul Pieter Brueghel's Children's Games (Berne, Switz.; Hallwall Press; 1964)