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A European roulette wheel contains the numbers 0 to 36. Who decided to put 37 numbers on a wheel, and why did they choose this number?

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    Documenting preliminary research will improve both the probability of an answer and the quality of the answer(s) Does Wikipedia answer the question? Is there any reason to believe that this is in scope for history? that historical sources and methods will help to answer this question?
    – MCW
    Commented Jul 12, 2023 at 14:39
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    There are several different types of roulette wheel. American wheels have 38 pockets (adding 00 to the house).
    – Steve Bird
    Commented Jul 12, 2023 at 14:42
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    The answer is probably down to mathematics and greed. The original tables were broken up into 36 elements because that divides neatly into 360 degrees. Then someone thought that the house needed an extra advantage and added the 0 (and then the Americans thought that the house needed an extra, extra advantage and added 00) Commented Jul 12, 2023 at 14:46
  • @KillingTime It would seem to be the other way around if the information in Wikipedia is correct. Commented Jul 12, 2023 at 17:15
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    37 is a prime number - could be a way break the symmetry that might favor some numbers over the others due to the table construction.
    – Roger V.
    Commented Jul 13, 2023 at 8:16

4 Answers 4

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The single 0 style roulette wheel was introduced in 1843 to compete against other casinos double 0 style roulette wheel that has existed at least since 1794.

Other versions had 70 (Biribi), some had less.


Roulette - Wikipedia:

The game has been played in its present form since as early as 1796 in Paris. An early description of the roulette game in its current form is found in a French novel La Roulette, ou le Jour by Jaques Lablee, which describes a roulette wheel in the Palais Royal in Paris in 1796. The description included the house pockets, "There are exactly two slots reserved for the bank, whence it derives its sole mathematical advantage." It then goes on to describe the layout with, "...two betting spaces containing the bank's two numbers, zero and double zero". The book was published in 1801. An even earlier reference to a game of this name was published in regulations for New France (Québec) in 1758, which banned the games of "dice, hoca, faro, and roulette".

The roulette wheels used in the casinos of Paris in the late 1790s had red for the single zero and black for the double zero. To avoid confusion, the color green was selected for the zeros in roulette wheels starting in the 1800s.

In 1843, in the German spa casino town of Bad Homburg, fellow Frenchmen François and Louis Blanc introduced the single 0 style roulette wheel in order to compete against other casinos offering the traditional wheel with single and double zero house pockets.

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  • That explains why 37 instead of 36 or 38. But why was 36 chosen initially?
    – Riemann
    Commented Jul 13, 2023 at 7:56
  • @Riemann I doubt that that can be reliably determined. Commented Jul 13, 2023 at 8:03
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36 is a Highly Composite Number:

A highly composite number is a positive integer with more divisors than any smaller positive integer has.

36 can be divided by 1, 2, 3, 4, 6, 9, 12, and 18. This allows for many ways to bet on groups of numbers with equal chances.

Remember that you can put chips not only on one number (plein), but on the line between two numbers (cheval), on the outside line of a row of three numbers (transversale plein), the crossing of lines between four numbers (carré), on the T of a line dividing two rows of numbers with the outside line (six numbers, traversale simple), on the twelve numbers 1-12, 13-24, 25-36 (douzaines) or in a column (colonnes), and various variants of betting on half the numbers (eighteen -- pair / impair, passe / manque, rouge / noir). This is possible only because 36 divides evenly into each of those (as well as nine, which is AFAIK not used for betting though).


Similar reasoning (highly composite numbers) is why dice have 6 sides, many customary units come in twelves, the day has 24 hours, an hour has 60 minutes or the compass has 360 degrees: Easy to divide any which way without having to deal with remainders.

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Perhaps a bit of historical context might help clarify the mystery, by comparing its numerical choice, to that of other games of chance ?


Though currently revered as constituting primarily a game of intellect, chess has its own dice–based version, played, of course, with 32 pieces, revolving around the four main divisions of ancient Indian military; namely, infantry (pawns), cavalry (knights), war elephants (bishops), and chariots (rooks).

A simple glimpse at a list of card games by number of cards reveals those played with of 52, 32, and 36 cards as the most numerous. Needless to say, most such decks consist of four suits, oftentimes colored red and black.

A list of traditional card and tile packs informs us that :

32-card packs [...] are very common in Europe.

36-card packs [...are] in use in western Switzerland [...] and [are] quite common in Russia

40-card packs are found mostly in Latin countries where they compete against local Italian or Spanish suited decks.


Full German-suited packs [...] contain 36 cards, organized into the four German suits

without the [four] sixes, [it is] used for many Central European games

The [...] frequently encountered Swiss-suited [...] Jass pack [...] contains 36 cards


The standard Spanish-suited pack consists of 40 cards

the standard Italian-suited pack consists of 40 cards

Though the standard 52-card deck is quite popular nowadays,

there are many countries or regions where the traditional pack size is only 36 (Russia, Bavaria) or 32 (north and central Germany, Austria)

40- or 48-card Italian-suited packs are common in Italy

40- and 48-card Spanish-suited packs on the Iberian peninsula

36-card German-suited packs are very common in Bavaria and Austria.

As far as French-suited playing cards are concerned,

The most common deck sold in France is the 32-card deck

The French-Swiss pattern [...] comes only in decks of 36

Belgian packs come in either 32 or 52 cards


The Dutch pattern [...] come[s] in decks of 32 [...] or 52 cards.

The North-German pattern [...is] usually in decks of 32 cards


Genoese type cards [...] come in 36 [...], 40 [...] or 52-card packs.

The Lombard or Milanese pattern come[s] in 40-card decks


The Russian pattern [...] usually contains 52 or 36 cards

[It] can be found in many countries that were once part of the Russian Empire or Soviet Union.

The Wikipedia article also contains a picture of a

Standard 32-card deck of the Paris pattern.

For Swiss-suited playing cards,

The most common deck has 36 cards.

German-suited playing cards

are a very common style [...] used in many parts of Central Europe characterized by 32- or 36-card packs

The typical northern German pack has 32 cards

Southern patterns have 36 cards

Northern patterns [...] were originally produced with 36 cards but this was reduced to 32 cards

Most [southern] games require only 32 cards

The Württemberg pattern [...] used to be produced in 36 card packs


The [...] Double German [...] pattern is popular throughout the former Austro-Hungarian Empire.

[It] come[s] in packs of 32, 33 [...], or 36 cards.

In Hungary and other eastern European countries they [...] come in 32-card packs.


In South Tyrol, 40-card, German-suited packs are still produced so that Italian games can be played with them.

German speaking South Tyroleans [...] play Italian card games that require 40 cards

Indeed,

The Salisburghesi deck originally consisted of 33 cards, being the 32 cards used for Tyrolean games [...] plus [...] a wild card

This has since been increased to 40 cards as per most other Italian decks

Speaking of which,

40-card stripped decks [...] are the most common format found in Italy today.

This is the result of popular 16th and 17th century games

Trentine cards are sold in either packs of 40 or 52.

The Bergamasche pattern comes in decks of 40 cards only.

The Trevisane deck [...] comes in sets of 40 or 52.

the Triestine pack [...] was created in the mid-19th century [...] now only 40 card decks are sold.

the 40 card Primiera Bolognese set [...is] used for standard games

Fiorentine cards come in packs of 40

the Sardinian deck only contains the standard Italian set of 40

When it comes to Spanish-suited playing cards,

a deck is usually made up of 40 or 48 cards

Stripped decks have 40 cards

The Castilian pattern is the most widespread pattern in Spain.

[It] come[s] in packs of 40 or 50 cards.

The Mexican pattern [...] come[s] in decks of 40 cards

the Old Catalan pattern [...is] found in decks of 40 or 48 cards.

The Cádiz pattern [...is] found in decks of 40 or 50 cards.

The Modern Spanish Catalan pattern is the second most widespread pattern in Spain and is very common in Hispanic America.

[It] come[s] in decks of 40 or 50 cards.

The Parisian Spanish [...] pattern [...is] sold in decks of 40 or 50 cards.

The Piacentine pattern [...] come[s] in 40-card decks.

In conclusion,

The Spanish, Portuguese, Italians, and Latin Americans use mostly 40-card decks.

Furthermore,

The most popular card game in 16th-century Europe was Piquet, played with a 36-card deck

Around 1700, it [...] create[d] the 32-card deck, which is now the most popular format in France.

32 and 36-card decks are the most widespread in countries that were once part of the Holy Roman (the Low Countries, Germany, and Switzerland), Austro-Hungarian, and Russian empires.

The encyclopedic article also includes a picture of

A 32-card Piquet deck.

Last, but not least,

Germanic, Spanish and Italian Tarot variants [...] creat[e] a deck with as few as 32 cards.

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Roulette combined the numbers of hoca/biribi with an English wheel used in at least three games: roly-poly or rowlet, ace of hearts, and E/O (even and odd). The English had begun playing roly-poly in 1720, when they spun a small ball around a horizontal wheel with several slots, including two that gave the banker an automatic victory. Around the same time, ace of hearts featured a farolike layout and cards painted on the wheel. After outlawed roly-poly and ace of hearts by British Parliament in 1739, one gamester circumvented the law by creating E/O, a wheel with 40 slots, 20 each marked odd or even, with one of each marked for the bank. When the French first began playing roly-poly or roulette, they played the unnumbered English original. Besides changing the wheel's colors to red and black from white and black, the French made no changes until, in 1796, someone fused the numbered balls and layout of the smaller, street version of biribi with 36 numbers (indoor version has 70) with the wheel of roulette.

Excerpt from David G. Schwartz: Roll the bones (The history of gambling)

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