Rouleno

Introduction

I discovered Roulino for the first time at the Max casino in Las Vegas on October 20, 2016. The name is a creative blend of roulette and keno, and the game is based on drawing six billiard balls, each numbered from one to six, and assessing the frequency of a ball's number matching the sequence in which it was drawn.

Rules

Here's a rundown of the game rules. Although it seems simple, explaining it has proven to be quite challenging. My proofreader struggled to grasp my explanation, so I hope this revised version will clarify things.

1. The game incorporates six billiard balls, each numbered from one to six.
2. Participants place their bets, after which the balls are put in a wooden box and drawn one by one. The drawn balls are arranged in a numbered sequence from 1 to 6. For example, the first ball that is drawn occupies position #1, the second one takes position #2, and this pattern continues.
3. Bets are evaluated primarily based on how many times a ball's number matches both its value and its drawn position (for instance, if ball number 3 is drawn in the third position).
4. The available bets are as follows.
   • Individual Number Bets — There are six bets available for individual numbers, one for each ball. A bet wins if the chosen number aligns with its position. However, certain sequences like 1-2-3-4-6-5, 2-1-3-4-5-6, and 1-2-4-3-5-6 are considered automatic losses. The payout for these bets is 5 to 1. For instance, a wager on number five is successful only if the number five ball is drawn as the fifth ball and the previously mentioned sequences are not drawn.
   • Winnings for Zero or Four Matches — This category wins if there are either zero matches or exactly four positional matches. The payout for these bets is 3 to 2. This is not a typographical error; the logic behind allowing both results was likely due to favorable odds, though it may create some confusion.
   • Any One or Four Matches — A win is achieved with either one or four positional matches. The payout remains at 3 to 2, and just like before, achieving four matches also results in a win.
   • Any Two Matches — A win occurs with two positional matches, and these bets pay out at 4 to 1.
   • Any Three Matches — A win is declared when there are three positional matches, with payouts set at 15 to 1.
   • Any Four Matches — This results in a win with four positional matches and offers a payout of 40 to 1.
   • Perfect/Perfect Reverse — This is won if the balls are drawn in a sequential manner, either in ascending or descending order. The payout for this condition is an impressive 300 to 1.

   Below is an image showing both sides of the rack card. Click on either side to see an enlarged view.

   Examples

   1. Let’s say the balls are drawn in the following order: 6-1-3-5-4-2. The only winning bets in this scenario would be for Individual Number 3 and 'One or Four matches', since ball number 3 is in its designated position. No other numbers matched their positions.
   2. Imagine the balls are drawn in this sequence: 1-2-3-5-4-6. In this case, successful bets would include Individual Numbers 1, 2, 3, and 6, as each corresponds to the position it was drawn. With four correct matches, bets placed on 'Zero or Four', 'One or Four', and 'Any Four' also win.
   3. Now, assume the balls are drawn in the sequence: 1-2-4-3-5-6. This is one of the three unfortunate exceptions regarding Individual Number bets. Typically, balls 1, 2, 5, and 6 would hit their positions correctly, but due to the specific sequence of 1-2-4-3-5-6, those Individual Bets would be voided. Nevertheless, bets with exactly four matches, along with 'Zero or Four', 'One or Four', and 'Any Four' still win, similar to the previous example.

   Analysis

   The table below illustrates the various winning combinations possible out of a total of 720, along with the winning probabilities and expected returns for each betting type.

   Rouleno Analysis

   Bet	Pays	Winning Combinations	Probability Win	Expected Return
   Individual Number	5	118	0.163889	-0.016667
   Zero or any four	1.5	280	0.388889	-0.027778
   Any one or four	1.5	279	0.387500	-0.031250
   Any two	4	135	0.187500	-0.062500
   Any three	15	40	0.055556	-0.111111
   Any four	40	15	0.020833	-0.145833
   Any 3, 4, 6, or perfect reverse	10	57	0.079167	-0.129167
   Six or perfect reverse	300	2	0.002778	-0.163889

   
   

   Strategy

   Given the minimal house edge of 1.67%, I suggest focusing on bets related to the individual numbers.

   External Links

   Discussion about Rouleno in my forum at Wizard of Vegas.

Written by: Michael Shackleford