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Last Updated: October 21, 2016

# Rouleno

## Introduction

I first saw Roulino at the Max casino in Las Vegas on October 20, 2016. The name and game are a hybrid of roulette and keno. The game is based on the draw of six billiard balls, numbered one to six, and how many times the number of a ball matches the order it was drawn.

## Rules

Following are the rules. For such a simple game, it is surprisingly hard to explain. My proofreader was totally lost on what I was attempting to say. Hopefully, this revised wording will be a little better.

1. The game uses six billiard balls, numbered one to six.
2. The player makes bets and then the balls are placed into a wooden box and drawn out one at a time. As the balls are drawn they will be placed in numbered positions from 1 to 6. For example, the first ball drawn will be placed in position #1, the second in position #2, and so on.
3. Bets will be adjudicated mostly according to the number of times a ball matches in number and position (for example ball number 3 in the third position).
4. The available bets are as follows.
• Individual Numbers — There are six Individual Number bets, one on each number. Each wins if the chosen number matches its position. An exception is that the sequences of 1-2-3-4-6-5, 2-1-3-4-5-6, and 1-2-4-3-5-6 are automatic losers. Pays 5 to 1. For example, a bet on number five would win if the number five ball was the fifth ball to be drawn from the wooden box and the abovementioned sequences are avoided.
• Zero or Four matches — Wins on zero or four positional matches. Pays 3 to 2. The "or" is not a mistake. I guess the math worked out better by giving the player a win on four matches as well as zero, although it certainly makes the bet more confusing to explain.
• Any One or Four matches — Wins on one or four positional matches. Pays 3 to 2. Again, a win on four matches wins also.
• Any Two matches — Wins on two positional matches. Pays 4 to 1.
• Any Three matches — Wins on three positional matches. Pays 15 to 1.
• Any Four matches — Wins on four positional matches. Pays 40 to 1.
• Perfect/Perfect Reverse Wins if the balls are drawn in sequence (in either direction). — Pays 300 to 1.

Below is a scan of both sides of the rack card. Click on either image for a larger version.

## Examples

1. Assume the balls come out in this order, from first to last: 6-1-3-5-4-2. The only winning bets would be on the Individual Number 3 and "One or Four matches". This is because ball number 3 came in position 3. There were no other positional matches.
2. Assume the balls come out in this order, from first to last: 1-2-3-5-4-6. Winning bets would be on the Individual Numbers 1, 2, 3, and 6, because they all match the order in which they were drawn. With exactly four matches, a bet on "Zero or Four," "One or Four," and "Any Four" matches win as well.
3. Assume the balls come out in this order, from first to last: 1-2-4-3-5-6. This is one of the three dreaded exceptions to the Individual Number rules. Normally, balls 1, 2, 5, and 6 match the position they were drawn, but bets on those Individual Numbers would lose, because 1-2-4-3-5-6 is one of three losing exceptions. However, bets on exactly four matches, a bet on "Zero or Four," "One or Four," and "Any Four" matches still win, as in the second example.

## Analysis

The following table shows the number of winning combinations out of 720 possible, the probability of winning, and expected return of each type of bet.

### 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

At the lowest house edge of 1.67%, I recommend sticking to bets on the individual numbers.

Discussion about Rouleno in my forum at Wizard of Vegas.

Written by: Michael Shackleford

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