Last Updated: July 23, 2017

# Diceball

## Introduction

I noticed Diceball at the Holland Casino in Amsterdam on July 19, 2017. It was closed at the time but a friendly dealer filled me in on the rules. Briefly, the game is loosely based on craps but with a baseball theme. At the Holland casino it was played in a small tub.

## Rules

1. The game uses two ordinary dice.
2. The same player shall roll the dice until he rolls a seven, which causes every bet to lose, except the Seven Out. The turn to shoot the dice shall rotate around the table.
3. For purposes of the two main bets, it takes four successful rolls of the dice to achieve a "run." A successful roll is one that is not a total of seven.
4. The Run Line bet may be made only before a new shooter throws the dice the first time. It pays even money for at least one run.
5. The Grand Slam bet may also be made only before a new shooter throws the dice the first time. It pays 1 to 1 for three runs, 5 to 1 for four runs, 15 to 1 for five runs, and 35 to 1 for six or more runs.
6. The Seven Out bet pays 4 to 1 if the next roll is a total of seven, otherwise it loses.
7. There are six different "Pass Line" bets, which work like place bets in craps. Each wins if the specified total(s) are rolled before a seven. Following is a list of the six available Seven Out bets and what they pay:
• Total of 2 or 5 — Pays 1 to 1
• Total of 3 or 4 — Pays 1 to 1
• Total of 6 — Pays 1 to 1
• Total of 8 — Pays 1 to 1
• Total of 10 or 11 — Pays 1 to 1
• Total of 9 or 12 — Pays 1 to 1
8. There are six different "Hard Line" bets, which work like place bets in craps. Each wins if the total is rolled the "hard way," meaning the two dice land on the same number, before a total of seven. It should be noted that, unlike hard way bets in craps, they do not lose, if the desired total is rolled the easy way.
• Total of 2 — Pays 5 to 1
• Hard 4 (2 & 2) — Pays 5 to 1
• Hard 6 (3 & 3) — Pays 5 to 1
• Hard 8 (4 & 4) — Pays 5 to 1
• Hard 10 (5 & 5) — Pays 5 to 1
• Total of 12 — Pays 5 to 1

## Analysis

Following is my analysis of the Run Line bet.

### Run Line

Event Pays Combinations Probability Return
Win 1 625 0.482253 0.482253
Loss -1 671 0.517747 -0.517747
Total   1,296 1.000000 -0.035494

Following is my analysis of the Grand Slam bet.

### Grand Slam

Event Pays Probability Return
6 or more 35 0.012579115 0.440269032
5 15 0.013504938 0.202574071
4 5 0.02800384 0.140019198
3 1 0.058068762 0.058068762
2 or less -1 0.887843345 -0.887843345
Total   1 -0.046912281

Following is my analysis of the Seven Out bet.

### Seven Out

Event Pays Combinations Probability Return
Win 4 6 0.166667 0.666667
Loss -1 30 0.833333 -0.833333
Total   36 1.000000 -0.166667

Following is my analysis of all the Pass Line and Hard Line bets. The expected value is expressed on a per bet resolved basis.

### Pass Line and Hard Line Bets

Bet Pays Probability Expected
Value
2 5 0.142857 -0.142857
Hard 4 5 0.142857 -0.142857
Hard 6 5 0.142857 -0.142857
Hard 8 5 0.142857 -0.142857
Hard 10 5 0.142857 -0.142857
12 5 0.142857 -0.142857
2 or 5 1 0.454545 -0.090909
3 or 4 1 0.454545 -0.090909
6 1 0.454545 -0.090909
8 1 0.454545 -0.090909
10 or 11 1 0.454545 -0.090909
9 or 12 1 0.454545 -0.090909