In the first section we will present elements of the game of Craps. Craps is a stateful game, and we’ll describe the state changes in some detail.
We will review some of the bets available on the Craps table in some depth. Craps offers some very obscure bets, and part of this obscurity stems from the opaque names for the various bets. Creating this wide variety of bets is an interesting programming exercise, and the first four exercise chapters will focus on this.
Finally, we will describe some common betting strategies that we will simulate. The betting strategies described in Roulette will be applied to Craps bets, forcing us to examine the Roulette solution for reuse opportunities.
Craps centers around a pair of dice with six sides. The 36 combinations form eleven numbers from 2 to 12; additionally, if the two die are equal, this is called a hardways , because the number was made “the hard way” . The table has a surface marked with spaces on which players can place bets . The names of the bets are opaque, and form an obscure jargon. There are several broad classification of bets, including those which follow the sequence of dice throws that make up a complete game , propositions based on only the next throw of the dice, and hardways bets. These bets will be defined more completely, below.
When the bets are placed, the dice are thrown by one of the players. This number resolves the one-roll bets that are winners or losers; it also determines the state change in the game, which may resolve any game-based winners and losers. The first roll of the dice can be an immediate win or loss for the game, or it can establish the point for the following rounds of this game. Subsequent rolls either make the point and win the game, roll a seven and lose the game, or the game continues. When the game is won, the winning player continues to shoot; a losing player passes the dice around the table to the next player.
In addition to the bets marked on the table, there are some additional bets which are not marked on the table. Some of these are called odds bets, or free odds bets, and pay off at odds that depend on the dice, not on the bet itself. An odds bet must be associated with a bet called a line bet, and are said to be “behind” the original bet; they can be called “behind the line odds” bets. The four line bets will be defined more fully, below.
There are slight variations in the bets available in different casinos. We’ll focus on a common subset of bets.
The dice form a frequency distribution with values from 2 to 12. An interesting preliminary exercise is to produce a table of this distribution with a small demonstration program. This frequency distribution is central to understanding the often cryptic rules for Craps. See Creating A Dice Frequency Distribution for a small application to develop this frequency distribution.
The Craps game has two states: point off and point on . When a player begins a game, the point is off; the initial throw of the dice is called the “come out roll” . The number thrown on the dice determines the next state, and also the bets that win or lose. The rules are summarized in the following table.
|State||Roll||Bet Resolution||Next State|
Point Off; the Come Out Roll.
Only Pass and Don’t Pass bets allowed.
|2, 3, 12||“Craps”: Pass bets lose, Don’t Pass bets win.||Point Off|
|7, 11||“Winner”: Pass bets win, Don’t Pass bets lose.||Point Off|
|4, 5, 6, 8, 9, 10||Point On the number rolled, p.|
Any additional bets may be placed.
|2, 3, 12||Nothing||Point still on|
|11||Nothing||Point still on|
|7||“Loser”: all bets lose. The table is cleared.||Point Off|
|Point, p||“Winner”: point is made, Pass bets win, Don’t Pass bets lose.||Point Off|
|Non-p number||Nothing; Come bets are activated||Point still on|
There is a symmetry to these rules. The most frequent number, 7, is either an immediate winner or an immediate loser. The next most frequent numbers are the six point numbers, 4, 5, 6, 8, 9, 10, which form three sets: 4 and 10 are high odds, 5 and 9 are middle odds, 6 and 8 are low odds. The relatively rare numbers (2, 3, 11 and 12) are handled specially on the first roll only, otherwise they are ignored. Because of the small distinction made between the craps numbers (2, 3 and 12), and 11, there is an obscure “C-E” bet to cover both craps and eleven.
Since Python is interpreted, you can enter the following directly in the interpreter and get the frequency of each number.
In Python, you will have to write and run a short program to produce the frequency distribution.
from collections import defaultdict freq= defaultdict(int) for d1 in range(6): for d2 in range(6): n= d1+d2+2 freq[n] += 1 print freq
There are four broad classification of bets: those which follow the sequence of dice throws that make up a complete game, those based on just the next throw of the dice (called proposition bets), the hardways bets and the unmarked bets. The game bets are called line bets, can be supplemented with additional odds bets, placed behind the line bet. There are actually two sets of game bets based on the pass line and the come line.
The following illustration shows the left half of a typical craps table layout. On the left are the game bets. On the right (in the center of the table) are the single-roll propositions.
Game Bets. The Game bets have two states. There is a set of bets allowed for the first roll, called the “come out” roll. If a point is established a number of additional bets become available. These are the pass line bets.
In addition to the basic pass line bets, there are also come line bets, which are similar to game bets.
Come Out Roll. When the point is off, the player will be making the come out roll, and only certain bets are available. Once the point is on, all bets are available.
The bets which are allowed on the come out roll are the Pass Line and Don’t Pass Line bets. These bets follow the action of the player’s game. There are several possible outcomes for these two bets.
Point Rolls. Once the point is on, there are three possible outcomes.
Come Line Bets. Once the point is on, the bets labeled Come and Don’t Come are allowed. These bets effectively form a game parallel to the main game, using a come point instead of the main game point. Instead of dropping the large “on” token in a numbered square on the layout, the house will move the individual Come and Don’t Come bets from their starting line into the numbered boxes (4, 5, 6, 8, 9, 10) to show which bets are placed on each point number. There are several possible outcomes for these two bets.
Propositions. There are also a number of one-roll propositions, including the individual numbers 2, 3, 7, 11, 12; also field (2, 3, 4, 9, 10, 11 or 12), any craps (2, 3 or 12), the horn (2, 3, 11 or 12), and a hop bet. These bets have no minimum, allowing a player to cover a number of them inexpensively.
Hardways. There are four hardways bets. These are bets that 4, 6, 8 or 10 will come up on two equal die (the hard way) before they come up on two unequal die (the easy way) or before a 7 is rolled. Hard 6, for example, is a bet that the pair (3,3) will be rolled before any of the other four combinations (1,5), (2,4), (5,1), (4,2) that total 6, or any of the 6 combinations that total 7. These bets can only be placed when the point is on, but they are neither single-roll propositions, nor are they tied to the game point.
Unmarked Bets. There are additional unmarked bets. One is to make a “place bet” on a number; these bets have a different set of odds than the odds bets behind a line bet. Other unmarked bets are to “buy” a number or “lay” a number, both of which involve paying a commission on the bet. Typically, only the six and eight are bought, and they can only be bought when they are not the point.
For programmers new to casino gambling, see Odds and Payouts for more information on odds payments for the various kinds of bets.
All of the Roulette betting strategies apply to Craps. However, the additional complication of Craps is the ability to have multiple working bets by placing additional bets during the game. The most important of these additional bets are the behind the line odds bets. Since these are paid at proper odds, they are the most desirable bets on the layout. The player, therefore, should place a Line bet, followed by a behind the line odds bet.
The other commonly used additional bets are the Come (or Don’t Come) bets. These increase the number of working bets. Since the additional odds bets for these pay proper odds, they are also highly desirable. A player can place a Come bet, followed by a behind the line odds bet on the specific number rolled.
Beyond this, there are the various proposition and hardways bets that can be placed in addition to other bets. While these propositions have odds that are incorrect, some players will count the number of throws in game, and place a “7” bet if the game lasts more than six throws. This is a form of betting against one’s self: there is a Pass Line bet that the game will be won, diluted by a 7 bet that the game will be lost. While the common rationale is that the second bet protects against a loss, it also reduces the potential win. We can simulate this kind of betting and examine the potential outcomes.
Craps has two forms of odds betting: right and wrong. The Pass Line and Come Line, as well as buying odds, are all “right”. The Don’t Pass, Don’t Come and Laying Odds are all “wrong”. Sometimes wrong betting is also called “the dark side”.
Right betting involves odds that provide a large reward for a small wager. The odds on a Pass Line bet for the number 4 are 2:1, you will win double your bet if the point is made. You put up $10 at risk to make $20.
Wrong betting involves odds that provide a small reward for a large wager. The odds on a Don’t Pass Line bet for the number 4 are described as “laid at 2:1” – in effect it is a 1:2 bet, you will win half of what you bet if the point is missed. You put $20 at risk to make $10.
This distinction can be ignored by novice programmers. None of our simulated players are wrong bettors, since this involves putting a large amount at risk for a small payout, which violates one of the basic rules of gambling.