Field Bet Analysis: Single Roll Bet Probability and House Edge
In craps, field bets are a popular type of wager that allow players to bet on certain numbers being rolled. These bets offer a relatively high chance of winning but come with a higher house edge compared to other https://spartanscasinoca.com/ types of wagers. In this article, we will delve into the probability of single roll field bets and calculate the house edge associated with these wagers.
Understanding Field Bets
Field bets in craps are made on the outcome of a single roll of the dice. There are two main types of field bets:
- One or Two : This bet wins if either a 1 or 2 is rolled.
- Any Craps : This bet wins if either a 2, 3, or 12 is rolled.
These bets can be made on either the come-out roll or during the point establishment. When placed on the come-out roll, these bets lose automatically if the shooter rolls a natural (4, 5, 6, 8, 9, or 10).
Calculating Probability
To calculate the probability of winning a single roll field bet, we need to consider the total number of possible outcomes. Since each die has six faces and two dice are rolled in craps, there are 36 possible combinations:
1-1 1-2 1-3 … 6-5 6-6
We can calculate the probability of winning a field bet by counting the favorable outcomes and dividing it by the total number of outcomes. Let’s consider each type of field bet separately.
One or Two
The probability of rolling either a 1 or 2 is calculated as follows:
- Favorable outcomes: (1-1, 2-1)
- Total outcomes: 36
Probability = Number of favorable outcomes / Total number of outcomes = 2 / 36 = 11/72 ≈ 0.1536
This means that the probability of winning a one or two bet is approximately 15.36%.
Any Craps
The probability of rolling either a 2, 3, or 12 is calculated as follows:
- Favorable outcomes: (1-1, 2-1, 3-4)
- Total outcomes: 36
Probability = Number of favorable outcomes / Total number of outcomes = 8/36 = 2/9 ≈ 0.2222
This means that the probability of winning an any craps bet is approximately 22.22%.
House Edge
The house edge (HE) is a measure of how much the casino expects to earn from each wager placed. It can be calculated as follows:
House Edge = (1 – Probability of Winning) / Probability of Winning
Using this formula, we can calculate the house edge for both field bets.
One or Two
Probability of winning: 11/72 ≈ 0.1536 House Edge = (1 – 0.1536) / 0.1536 ≈ 0.8464
The house edge for a one or two bet is approximately 84.64%.
Any Craps
Probability of winning: 2/9 ≈ 0.2222 House Edge = (1 – 0.2222) / 0.2222 ≈ 0.7778
The house edge for an any craps bet is approximately 77.78%.
Comparison with Other Bets
To put these house edges into perspective, let’s compare them to other common wagers in craps.
- Pass Line : House edge: 1.4%
- Don’t Pass : House edge: 1.36%
- Come Bet : House edge: 1.17%
- Odds Bet : House edge: 0%
As we can see, field bets have significantly higher house edges compared to other wagers in craps.
Conclusion
Single roll field bets are a popular choice among craps players due to their relatively high chances of winning. However, these bets come with significant house edges that can eat into the player’s bankroll over time. Understanding the probability and house edge associated with each type of wager is crucial for making informed decisions at the table.
In this article, we calculated the probability and house edge for one or two and any craps field bets. While these bets offer a relatively high chance of winning, their house edges are significantly higher than other wagers in craps. By knowing the probabilities and house edges associated with each bet, players can make more informed decisions at the table and potentially minimize their losses.