Understanding the Basics of Expected Value
Before diving into the calculation of expected wins with different bet sizes, it’s essential to have a solid grasp of the concept of expected value in gambling. Expected value (EV) is a mathematical term used to describe the average return on investment that a player can https://wildwestgoldblazingbountygame.com expect from a particular game or betting strategy.
What is Expected Value?
Expected value is calculated by multiplying the probability of winning by the amount won and subtracting the product of the probability of losing by the amount lost. In simpler terms, it represents the difference between what you might win and what you might lose in the long run.
For example, let’s consider a simple game where you bet $1 on a coin flip. If you win, you receive $2; if you lose, you lose your original $1. The expected value of this game can be calculated as follows:
Expected Value = (Probability of Winning x Amount Won) – (Probability of Losing x Amount Lost) = (0.5 x $2) – (0.5 x -$1) = $1
In this case, the expected value is $1, meaning that if you play this game many times, you can expect to break even on average.
Calculating Expected Wins with Different Bet Sizes
Now that we have a basic understanding of expected value, let’s explore how to calculate it for different bet sizes. This calculation involves determining the probability of winning and losing, as well as the amount won and lost, for each possible outcome.
Let’s consider a simple slot machine game where you can bet between $0.10 and $1 per spin. The game has an expected return-to-player (RTP) of 95%, which means that over time, it pays out $0.95 in winnings for every $1 bet.
Calculating Expected Value with Different Bet Sizes
To calculate the expected value with different bet sizes, we’ll use the following formula:
Expected Value = (Number of Wins x Amount Won per Win) – (Number of Losses x Amount Lost per Loss)
We’ll also need to determine the probability of winning and losing for each possible outcome.
For this example, let’s assume that the slot machine has a 40% chance of paying out on any given spin. This means that for every $1 bet:
- The number of wins = $0.4
- The amount won per win = $2 (since it pays out at an RTP of 95%)
- The number of losses = $0.6
- The amount lost per loss = -$1
Plugging these values into the expected value formula gives us:
Expected Value = ($0.4 x $2) – ($0.6 x -$1) = $0.8 + $0.6 = $1.40
This means that if you bet $1 on this slot machine, your expected win is $1.40.
Calculating Expected Value for Different Bet Sizes
Now that we have a basic understanding of how to calculate the expected value with different bet sizes, let’s explore some examples:
- Bet Size 0.10 : If you bet $0.10 on this slot machine, your number of wins would be $0.4 / $0.10 = 4. Your amount won per win remains at $2. Your number of losses would be $0.6 / $0.10 = 6, and your amount lost per loss is still -$1.
- Bet Size 0.25 : If you bet $0.25 on this slot machine, your number of wins becomes $0.4 / $0.25 = 1.6. Your amount won per win remains at $2. Your number of losses would be $0.6 / $0.25 = 2.4, and your amount lost per loss is still -$1.
Using the expected value formula for these different bet sizes gives us:
- Bet Size 0.10 : Expected Value = ($4 x $2) – ($6 x -$1) = $8 + $6 = $14
- Bet Size 0.25 : Expected Value = ($1.6 x $2) – ($2.4 x -$1) = $3.2 + $2.4 = $5.60
As you can see, the expected value changes with different bet sizes.
Tips and Strategies for Maximizing Wins
While calculating expected wins is a complex task, there are some general tips and strategies that can help maximize your chances of winning:
- Choose games with high RTP : Games with higher RTPs tend to offer better expected values.
- Bet within your means : Avoid betting more than you can afford to lose.
- Use bankroll management techniques : Divide your bankroll into smaller units to manage risk and maximize potential wins.
By understanding how to calculate expected wins with different bet sizes, you’ll be better equipped to make informed decisions about which games to play and how much to bet.
