The algorithm you described is called Binary Search. Here is a Python code implementation of the Binary Search algorithm:

```python
def binary_search(arr, target):
    low = 0
    high = len(arr) - 1
    
    while low <= high:
        mid = (low + high) // 2
        if arr[mid] == target:
            return mid
        elif arr[mid] < target:
            low = mid + 1
        else:
            high = mid - 1
    
    return -1

# Test the binary search algorithm
arr = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19]
target = 7
result = binary_search(arr, target)

if result != -1:
    print(f"Target {target} found at position {result}")
else:
    print("Target not found in the list")
```

This code defines a `binary_search` function that takes a sorted list `arr` and a target value `target`. It then performs the binary search algorithm to find the target value in the list and returns its position if found or `-1` if not found.

Feel free to test this code with different lists and target values to see how the Binary Search algorithm works.