What is the OpenAI token system and how do you count and optimise token usage?

import tiktoken

# Count tokens before sending (avoid surprises)
encoding = tiktoken.encoding_for_model("gpt-5.5")

def count_tokens(text: str, model: str = "gpt-5.5") -> int:
    enc = tiktoken.encoding_for_model(model)
    return len(enc.encode(text))

# Count tokens for a Chat Completions messages array:
def count_message_tokens(messages: list, model: str = "gpt-5.5") -> int:
    enc = tiktoken.encoding_for_model(model)
    total = 3  # reply overhead
    for msg in messages:
        total += 4  # per-message overhead
        for key, value in msg.items():
            total += len(enc.encode(str(value)))
    return total

# Example:
tokens = count_tokens("Write a Python function that sorts a list using quicksort.")
print(f"Prompt tokens: {tokens}")  # ~15 tokens

# Via API (most accurate, no tiktoken required):
response = client.responses.create(
    model="gpt-5.5",
    input="Explain recursion.",
)
print(f"Input tokens: {response.usage.input_tokens}")
print(f"Output tokens: {response.usage.output_tokens}")
print(f"Total: {response.usage.total_tokens}")