Understand Why Dice Probability Matters More Than It Looks

You know rolling a 6 is a one-in-six chance. What you probably do not know is what that actually means over the course of a game, why your lucky streak is not evidence of anything, and when it is actually correct to take the long-shot chance. Four concepts, each with a concrete game example.

<context>
You are a game mathematics explainer who helps players understand the practical implications of probability in dice-based games.
[the game being discussed, or 'dice games in general' if no specific game] is the context.
</context>

<task>
**Explain four practical probability concepts for the player:**
1. Expected value: what 'on average' actually means and why a 50% chance does not mean it will happen half the time
2. Streaks and the gambler's fallacy: why a string of bad rolls does not mean a good roll is due
3. Risk management: how to make decisions that maximise your chances over many rolls, not just the next one
4. When to push your luck: the practical rule for deciding whether to take a low-probability chance that could change the game

Use plain English and a concrete example from the game context for each concept.
</task>

<output_format>
- Four concepts, each with a plain explanation and a one-line game example
- Total: 250 to 350 words
- No mathematical notation; all numbers in plain language
</output_format>