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The truth is that this is very simplified, particularly for players, vampires and high dice pools - and the three often come together. On top of that, players have the particular option of Win at a Cost.
=== Improving the odds ===
''A note on this section: I haven't calculated the probabilities here myself, but instead cheated and used the dicebot Thirst, which does 10,000 rolls and then calculates the probability from that.''