[feanaro]

I've been playing a board game daily for the last two weeks. As part of this game, a player has to draw one out of six unique cards. In the last five games, I've repeatedly drawn the same card. This is a real example.

1 / (1/6)^5 ≃ 7776

[MaximumYComb]

You can't rely on odds after an event has happened to determine probably. I could shuffle a deck containing 1000 unique cards and then look at their order. It's astronomically low that this order occurs but it did happen.

[joshuamorton]

When discussing conditional probability, this is absolutely what you can do.

Let's use your example. Conditional probability is P(A|B), the probability of event A, given that event B was observed. What's the probability that I am a magician, given that I shuffled the deck and when you saw it it was still in new deck order?

Now certainly, there is an astronomically small chance that this was observed due to random chance. And yet if you observed this, I'd expect that you would, with relatively high confidence, believe that I stacked the deck.

[feanaro]

I'm not doing anything different than what we are doing when discussing the improbability of a hypothetical 10-heads-in-a-row event.