I'm working on a little tool for drafting cards, but I'm having trouble wrapping my head around a probability problem I've run into.
The scenario is the following: (context is changed for easier explanation)
There's a deck of 10 cards, numbered 1-10. All the cards are red, except the last 2 (9 and 10), which are blue.
Then 3 players get "random" cards:
John will get a random red card
Bob will get a random red card
Annie will get a random card from the deck
In order to make sure a larger number of people can participate without their "pool" being empty when it's their turn to randomly get a card, the player with the smallest "pool" available gets to pick first. (In this case the guys who can only get red cards).
Now here's the thing.
Since John and Bob has already taken 2 of the red cards, it seems to me that the chance of Annie getting any one of the red cards is smaller, and thus, the chance of her having a blue card is greater.
Let's say I were to guess at which card Annie has. Would I be better off guessing "10", than say, "2"?
And if yes - is this possible to mitigate in some way, by for example applying a higher "Weight" on the random number generator to the pool already chosen from by others?