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The Question I Have Involves the possible change in chance based on a changing sample size, if that sounds correct.

The Example is, you have 100 tiles, with 5 players, each grabbing 8 tiles each. Lets use this example for each player grabbing 8 at a time, or 8 one by one, turn by turn.

Does the Chance of getting particular tiles change as you go around for each person, with the first person with high odds of getting good tiles and the last the worst odds for getting good tiles? Or do you consider the bag of tiles as a whole for all players with equal odds of getting any tile?

Dylan Evans
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The odds on getting good tiles does not depend on the round, but it does depend on what you know has already been distributed -- perhaps by looking at your own rack and perhaps by peeking at other racks. If you have no information about what has been distributed, then the odds are the same in the last round as in the first. If two players have different information about what's been distributed, then they will calculate different odds for getting a good tile on the next round.

For example, consider the sole $K$ tile. Let $D_i$ be the draw at the $i$th step. Conditionally, $P(D_{i+1}=K|D_i=K)=0$ (there really is only one $K$ tile!) but unconditionally $P(D_{i+1}=K)=1/100.$ Likewise, $P(D_{i+1}=K|D_j \ne K~for~1 \le j \le i)=1/(100-i).$

Peter Leopold
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