So me and a friend else were having a debate recently. And I thrive to get a good answer to explain who's right.
So it's mainly about doubling someone's chances.
Here's the situation: There are 10 people at a party, and they all place their names (on a piece of paper) in a hat. The host of said party (who is included in the 10 people) is a nasty cheater and wants to double his chances. So he places his name in twice.
My friend claims that he Successfully doubled his chances because everybody else's chances are at 1/11 and his is 2/11, and 2/11 = 1/11 * 2.
But my logic goes as follows: he originally had 1/10 chance. Double that is 2/10. But by adding his name in twice he also increased the amount of names, so his new chance is 2/11. But 2/11 < 2/10, so he increased it by LESS than 2x.
Either my logic is really messed up, or his is. Who's correct.