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I know that the probability is fair for the normal version (i.e. you stop drawing after the only short straw is drawn.) But what if there are 2 short straws? Wouldn't the odds change after the first is drawn?

Boyd Allsbrook
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    It may help to describe the "normal version" explicitly (how many people? how many straws? what is the goal?) for context. – angryavian Sep 13 '20 at 18:56
  • Say the normal version was 1 short straw, 3 long straws, 4 people. My question is, would the math hold true for 2 short straws, 2 long straws, 4 people, after the first of 2 short straws had been drawn? – Boyd Allsbrook Sep 13 '20 at 19:03
  • If the order of the people drawing is fixed, then the two scenarios are entirely different: in the second scenario, it is impossible for the 4th person to "lose" (get a short straw). – angryavian Sep 13 '20 at 19:05
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    What do you mean by "does the math hold true"? I still don't understand what question you are asking. – saulspatz Sep 13 '20 at 19:05
  • With four straws, two of which short, and all straws drawn, each of the possible pairs of people of the four are equally likely to have received a short straw and each of the four people have a $\frac{1}{2}$ probability of having drawn a short straw. Now... given that the first short straw was drawn by the first person then each of the three remaining people have an equally likely chance of drawing the remaining short straw. So, in that sense "after the first is drawn" yes, the odds change given that information... but it isn't clear if this was what you were after. – JMoravitz Sep 13 '20 at 19:08
  • This sounds a lot like If you draw two cards, what is the probability the second card is a queen?... that you are concerned about how a first draw impacts future draws. – JMoravitz Sep 13 '20 at 19:10
  • Is it that the first person to draw the short straw loses, and everyone else wins? – saulspatz Sep 13 '20 at 19:11
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    Now... if, as your comments suggest, you just draw until any short straw is drawn and stop drawing... then as pointed out after three straws are drawn at least one of them is guaranteed to have been a short straw (by pigeonhole principle), so a fourth person in line will not have had an opportunity to have drawn. – JMoravitz Sep 13 '20 at 19:12

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