Heheh maybe he wants the bead as a consolation prize. Yeah raccoon I didn’t even see that on Mythbusters. When first heard of it I couldn’t believe it myself, but that lady with the high iq explained it well.
He picks, and his chances are 33.3. But if you were to make it 100 shells, his chances are 1. She went on to say 100 or 3 shells it’s still the same idea. If he takes away 98 empty shells your better off switching, just as if he takes away 1 out of 3. Really interesting stuff cause you wouldn’t believe it unless they ran a computer simulation to prove it’s true.
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Aye… I got thinking about it though. That’s right the only way to get true 50/50 odds is to switch. The odds become 50/50 after the shell is taken away, but not for you until you switch shells… Man I always thought it was one of those things that is what it is lol
The clown and shell riddle reminded me of another classic.
A clever man in ancient times was due to be tried for murder. He was given the opportunity to be tried by ‘Chance’. There would be 50 black beads and 50 white beads placed in a bowl. He would then be blindfolded and asked to pick. If the bead was white he would live. If it was black he would die.
He asked the court if he could distribute the beads into two bowls. He would then be blindfolded and the bowls shuffled around. He would then have to pick a bowl, without touching it, reach in and take a bead from it. There would still be 50 black beads and 50 white beads in total and he would still be blindfolded. The court decided they would grant his wish as they could not see how it would make any difference.
This clever man was delighted. He managed to increase his chances of survival to almost 75%. How did he do it?
BTW this is supposed to be a true story from ancient texts and in the original this guy was still very unlucky because despite shifting the odds very heavily in his favor he still ended up picking a black bead.
Well, it sounds good, but upon analysis, he still really had a 50% chance of losing. The idea, I guess, is that he had a 50% chance of a 50% chance of picking a black bead, for a total of 25% probability. The problem with this logic is that he also had a 50% chance of a 50% chance of picking a white bead, which means that he had equal probability either way. The only way he could increase his odds of living would be to pick twice. Of course, even a 50% probability of living, strictly by chance, in a murder trial, is already quite generous.
I don’t know if you’re directing this to me, or not. Here is what I’m saying. The man had asked for the beads to be divided into two bowls. The riddle didn’t specify how the beads were divided, but there are two ways that would make sense.
1) Equal amounts of both black and white beads in each bowl.
2) One bowl with all black beads and the other with all white beads.
If the idea was to increase the chance of survival, dividing into an all-black-beads bowl and all-white-beads bowl would not have helped because his “choosing” action would still yield exactly 50% statistical chance of picking the right bowl, then 100% chance of getting whichever color was in that bowl.
So, that leaves the method of dividing black and white beads evenly into two bowls. Going by the earlier comparison to the other bead riddle, I assumed this is what was meant. And looking at the supposed statistical benefit of changing one’s choice after a known bad choice is removed from the equation, it would seem the same benefit could be gained here. The idea is that he is now choosing twice - once for the bowl, and again for the bead, but not so. The choice of which bowl to pick from will statistically yield 100% chance of getting an equal amount of each color of beads, so it is effectively a non-change. Then, you are still left with a 50% chance of getting the right (or wrong) color of bead from whichever bowl you pick from.
Thinking even further into it, the man may have actually decreased his luck by dividing the beads. Even though in pure statistical chance, his odds are the same, in reality, he had fewer beads to draw from. If you think of polls that are done, or any sampling that is performed, the desire is always to have a larger percentage of the whole to be sampled. And, the larger your sample, the more accurate your results are considered to be. Same thing with star ratings of products we buy online. If five people out of five say the product is good, do you trust that? What about 9995 out of 10,000? Even though 5 out of 5 is a “better” rating, it is less reliable because you know there are billions of people in the world and a lot of them may just be not buying it because they already “know” it’s not worth having. So, back to the beads in the bowls. The guy could have had twice as many opportunities to grab a white bead. Although statistically he would have still had an equal chance at getting a black bead, in reality he may have fared better had he kept them all!
Here’s one of my favorites because although we use it as the expression for an unsolvable question it is actually very easily solved. (Hint: Think laterally.)