This is my response to TheMathGuy's video The Monty Hall Paradox
http://www.youtube.com/watc...
This is one of my favorite math problems and Nate did a fantastic job explaining it. I've decided t...
This is one of my favorite math problems and Nate did a fantastic job explaining it. I've decided to look at a Monty Hall variant. Other Monty Hall variants can be found at Jason Rosenhouse's blog at:
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This is so simple. I think the poor guy donig the video may have overthought it completely.
You still have to stick with what you did.
Even if you changed it and took back your ace and happened to pair it up, ONE PAIR is virtually never going to be the best hand out of 8 players in the game.
Yes, you'll miss the flush almost every time but it's IRRELEVANT. You still have to try. The flush is your only chance to WIN against this number of opponents.
So going for the flush would be like (forgive the football analogies) an onside kick or going for it on 4th and long: a low probability play, but you do it anyway if it's your only shot at winning.
Sorry, my original math was off. You have a 44% chance of improving, a 48% chance of weakening, and a 6% chance of staying the same. These numbers were all rounded down, so may be off by a percentage point each.
To answer the "do you change your mind" question: no. If you discard the ace and then you should recant (since you now have a 75% chance of weakening your hand by discarding it). If you discarded the 2 then, you have actually got a better chance (30%, was 25%) of improving your hand now by staying with your original discard. Your chance of a flush has dropped to 5%.
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You still have to stick with what you did.
Even if you changed it and took back your ace and happened to pair it up, ONE PAIR is virtually never going to be the best hand out of 8 players in the game.
Yes, you'll miss the flush almost every time but it's IRRELEVANT. You still have to try. The flush is your only chance to WIN against this number of opponents.
So going for the flush would be like (forgive the football analogies) an onside kick or going for it on 4th and long: a low probability play, but you do it anyway if it's your only shot at winning.
That makes sense.