We all know the drill. You pick door 1. Monte opens door 3, which is a loser. Are the odds in your favor if you switch picks to door 2, or do you stick with door 1?
The tons of rhetoric behind this issue is ludicrous. Everyone seems to be missing the simple answer.
First, we must know UNDER WHAT CIRCUMSTANCES Monty shows the losing third door. There are three possibilities:
- He only opens the odd (extra losing) door when the contestant is correct.
This info would soon be detected and exploited by the public, so it can be dismissed as a viable option.
- He only opens the odd door when the contestant is wrong.
- He opens the odd door as dictated by the hair that happens to be up his ass at the moment (randomly), OR he ALWAYS opens the odd door (since, after all, there is ALWAYS a loser door to open at this point).
Question: Do I change or stick with my original pick?
Answer: It doesn’t matter. Hell, if for no other reason, think about this…if a certain “pattern” of revealing doors in certain circumstances existed, then the “Let’s Make a Deal” staff would’ve figured it out long ago…
Once Monte opens one of the loser doors, your odds of winning BECOME 50/50. Your OVERALL odds of 33.3% haven’t changed, only NOW you know that AT THIS POINT you have a 50/50 shot. One door wins, one door loses. Period. Initially, your odds are 1/3. One door wins, two doors lose. HOW THE WINNER IS REVEALED has NO EFFECT on your initial odds of winning. Monte can always open one loser door and make it APPEAR that you now have a 50/50 shot, but in reality, your initial 1/3 odds haven’t changed. This is so painfully obvious that I can’t believe the amount of discussion that this topic has generated!
Case in point:
A coin flipped 100 times will, on average, land on heads/tails with a 50% rate. Say I flip a coin 10 times, and every time in comes up heads. Would you put your money on tails for the next flip? You might, but you’d better understand that there is still a 50/50 chance that it will come up heads again. The coin DOESN’T KNOW that it just came up heads for the 10th time, now does it?
Monte has 11 doors. You pick one. Your odds are 1 in 11. You’ve got one door, he’s got 10. He opens 9 of his 10, all losers. Now, he’s got 1, and you’ve got 1. One wins, one loses. Your odds AT THIS POINT are 50/50. Do you switch doors with him? Well, you can if you want, but it still doesn’t increase your OVERALL odds of winning. Your OVERALL odds of winning are still 1 in 11! Your OVERALL odds of winning do not change simply because you know how many losers there are AFTER THE FACT.
You buy a raffle ticket at a school. 1000 tickets were sold. Your odds of winning are 1 in 1000. You go to the raffle event. They call out 500 losers. You’re not one of them. Your odds are NOW 1 in 500 that your name will be called as a winner. This does NOT change the fact that your OVERALL odds are STILL 1 in 1000. Even if they call out all but you and someone else remaining to win. Your odds of winning NOW are 50/50. But, your OVERALL odds of winning in the first place are still 1 in 1000.
It doesn’t matter whether or not Monte reveals a loser door, as long as he does it without bias or circumstance. Your OVERALL odds of winning are 1 out of 3, no matter which way
you slice it. One door wins, two doors lose AT THE TIME YOU PICKED. NOTHING CHANGES THIS.
Those other arguments about “A boy shows up one day, and with a birth rate of 50/50, what are the odds that a girl will show up the next day” are ALL BS!! The coin didn’t remember what it “flipped as” last, why should a previous gender determine which gender should show up next?
50/50 is 50/50 is 50/50 no matter what happened in the past. The past doesn’t mean shit. The same can be said for any other win/lose ratio.
How do you think casinos stay in business? They stack the odds slightly in their favor, and live fat. If past occurrences had any actual effect on present odds, then the casinos would change their odds daily.
Coins don’t remember. Roullette wheels don’t remember. Past occurrences mean squat.
“A girl showed up yesterday, so odds are a boy will show up today”. Bullshit. If the birthrate is 50/50, then the odds of a boy/girl showing up today is 50/50, no matter who showed up before.
This seems so obvious…how can intelligent people get confused here???