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Your logic would be the same as: You have a form of cancer that is operable. 80% of patients die on the operating table. But, your logic is you either “die or you don’t” so it’s 50/50.

66% is 66% There is no other possibility.

Yes, but, I took away a card at random before he was forced to pick a goat. Which now gives me the information I need to pick the car 66% of the time. You seem to think pulling out the card or door randomly at first doesn’t matter. It absolutely does.

Nope. I’m guaranteeing I will win 66% of the time.

It’s a suckers bet the other way around too. I tell you, You take three cards. 2, 2, A. You mix them up and I pull a card off to the side You get to look at both cards. And you absolutely have to turn over a 2. You cannot turn over the A. I will never look at the card I off to the side. I...

You went wrong because you got to take on door away randomly. He doesn’t get to make a random choice. That’s where you went wrong. His two cards are of random choice. But his choice is not allowed to be random.

Because you pick one first. It’s 1/3 or 33% that you pick the car. Which means by default, you will lose 66%. Which means by default, he will have the car under one of the two cards 66% of the time. He’s *NOT* allowed to flip over the car. So, if he has the car 66% of the time, he has to show...

A non conditional scenario would be: You pick a card at random. I pick a card at random. We turn over the last card. 33% of the time, that card is the car. So, let’s say 100 times. So, you lose 33x right away. Now, there’s 66 other times you get to pick 2 cards. You’ll win 33 times and lose...

The statement that it’s 50% is absolutely wrong. It would only be 50% if the goat he opens is random. And that’s only 50% of the 66% of the time he doesn’t randomly turn over the car.

Again, if you keep your choice, you are 33%. If you swap, you are 66%. You are *always* wrong not to swap. If Monte didn’t get to look at the cards, that changes the entire scenario.

You should *always* swap doors in the scenario listed. It’s never the right play to keep your door. Ever. 1 time or 800 billion times.

Well, you let me know when you want to buy a new house or an island or whatever. I will bring as much money as you want to get. $55 when you win. $50 when I win. Or $150 and $100. Tell me when. I’ll bring as much money as you want to win.

If you’re so sure, you should be begging me to bring you money with better than 1/1 on your odds. The proposition I gave you, if you are correct, you could *never* lose in the long run. And I told you I would *never* quit.

That’s not the scenario.

So, how about my $150,000 to your $100,000 1,000 hands. 2, 2, A. $150 to $100 per hand We mix the cards. You pull one aside without looking. I look at the other two, and flip over one. You then flip over your hand. You do *not* have the option to swap. As you are getting 3/2 on what you say...

Your *unconditional* probability is 33% when you pick a card randomly. By default his *unconditional* probability is 66%. By looking at those two cards *AND* giving you a choice to swap, *after* he showed you 50% of the losing cards, he has now given away that 66% edge if you swap cards. This...

You were a 66% loser when you picked your card. He showed you 50% of that. With the knowledge that he can *NOT* flip the car over. That’s where your logic is flawed. You’re applying non conditional probability to a conditional probability scenario.

Then please take my money. I’m offering you better than 50% on what you say is 50%. And I’m telling you I will *never* quit. The only stipulation is we play at least 100 times. After 100x, you decide when we quit. I’ll keep playing you. I’ll bring $100,000 if you want.

Google it. They have literally run simulations on this.

Please come take my money. Your $50 vs my $55 per try. You can’t switch your hand. We can play 100 times, or 1 million times. And I’ll never quit.