Does an opponent showing a card effect odds of them having a 1 outer?

Question

Let's say that you win in every possible situation except the other player having exactly the Ace of Spades. If they show you one of their cards is a 10 of Hearts, does that change the odds of them having that Ace?

My thinking here is that you already knew that at least one of their cards was not an Ace of Spades, so you aren't gaining any information by them showing you what one card is. They aren't randomly picking a card to show you, they are purposefully showing a card that is not an Ace of Spades, and no matter what hand they had, they always had a card that was not that Ace.

Answer 1

One card actually does reveal some information. You can try and figure out your opponents range in this certain spot. And then you can split the range into two parts: one without the ace of spades and one with the ace of spades. You have yourself a percentage of hands that contain the ace of spades. Now you can cross out the combinations that aren't possible anymore given the card that your opponent showed. What you are left with are the possible hands that contain the ace of spades that your opponent could have had in that spot. Which could definitely be a different percentage from the previous range of hands that contained the ace of spades.

Answer 2

I agree it is directly telling you nothing. It changes nothing about the other card if they got to pick. Clearly they have one card that is not the ace of spades.

But it is information. If it is the 7 of clubs and they opened early, called a big raise, or raised then you can factor in playing A7o is not as likely.

If they show you a card that makes no sense with that ace then they are just plain stupid or they were playing a wild hand and want a call. It is much different than a card you happened to see - it is a card they wanted you to see.

If it is a spade then Ax suited makes sense. A king or queen validates the other could be an ace.

You get to run the bets knowing one card and decide if their story makes sense.

ATo is a hand they could be playing from mid to late position and in the blinds. They could even be playing ATo light from early position. It tells you the other card could be an ace.

I would say they want you off the hand so you should call. But a very advanced player could be two steps ahead.

It is breaking the rules and they could get a penalty but I seriously doubt they would kill the hand. I don't think they should kill the hand.