Therefore it is always better switch.
Edit:
The probability of the discarded option is added to the free option, because you have chosen before with a probability of 1/3. Many mathematicians judged Monty Hall because you would think that the odds would be 50/50, but that is not the case.
What you’re describing is the solution to the Monty hall problem where the probability goes from 1/3 to 2/3 when you switch. This puzzle is different, well because you’re given the fact that one of the private keys revealed a bitcoin. Just with this statement you know that the probability of your wallet picked being the 2 BTC wallet is no longer 1/3.
Here are all the possible wallets with keys laid out but we don’t know which wallet is which.
Wallet1 key 1: 1btc
Wallet1 key 2: 1btc
Wallet2 key 1: 1btc
Wallet2 key 2: 1ltc
Wallet3 key 1: 1ltc
Wallet3 key 2: 1ltc
As soon as it’s revealed we have a private key with 1 btc in our wallet. We know it’s between wallet 1 and 2. Now if we look at what the odds are of being wallet 1 or 2, we would see that it’s 2/3 odds that’s it’s wallet 1 based on the fact that we know we found a btc key (there are 3 btc keys between wallet 1 and 2), hence wallet 1 has 2/3 cases where the btc was from and wallet 2 has 1/3 cases.
Now that we know that we have a 2/3 probability of us picking the wallet with 2 btc, it becomes pretty clear that switching would reduce it to 1/3 and therefore we should not switch!