Michael

And there's £10 in my envelope. So what are the possible values of X where the sample space of the other envelope is ? It can't be 10, because 10 can'...

Yeah, which is \small B = \cfrac{\cfrac{10}{2} + 2*10}{2} = 12.5, hence the .25 gain.

Ironically, I coped your code from here and amended it as required.

1. There's a 50% chance that I have envelope X and a 50% chance that I have envelope 2X. 2. I have £10. 3. Therefore, there's a 50% chance that the ot...

England are genuinely the worst at penalties. Reality Check: Are England terrible at penalty shootouts?.

The issue is that there’s an expected gain for each game individually but that because each game that actually gains is offset by an equivalent game t...

Sigh

@"BlueBanana" Every amount has a 50% chance of winning for a 2:1 payout. It’s just that, like every after-the-fact bet, the result is prior to the bet...

Gareth Southgate.

You keep thinking about it as what would happen if you play repeatedly. I'm just talking about playing a single game. There's a 50% chance of winning ...

Everyone gets a fair chance. What’s the difference between me offering you a £20 bet regardless of your choice and me offering you a £20 bet only if y...

I offer you a fixed amount of £20 whether you pick the winner or the loser. It's just that if you pick the loser then I will offer someone else who pi...

The point is that it's an advantageous bet, even though I will ask you to bet £20 if you guess wrong and another person £10 if he guesses right, so th...

Clearly not clearly enough, as I didn't understand it. What is the sample space of the other envelope?

I have flipped a coin and know the result. I will let you bet on it with a 2:1 payout if you win. However, I decide how much you have to bet, and only...

Yes, and then I asked you what the sample space is for the other envelope, given that your envelope contains £10.

is our sample space for both envelopes, but given that we know that there's £10 in our envelope, what's our sample space for the other envelope?

Don't mention the war.

And officially.

On a related note there's this. Apparently one can use something called "Cover’s switching strategy" even if there is no upper bound for the amount th...

Such as this?

So you're saying that if there is no maximum then my switching strategy wouldn't make a difference, whereas if there is a maximum then my switching st...

There's always going to be a maximum because there's a finite number of games. One (or more) of them is going to have the highest randomly selected X....

Then why does this work?

Yes, so we bet £5 of our £10 and if we win we get £15 back (+£5 left over = £20) and if we lose we get £0 back (+£5 left over = £5).

So with this in mind I have a new strategy for repeated games. You switch on your first game and then in subsequent games only if your chosen envelope...

When you average it you change the value of the first envelope chosen, despite the fact that the question is "what should I do, given that I have £10 ...

So let's say I flip a coin and it lands heads, but I hide the result from you. How would you model the probability that you will win with a guess of t...

It is the game. I know that there’s £10 in my envelope. There’s a 50% chance that the other envelope contains £5 and a 50% chance that it contains £20...

Then forget about averages and just consider a single game. There’s a 50% chance of winning £10 and a 50% chance of losing £5. Is it advantageous to b...

I’m talking about the specific situation where I have £10 and there’s a 50% chance that the other envelope contains £5 and a 50% chance that the other...

How do you get that? If we play that game 100 times and switch then 50 times I win £20 and 50 times I win £5. That's £1,250. If we play that game 100 ...

Yes it does. It shows that there's a 2:1 payout with an even chance of winning. How is that not advantageous?

That's exactly what I've said. There's a 50% chance that my £10 envelope is envelope 2X, so a 50% chance of a switch getting me £5. There's a 50% chan...

The amount in my envelope is also fixed. So as the amount in my envelope is fixed to £10 and if X is fixed to 10 then it would be false to say that th...

That doesn't model the case we're considering, which is that we know we have £10. This goes back to what I was saying here:

That's the frequentist's interpretation. Although I don't understand what this has to do with my argument. I'm not saying that you're more likely to w...

So does yours. Here was your argument: There's a 50% chance that switching gets you X, and a 50% chance that it gets you 2X. Likewise if you stay. The...

Yes it can. We bet twice on a coin toss with a 2:1 payout. Half the time we bet £10, half the time we bet £20. We'd expect to break even. We switch en...

Like others you're conflating different values of X. Given that I know that I have £10: Thus, as you said, you either drew X or 2X. Therefore, there's...

I'm not talking about averages at all. I explained why this is misleading with the example of betting on a coin toss with a 2:1 payout, but where you ...

Yes, and you haven't explained how the reasoning is fallacious. In fact you agreed that my premises were true and the inferences are valid, the final ...

Neither am I. And this is misleading. Again, consider the case of betting on a coin toss with a 2:1 payout, but half the bets are £10 and half the bet...

What do you mean by switching being more profitable? I'm certainly not saying that if you switch then you will earn more money, because I accept that ...

So the premises are true and the inferences are valid but the argument isn't sound? That doesn't work.

Which step does it show to be wrong? Presumably it must be 2), 4), or 5)?

Regarding this, and the example of repeated games, consider betting twice on a coin toss with a 2:1 payout, but in the first game you bet £10 and in t...

We're not saying that you're more likely to have chosen the smaller envelope. We're saying that the amount you can win by switching is greater than th...

This is misleading reasoning. Compare: 1. I flip a coin and hide the result. I ask you for the probability that it is heads. You say 50%. 2. I flip a ...

This doesn't address my question. After having picked an envelope, but before looking, would I be right in saying that there's a 50% chance that my en...