I know this is just a hypothetical question thread but what do you mean by "with a chance of 2 to 1"? Do you mean that I can either get 1 btc or 2 btc if I chose the 5 btc after gambling it? if so, wouldn't the 5 btc be the best option since there was no mention of the possibility of not getting anything if you chose the 5 btc?
It seems to me that the OP is one of those who post here because they are paid but don't actually gamble. There is no sense in what he says as he puts it.
But I'm going to assume he does make sense. In terms of EV, the 5 bitcoin possibility is more profitable than the bitcoin in hand. If we take the statement literally (which would be impossible in reality) that every time I try to win 5 bitcoin I win twice, i.e. 10 bitcoin, obviously this possibility has a higher EV. But let's assume that he meant the opposite, that every second time I try I will win once, and I only have one try. In other words, I have a 50% chance of winning. If I take the bitcoin I get 1 bitcoin, but if I try this bet, the EV is 2.5 bitcoins. Therefore, the second option is also more profitable.
So I would particularly go for the bet but I understand that for people that 1 bitcoin can solve their life, they would not risk staying with 0 for the possibility of winning 5 bitcoins.
One particular aspect to be considered is also the fact that it's not EV the only parameter.
Take this, for example: you pay 0.01 BTC to enter a lottery, and you get 0 with 50% probability, or 0.02 BTC with 50% probability?
The game is fair, would you enter? maybe yes, if you are risk-neutral.
Would you enter a lottery where you pay 1 BTC to enter to get 0 with 50% probability or 2 BTC with 50% probability?
It is the same exact chance of winning, but the payoff is greater. Maybe the risk of losing is shifting your risk aversion, so you want a hedge to the upside in your bet: you might want to enter a lottery where you pay 1 BTC to get 0 with 50% probability or 2.1 BTC with 50% probability.
This is only a simple model to make you understand how difficult is to estimate risk aversion.