Simulation for BTC1 bet:
EV = (83% x -BTC1) + (17% x BTC11) = +BTC1.04
Edit: calculation corrected, credit to Saint-loup
Correct, if the payout for correctly guessing the dice roll is x12 of your stake, while the odds of winning are 1 in 6, then the expected value can be calculated as follows:
EV = (1/6) * 12 - (5/6) * 1 = 1 - 5/6 = 1/6
The positive expected value suggests that over the long term, you would be expected to make a profit by taking this bet. However, in the short term, there is a high likelihood that you will lose your bet.
It's not the good EV calculation for me because x12 is usually used in the same way as @12.00 in decimal odds. For example at dice game or coin toss you say you are paid x2 if you win, you don't say you're paid x1. It means your stake back is usually included in the winnings while it's not a winning.
Then to get the EV of the game you need to do instead :
EV = (1/6) * 11 - (5/6) * 1 =11/6 - 5/6 = 6/6 = 1
It means you will win $1 on average each time you bet $1 at this game.