See
my post here which lays out such a sequence which gives you a 49.649% chance of doubling your bankroll, compared to the 49.5% chance offered by the single 2x bet you propose.
I think that's far too complex for most people to understand.
I think a simple 2 (non-recursive) step process is best to convince people it's even possible.
* Get half your bet (0.5 BTC) and bet at @ 3x.
* If you win (33%), you've made a profit of 1 BTC, and have terminated the sequence! Congratulations!
* If you lost the first bet (67%), you'll still have 0.5 BTC. This time bet it at 4x (to win back your loss from step 1, and make a net profit of 1 btc).
* If you win the second bet (24.75%), you'll have made by your loss from the first bet, and be up 1 BTC, and terminated the sequence. Congratulations!
* If you lost the second bet (75.25%), you'll be out of money, and have terminated the sequence. Awww
![Sad](https://bitcointalk.org/Smileys/default/sad.gif)
So basically there's 3 possible outcomes:
1. You won 1 BTC with 1 bet (33%)
2. You won 1 BTC after 2 bets (67%*24.75% = 16.5825%)
3. You lost 1 BTC by losing both bets (67%*75.25% = 50.4175%)
In other words, you have a 49.5825% of winning, compared to the traditional 49.5%!
(Or course, Dooglus' solution is better. But it works in pretty much exactly the same way by minimizing the amount you wager)