Another way of thinking about it is betting your entire bankroll for 99.9…% certainty that you will win $1.
Say you go into the casino with $1000.
Bet:
<span style="color:#323232;">$1 lose.
</span><span style="color:#323232;">$3 lose.
</span><span style="color:#323232;">$9 lose.
</span><span style="color:#323232;">$27 lose.
</span><span style="color:#323232;">$81 lose.
</span><span style="color:#323232;">$243 lose.
</span><span style="color:#323232;">$729 oh wait you can't bet that much, you only have $457 left. Dang, do you bet $457 or find another $272?
</span><span style="color:#323232;">
</span><span style="color:#323232;">Bet $457 and you win $914! Congrats you're now only down $86!
</span><span style="color:#323232;">Or maybe you lost and are down $1000.
</span><span style="color:#323232;">
</span><span style="color:#323232;">Or maybe you scrounged up $272 so you could keep playing
</span><span style="color:#323232;">Bet 729 and lose. Now you're down $1272.
</span><span style="color:#323232;">Or
</span><span style="color:#323232;">Bet 729 and you win 1458. Pay back the $272 you borrowed from your buddy, you're still up $186.
</span><span style="color:#323232;">You just bet $729 dollars for a %50 chance of winning $186.
</span>
But what are the chances of getting 6 or 7 losses in a row? 1 in 64, or 128 respectively, actually worse because roulette wheels aren’t 50/50, they’re 18/19 (18 wins and 19 losses in 37 plays on average) or worse. So losing 6 times in a row will happen 1 in 54 plays, 7 losses is 1 in 106.
Google says roulette wheels spin 55 times per hour so with your strategy you will lose your bank roll in about one hour assuming your starting bet is 0.1% of your bank roll.