[itsdsmurrell]

Probably depends on your aversion to losing it all. If it's a dollar go for it. If it's 100 dollars, again, take the bet. If it's your life savings of 50000 dollars and going to 0 would be worse for you than 70/30 doubling your money, you don't want to go for it.

[kqr]

Sure, much like the Kelly criterion would tell you. If your life savings are $50,000, and someone offers you an even odds bet but with a 70 % chance of winning, you get optimal growth by wagering $20,000. However, that assumes you'll get a large number of similar offers so that you can make your losses back later if you get unlucky now.

That said, growth is pretty close to optimal even for smaller wagers. This plot shows growth rate as a function of wager size: https://www.wolframalpha.com/input/?i=plot+log%2850+-+x%29*0...