From the get go the double or nothing gives you a 40% chance of doubling, but every double gives the next double a 25% point reduction, so 15% for the next, with 5% being the lowest. You can add 0.1% win chance per second you wait up to the 40% max. You can upgrade this, this is just the base.
So... Don't press the button... At most, once for a worse than roulette odds win, then wait 150 seconds before another press.