Gambling chances and buying insurance to increase winning chances problem

[Asstragal]

Hi,
I'm trying to figure out if it is worth buying insurance for a percentage increase of winning in this theoretical scenario. The math problem is as follows:

Suppose there is a gambling game where we need to bet 1000 dollars to roll the dice, or have the chance of winning. And we have a 30% chance of winning with each bet, 70% chance of failing. The goal is just to win. However, the gambling system allows us to buy insurance to increase our chances of winning. It will cost us 800 dollars to buy an insurance that will increase our chances of winning by 20%. So now, it will cost us $1800 to have a 50% chance of a random roll to win. The question is, is it worth it to buy that insurance? How do I write this in a mathematical equation and understand this problem a bit better?

Thank you in advance!

[Kalisspera]

You forgot to include how much you would win? It's worth buying if the expected net profit is positive, and that requires your answer to my first question.

[BrennanGardner]

Without insurance, you’re betting $1000 with a 30% chance of winning. The expected value depends on how much you stand to win. On the other hand, with insurance, you’re paying $1800 total for a 50% chance of winning.
To figure out if the insurance is worth it, you’d compare the expected outcomes of both scenarios. If the payout for winning is high enough, the insurance might be a good move. Otherwise, you’re probably better off sticking to the original bet. The missing piece here is knowing how much you actually win if you hit the jackpot—everything hinges on that.
Personally, I like keeping things simple when it comes to gambling. Playing online at http://bonusbet.com/ is more my style—no math required, just the fun of seeing how the odds play out.