I need an algorithm for a chance game

Hi,

I need an algorithm made for a simple chance game.

The chance game is just a simple 50/50 game where you either win or lose. Some examples include red or black, heads or tails and Yes or no.

The algorithm needs to favor towards the creator so that it keeps track of current profit and decide whether they are a winner or loser.

If they win with a bet of £10 for example they would win £10 and be left with £20 they would then have the option to bet that. If they win with that bet they would win £40 and be left with £60. They could then choose to bet that for the chance to win £180 and be left with £240

So to clarify the winnings:

1st game = 1 x bet
2nd game = 2 x bet
3rd game = 3 x bet
4th game = 4 x bet
5th game = 5 x bet

They can continue to do this as many times as they like, The algorithm should stop them from winning to much and keeping the house profitable! Every now and then it should allow them to win a fair amount of money.

I would like to highlight that this is for a school project to demonstrate fairness! It will be used to highlight how a software developer can control all the variables!
Al money used is fake and not real! The algorithm will only be used for students to convert in to a game of either their choice or this algorithm.