Need a random process/distribution where I can pass a certain level of bias for producing an outcome

My first question here if am not clear please let me know. My objective a startup Sportsbook wants to test its algo to see how it manages game lines for incoming bets placed on a particular game. For example, as bets come in for a particular team the algo checks the book to see if it can cover and when the book is lob-sided it will adjust the line/odds giving the other team more favorable odds to balance the book on that particular game.

Where I need help with a simulation that picks the games. At the start, the assumption is that teams are 50/50. Once a team changes to 60/40 based on betting action I need a random process that would take this into account and change its propensity to pick the team at 40 since its odds of winning now are more favorable now. This balance continuously changes back and forth until the line closes.

What distribution or random process can I use where I can pass a parameter(s) and it will provide a bias in favor of the new odds as it changes in real-time. The outcome is 0 or 1 based on bias passed it should favor one more than the other based on odds passed in the parameters. Hope that makes sense.