please help me with this math probability question.

Question

Your friend is betting on a game in which the probability of winning is 1 in 5. He has lost 5 games in a row, so he says he will double his bet on the next game. What do you tell your friend?

Answer 1

If the game's events are independent, similar to flipping a coin, then the probability never changes, it's still 1 out of 5 chance of winning each time. The coin has no memory, so it will always have the same probability on each flip. If the games' events are like that, a losing streak doesn't mean a win is now more likely.

But if the events are not independent, it may make sense to increase the bet. for example, a bag has 10 coins and 2 are worth 100. You reach in and pull out 5 coins, all worth only a penny each. Your odds of getting one of the 2 $100 coins is now much greater than the original 1 out of 5 chance. You originally had a 2 out of 10 chance on the first draw. But now it's up to 2 out of the remaining 5 or 40% chance of winning.

There is another reason someone may wish to double their bet. If you doubled your bet each time you lost, you would eventually recoup all your losses. It can work. The only problem is you may also go bankrupt before you're able to double your bet enough times. That risk is usually considered too great to double your bets on independent events.