Rohit Sharma’s 15 Tosses and the House Edge

A Cautionary Tale of Martingale and Casino Odds

As expected, Rohit Sharma, the captain of the Indian cricket team, lost yet another toss, extending the team's coin toss losing streak in ODIs to 15 in a row. If you do the math, the odds of this happening are (0.5)^15, which come out to roughly 1 in 32,768. Pretty rare, right? And yet, here we are.

This got me thinking about why casinos are so good at what they do.

Take Roulette, for example. The probability of winning is 18/38, or about 47.37%. Sure, the house has an edge, but it’s not outrageous compared to some of the other games they offer.

For the longest time, I used to believe the Martingale strategy could work. It’s a simple approach: after every loss, you double your bet. The idea is that, sooner or later, you’ll win, and when you do, you’ll not only recover all your losses but also pocket the initial bet.

Here’s how it plays out if you start with 1,000 and bet 10:

• Lose → Bet 20 (Total lost: 10)

• Lose → Bet 40 (Total lost: 30)

• Lose → Bet 80 (Total lost: 70)

• Lose → Bet 160 (Total lost: 150)

• Lose → Bet 320 (Total lost: 310)

• Lose → Bet 640 (Total lost: 630)

By the end of the sixth loss, you’re left with 370, which isn’t enough to double your bet for the seventh round. Even if you’re starting with what seems like a decent amount, a streak of six losses can quickly wipe out your bankroll.

Now of course, six losses in a row is just bad luck, but remember its six if you are betting ten, to win ten. To win big, you would have to bet big, which would reduce the number of tries you get. And with the casino capping maximum bets, you can’t just keep doubling forever.

If 100 people go to a casino for a day, and 3 out of those 100 people go bankrupt, we may conclude that the probability of going bankrupt in the casino in a day is 3%. On the other hand, if 1 person goes to the casino 100 times, he isn’t playing with those 3% odds anymore. What’s interesting here is you cannot apply that 3% group probability to the individual time probability. Repetition matters.

All that to say, casinos have it figured out, and Rohit Sharma might want to stay away from one. Or rather, go to one if you think he’s already exhausted his so called “bad luck”!

Cover image taken from Unsplash