Math Just Got Important

Added: 2026-05-30

[00:00:00]Hey, this is Presto Walker.

[00:00:03]Recently, Leila Hormozi tweeted, "Becoming successful is not luck. It's math.

[00:00:09]If your probability of success is 1 over 100, and you try 100 times, you have a 100% chance of success."

[00:00:19]This tweet got 3.7 million views, and I think you might understand why it has some of the ingredients for getting so much attention.

[00:00:28]Here we have a successful businesswoman, but she said that the success is not luck. It's mathematical.

[00:00:36]But then she makes an obvious mathematical mistake.

[00:00:41]This is when the internet loves to get together and try to humble someone who shows confidence.

[00:00:48]But I'm here to say it's a completely understandable mathematical mistake, and the entire episode actually has a pretty nice ending.

[00:00:56]So first, let me go through the math.

[00:00:58]It's understandable why you would make a mistake. If you have a coin, or you have two equally likely outcomes, in two tosses, you can expect a particular outcome like a heads. If you have a six-sided dice, you have six equally likely outcomes, so in six rolls, you can expect to see any particular number.

[00:01:18]If we extend this logic to a 100-sided dice, where you have a 100 equally likely outcomes, then in 100 rolls, you can expect to see one of the numbers.

[00:01:29]However, you are not guaranteed a success.

[00:01:32]In order to understand this process better, let us visualize what happens in 100 trials where you have a 1 over 100 chance of success in each trial, and a 99 over 100 chance of failure in each trial.

[00:01:47]So at the very first trial, you have a 99% chance that you'll fail. This is the bar that's denoted zero, and you have a 1% chance that you will succeed.

[00:01:58]If we increase the number of trials, slowly the chance that you will be at zero with no successes will decrease.

[00:02:07]But even as you get to 100 trials, there will still be about a 36.6% chance that you will have failed through 100 trials. So, you're not guaranteed a success in 100 trials, but you do have a high chance of success. So, if the chance you fail in 100 trials is about 37%, then the chance you will have at least one success is going to be about 63%.

[00:02:33]Let's calculate this by hand. Let's say we have a 100-sided dice, and we just want one of the outcomes to be a win, so one out of 100, and all of the other rolls will be a failure.

[00:02:44]The probability that we win in any of 100 rolls will be equal to 1 minus the probability that we lose for each of the 100 rolls.

[00:02:54]But since each roll is independent, this will be 1 minus the probability that we lose in the first trial, we lose in the second roll, and so on through all 100 rolls.

[00:03:05]So, this will be 1 minus the probability that we lose raised to the power of 100.

[00:03:10]The probability we lose will be 99 over 100, so this works out to be approximately 63.4%, and it's fun to generalize this calculation.

[00:03:21]Imagine we have an n-sided dice where we have n equally likely outcomes.

[00:03:26]The probability we win will be exactly one of those n outcomes.

[00:03:31]So, the probability that we win in any of n rolls will be 1 minus the probability that we lose in each of the n rolls.

[00:03:38]Since each trial is independent, we can multiply these probabilities together, so we end up with 1 minus the probability of a loss raised to the power of n.

[00:03:48]But the probability of a loss is 1 minus 1 over n, and now we need to raise that to the power of n and this is a famous limit.

[00:03:56]As n goes to infinity, this will tend to 1/e.

[00:04:00]So, this entire quantity is going to go to 1 - 1/e, which is approximately 0.632.

[00:04:08]It's a wonderful thing in probability when the number e just comes out of nowhere.

[00:04:13]But, the lesson is that if you have a probability of success of 1/n, you have n equally likely outcomes, then even if you try n times, you're still going to be limited to a success rate of about 63%.

[00:04:27]So, how do we increase the odds? Well, we're going to need to increase the number of trials. So, let's go back to the case where we have a probability of success of 1%. Imagine that we take 500 rolls.

[00:04:39]Well, the probability that we have a success in any of the 500 rolls will be 1 minus the probability of a loss in each of the 500 rolls. Each trial is going to be independent, so we do the same sort of calculation and we substitute in and we're going to get in this case that your probability of success is about 99.3%.

[00:04:59]So, now looping back to the original tweet, it was quite interesting that this garnered so much attention that readers decided to add context of the actual calculation. Trying 100 times with a 1/100 success probability per independent trials gives a 63% chance of at least one success, which is 1 minus 0.99 to the power of 100, so it's not a 100% success rate.

[00:05:26]What is quite interesting is that Leila Hormozi saw this and actually replied, "Community note is right. The chance of success is about 63% not 100%.

[00:05:37]Somehow I managed to function and become successful in business despite being atrociously bad at math, lol. Not a secret, you can ask my team.

[00:05:46]Here's what I meant to say. One attempt is equal to 1% odds, 100 attempts is equal to 63% odds, 500 attempts is equal to 99.3% odds.

[00:05:58]Persistence doesn't guarantee success.

[00:06:01]It does compound your probability until the math is eventually on your side.

[00:06:07]And now we know that the worse you are at math, the less time it takes. It was quite refreshing to see the response. In spite of all the negativity, in spite of all the names people called her, she eventually just admitted that her math was wrong and the community noticed right and she then corrected her mistake and gave the correct answer. You don't have to be perfect in math class, in every single word you say.

[00:06:31]People come at me for every single word that I say in my video. That's not what math is about. Math is about putting things out there, making calculations.

[00:06:40]Sometimes you're going to make mistakes.

[00:06:42]No one is perfect. But the good point is that you should learn from your mistake and you should keep trying. Success is about persistence and you have to keep trying a lot more than you would initially expect. Many people would give up after one attempt. Many people would definitely give up after 100 attempts.

[00:07:00]But it's the few people who try 500 times that have a higher chance of success.

[00:07:07]We can see this visually. When we try 100 times, we only have about a 63% chance of success.

[00:07:14]But bring this back to the beginning.

[00:07:17]When people see that if you try, you have a 99% chance of failure, most people will go even one step further and they won't even try at all.

[00:07:28]But I will tell all the armchair quarterbacks out there that you then have a 100% chance of failure because you miss 100% of the shots you don't take.

[00:07:39]You should always get out there and always try your best.

[00:07:44]Because failure is acceptable. It is not trying which is not acceptable.

[00:07:50]Action is better than inaction.

[00:07:54]Thanks for making us one of the best communities on YouTube.

[00:07:57]See you next episode of Mind Your Decisions where we solve the world's problems one video at a time.