How Mathematics Helps You To Find The Best Porta Potty

The next time you get in line to use one of the portable restrooms at a fair, concert or any event, you might want to use mathematics to pick your potty. Yes, you heard it right, Maths.

The Secretary Problem, a Mathematical theory could be your best solution for this. But if you literally shit in your pants hearing the name of Maths, and no one’s blaming you there, you can always pick the best porta potty without an equation; just use Porties!

But for the sake of having some harmless fun, let’s go back to the toilet mathematics:


No need to panic the next time you have too much Pepsi to drink at a concert or festival and have to make a beeline to the portable toilets. According to a sequence of recent mathematical experiments, there is an ideal value that can be considered. For instance, consider a design model that consists of 3 different toilets. Let us label the toilet on the far left as Number1. Toilet 1 is amazingly clean, the very cleanest of the 3. The middle toilet is labeled Number 2 and is slightly dirtier than the first one. Toilet Number 3? A complete disaster zone. For obvious reasons, the toilets in real-time aren’t going to be limited to 3 nor will they be so pleasantly ordered. However, for this demo, we will stick with the 3 ordered toilets.

There are 6 different permutations; the different number of possible ways a group of toilets can be arranged in this model. This means that the probability of you hitting toilet number 1 gets worse as you keep adding more and more toilets. However, with just 3 toilets you have a 50% chance of picking toilet 1 if you follow the golden rule of rejecting the first toilet you check out and go for the portable potty that is, in your guess, the best so far. In all 6 probabilities, there is an average 50% chance of hitting the jackpot.


As mentioned before, adding more toilets decreases the odds of picking the most delightful toilet of all. If the demonstration given above had 4 toilets to choose from instead of 3, the percentage of success will drop to around 46 percent. With each new toilet thrown into the model your odds of succeeding drop by about 4%. The simulation illustrated works decently in limited toilet situations, obviously. However, many events offer far more toilets. In order to work on a bigger scale, another mathematical answer arises. Go through the text that is followed to learn the real trick (other than just using Porties) to find the best porta potty among a larger selection by using mathematics.


Mathematical theories suggest that you will have the best shot at finding the cleanest toilet by scoping out exactly 37% of the toilets out of the total number of toilets. After checking out at 37%, you can then follow the ‘best so far’ rule. After 37% of the restrooms have been tested, go for the very next toilet you find that seems better than all those you already tested. For example, if there are 100 toilets at a music concert, you must peek inside 37 of them to get past the tipping point. Only then your choice of whichever toilet after that appears better than all the restrooms you saw before, with a higher rate of a positive result in doing so.

There you have it now on how to use mathematics when trying to choose the best porta potty. No one can ever imagine in their wildest dreams that toilets and math had so much to do with each other. The next time you get into a hazardous toilet situation, test out this Secretary Problem mathematical theory. You might get surprised at how a little mathematics can help you go a long way when it comes to picking the most delightful toilet.

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