This topic is probability neglect, the dangers of small probabilities. Another about how small probabilities are pushed down in the mind of the trader to become even smaller than they actually are. They are literally neglected in many cases. But there’s also another thing neglected that is probability; sometimes the neglect isn’t in the size of the probability but it’s in the opposite direction. It’s in over estimating a small, extremely small probability or extremely large probabilities in the opposition manner. This happens often in trading. In trading people are susceptible to it. Conservative traders tend to inflate small probability and make irrational decisions based on those inflations. You have 2 dangers here. You have either neglect probability or inflate probability.

So let’s start with an experiment that proved this cognitive bias. How much would you pay yourself from an electric shock the electric shock? if I told you ninety-nine percent probability that you would get a painful electric shock how much would you be willing to pay me not to press that button? In the experiment done on this exact same question, the average value is about $10. Most of these experiments done are on poor college students so they don’t have a lot of money but $10 for them is a decent price to spend to avoid that electric shock. The interesting part is when you give them a second probability. So you’ve got two groups in this experiment; one hears you got a 99% being shocked when I press this button; and the other one hears you have a 1% probability of being shocked if I press this button. How much would you pay me not to press the button if you have a 1% probability of getting shocked? In the second experiment they found that the average value was $7, very close to $10. but the difference in probability was almost zero to hundred that difference was so large but the difference in the money was so small it was almost as if people didn’t even care about the probability they just paying to avoid any possibility of that shock.

As you can imagine this affect Traders too. (**low probability high lost trades**)think about the negatives first, such as shorting a stock. When you short stock if you’re aware of the risks of shorting stock, technically you have infinite negative risk. if I short a stock and the owner of the company creates the cure cancer the next day the stock shoots up the moon , to numbers never seen before in the stock market, and you basically pretty much everyone shorting stock basically goes bankrupt. That’s the risk, the risk is bankruptcy. If you buy a stock, the risk is already embedded into the money just spent because he can’t lose more than what you spent on that stock. What’s the probability that the stock you shorted really does jump up all the way to a million? if it’s hitting a million dollars per share mean something amazing happened someone invented the cure for cancer, a new a new technology was invented that makes the internet superfluous, something amazing happened. That probability is probably less than 0.000001%. But the fact that infinite risk exists by shorting stock makes a lot of Traders avoid that particular strategy.

**(low probability High pay off trades**)Then there are things like breakouts, where small probability will benefit you. For example you’re on the other side of a trade you buy a penny stock and you hope that they’re going to cure cancer. If it happens you probably will be rich. it’s like buying a lottery ticket and this is the same reason people buy lottery ticket. Those probabilities or some people just like the idea of being exposed to that possibility. People in the math community will say never mind lottery ticket because the probabilities don’t make sense but he personally bought lottery tickets every day because he said he needs to make a bet every day. he needs to expose himself to possibilities that will improve his life so that was his irrational way of justifying buying a lottery ticket, even though he was a math professor.

In addition there’s option pricing. If you play options, you notice it when you buy an option you have lots of different prices. Basically anybody within margin accounts can buy an option. you need props $5 or $50 to buy a decent option, but those cheap options so popular and they’re popular because of the low probability of being inflated. They usually don’t pay off, you usually lose money by buying out of money short-term options. There’s always the in the money, long-term option, they cost a lot of money and they don’t seem as attractive as the options that are very unlikely to pay off but when they do pay off their payoff in ROI with four figures. So Traders are naturally drawn to these low probability High pay off trades and they stay away from the low probability high lost trades. It’s neither of those strategies are statistically appropriate. What you should be doing is calculating expectations .the expectation can be easily calculated through calculus or even through computer program. All you do is you check out the long term pay off versus what you pay and you get an expectation that tells you what you should be spending on that particular investment. The expectation in the long run this is what you should expect to make. You should probably take at least an entry-level statistic familiarize yourself with probability. You can also take a probability course. You don’t want to inflate or neglect small probabilities. Use expectations when you’re dealing with these small properties and in most cases the expectations will give you a good number to associate with those probabilities.