Mathematics and statistics are important to Texas Holdem poker and online option and stock trading because they help you better understand the risk and reward of the situation. Knowing the risk and reward in turn will help you gain realistic and Healthy Expectations. This way when things are going well, you will not go crazy and expose yourself to too much risk. Conversely if things are not going well, you will not give up.
Here’s is a Texas Holdem poker example.
My worst string of losing AA was 7 in a row.
We will assume that there was only a 20% chance of losing each of the 7 pocket aces. This means statistically the chance of losing seven AAs in a row is (20%*20%*20%*20%*20%*20%*20%) = .00128% or 1 out of 78,125. Does this mean it’s wrong to play AA? Of course not, you still welcome those situations because you know that your Expected Value is positive and that you will win in the long run.
Some people would call this bad luck. But it’s just statistics. If you play 10 tables at a time at 50 hands per hour for 4 hours a day, that equals 2000 hands a day. You do this for 2 years (we’ll use estimate 300 days/year) then you would have played 600*2000 = 1,200,000. With that knowledge, it is no longer surprising that a situation that happens only 1 out of 78,125 occurred. (I’m just surprised I’ve never lost eight AAs in a row! j/k. Knock on wood.)
Our Texas Holdem poker-like option positions are the same. Even though the winning percentage is currently 100%, 3 for 3, we know that there will come a day when we will take a loss. In fact, we can expect a losing month for every four winning money if our winning percentage is 80%. But that’s okay as long as the money we gain from the four winning month is greater than the loss we take on the losing month.
Looking at the math and stats will give a lot of people headaches. But knowing the mathematics and statistics when so much money is on the line will help you sleep better at night.
Expected Value (EV) - Texas Hold’em Poker Expected Value - n. The sum of all possible values for a random variable, each value multiplied by its probability of occurrence.Let us first apply this to Texas Hold’em Poker. The game starts with each player being dealt TWO cards.
- We will pretend that we have the strongest starting Texas Hold’em Poker starting hand, AA.
- We will also assume that our opponent was dealt the second strangest Texas Hold’em Poker starting hand, KK.
Because these hands are the two best starting hands, players often end up betting all their chips against each other (a.k.a. All-In). When this happens the KK opponent will only have a 18.55% chance to win, at best, while the player holding AA, will win 81.06% of the time. If we bet $1000 against each other our Expected Value formula will look like:
EV = (Winning Amount x Winning %) + (Losing Amount x Losing %)
EV = ($1000 x 81.06%) + (-$1000 x 18.55%)
EV = $810.6 - $185.5
EV = $775.1
This means that in the long run you will gain an average of $775.1 every time this situation happens.
In Texas Hold’em poker, you can sit in with $5, $10, $25, $50….even $2000, but
- There is a limit to the availability of high limit games
- Playing at higher limits equals harder competition (less positive EV situations)
- Time consuming - you only get dealt AA once every 225 hands
Expected Value (EV) - Stock or Index Option Trading Strategy
Stock or Index options allow us to create positions that are similar to having AA in a Texas Hold’em poker game but
- Allow us to trade at a much higher limit. In fact the minimum to establish a S&P Index Option position is approximately $2000.
- Increased limit does not decrease positive EV situations because of the size of the stock and option market. A $20,000 position will have the same risk/reward ratio as a $2000 position.
- Not time consuming. You can trade options on your own schedule.
