The first crucial step begins by determining the feasibility of your plan before you venture into the unknown.
The secret to all gambling is to identify a good bet, which is when your mathematical expectation is positive.
It is your overall outcome in the long run that matters whether you can stay victorious.
To begin, let us start with something familiar, a coin toss.
We all know that there are only 2 equally likely outcomes: either heads or tails with probability of each appearing is 0.
5.
Intuitively, if you were to bet $1 on say heads, you will end up not expecting to lose or win.
In fact, this result can be summarised mathematically as follows: Expectation = (Probability of Outcome 1)*(Profit/Loss if outcome 1 occurs) +(Probability of Outcome 2)*(Profit/Loss if outcome 2 occurs) where probabilities of both outcomes sum up to 1.
For this particular example, we have Expectation = (0.
5)*1 + (0.
5)*(-1) = 0 since you earn $1 if heads turns up with probability 0.
5 and you lose $1 should tails turn up with probability 0.
5.
Now what does this mean? It means in the long run, this is a fair game offering no advantage to the gambler.
Since most people are risk averse, they would most likely avoid this gamble.
Now let us consider the next scenario: Suppose a friend of mine wanted to profit from trading on horses.
He believe that he had found a fool-proof system to profit from betting on horses.
He decided to lay horses that have only a 0.
01 probability of winning (1%).
He claimed that these horses will be guaranteed to lose and he can thus collect money 99% of the time.
Sounds too good to be true? Let us assume he can collect $100 if the horse indeed lose.
However, if in the event that the black horse really wins, he had to suffer a loss of $10 000.
Is this a winning proposition? This question can be answered using mathematical expectation.
Expectation = 0.
99*(100) + 0.
01*(-10 000) = -1 In fact, the expectation is negative! Thus, in the long run, my dear friend is expected to lose even though he expects to win most of the time.
What had gone wrong here? The logic is that ultimately, granted enough games, a black horse has to win eventually.
For our example here, the black horse has to win 1 in 100 games.
The loss suffered by the gambler as a result of the black horse winning is far too great to be offset by the numerous times the gambler wins.
Thus, it is hardly a winning formula after all! Exercise: A successful trader earns $3 20% of the time, $5 30% of the time and $8 10% of the time.
He loses $4.
50 for the remaining 40% of the time.
What is his expectation? Solution: E = 0.
2*(3) + 0.
3*(5) + 0.
1*(8) + 0.
4*(-4.
50) = + 0.
82 As you can see from this example, without doing the necessary calculations, it is very difficult to gauge the profitability of a system.
One can avoid risking unnecessary capital testing his system by simply calculating the expectation to determine the feasibility of his plan.