**Trading** is a game of **probabilitie**s. Thinking in terms of probabilities and not ‘right and wrong’ is perhaps the most important mindset shift.

This **note** includes the following topics:

- Thinking in Probabilities
- The Casino Paradigm
- The Expectancy
- Win Rate VS Profit-to-Loss Ratio

### Thinking in Probabilities

- No one has the certainty to predict the future. It’s like asking what the next coin flip will be.
- None of the following entities can predict the future.
**AVOID**seeking the next**HOT stock tip**.- Nobel Prize-Winning Economist
- Financial Experts
- Newsletters
- CEO
- CNBC

**Question:** If nothing is predictable, how can we make money trading?

– Probability. With an **EDGE** *(probabilistic advantage)*, you will always win in the long run.

### The Casino Paradigm

- The Casino industry is built around the concept of
**probability**. - Take a Roulette game, where the outcome of the next spin is
*random*. But the casino/house is still profitable. *Why does the house win?*- The outcome of 10,000 spins is
*less random* - Betting on Red Or Black
- Probability of House Winning: 52.6%
**[EDGE]** - Probability of You Winning: 47.4%

- Probability of House Winning: 52.6%
- The outcome of 1 spin/trade is
*random*. But if you have an**EDGE**, you will make money after many trades.

- The outcome of 10,000 spins is
- No Edge, No Trading!!

### The Expectancy

- Expectancy: How much money can I make per trade?
- Three key elements
**Win Rate a.k.a Batting Average**: Number of profitable trades / Total number of trades**Average Profit**: Total profit / Number profitable trades**Average Loss**: Total loss / Number of unprofitable trades

**Use case**- If your expectancy is $100 and your total trades in a year is 150.
- You can
*estimate*your yearly profit to be $15,000.

```
Expectancy = (Win Rate x Avg Profit) - (Loss Rate x Avg Loss)
Sample:
Win Rate: 40%
Avg Profit: $1,000
Avg Loss: -$500
Expectancy == (40% * $1,000) - (60% * $500) = $100
i.e. You can expect to make $100 per trade over the long run.
```

```
Will you make $100 in every trade?
- No. In fact, 60% of your trade will be a loss.
- But you will still make an average of $100 per trade if you stick long enough with your plan.
```

### Win Rate VS Profit-to-Loss Ratio

**Win Rate a.k.a Batting Average**: Number of profitable trades / Total number of trades**Profit-to-Loss Ratio**: Average Profit / Average Loss- a.k.a Payoff Ratio or Avg Risk/Reward

```
## Best trading strategies have
- High Profit-to-Loss Ratio: >3
- Respectable Win Rate: >40% to 50%
```

**HIGH** Win Rate + **LOW** Profit-to-Loss Ratio

- Psychologically easy to trade since you win often. Hence attracts more people who can’t think in probabilities.
- But less robust since you do NOT have direct control over the market or
**win-rate**when the market changes.

**HIGH** Profit-to-Loss Ratio + **LOW** Win Rate

- More forgiving. With a
**Profit-to-Loss**ratio of 3, you can be wrong 7 out of 10 times and still make money. - Difficult to trade when losing streak occurs. Must be able to think in terms of probability and NOT certainty

```
Profit-to-Loss Ratio = Average Profit / Average Loss
Sample:
Avg Profit: $1,000
Avg Loss: -$500
Profit-to-Loss Ratio == $1,000 / $500 = 2:1
```

#### Breakeven Chart

- With a Profit-to-Loss Ratio of 2:1
**Break-even**: Even if you are correct only 35% (win-rate) of the time, you can still break even. i.e You can be wrong 65% of the time and still be break-even.**Profit**: Even if you are correct only 45% (win-rate) of the time, you can be making money. i.e You can be wrong 55% of the time and still be profitable.