Trading: A Game of Probability

Trading is a game of probabilities. 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%
    • The outcome of 1 spin/trade is random. But if you have an EDGE, you will make money after many trades.
  • 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)

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

Avg Profit: $1,000
Avg Loss: -$500

Profit-to-Loss Ratio == $1,000 / $500 = 2:1

Breakeven Chart

Win Rate VS Profit-to-Loss Ratio

  • 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.

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