← Back to context

Comment by mettamage

8 hours ago

Hey I've started playing poker occasionally again, wanna have a chat about poker? My email is in my profile.

I used to be a winning player at small stakes about 20 years ago, so nothing major but enough for me to show that it's a game of skill.

But yea, for anyone interested why poker is a game of skill, it's due to the law of large numbers. You can easily see the law kick into effect when you simulate a dice roll and you win from 1 to 4 and the other wins 5 to 6 and you both get $1 if you win. I recently had to explain this concept so I happen to have the JS still lying around in my Chrome console.

  const rolls = 10_000;
  let a = 0;
  let b = 0;
  
  for (let i = 0; i < rolls; i++) {
    const die = Math.ceil(Math.random() * 6); // 1–6
    if (die <= 4) a++;
    else b++;
  }
  
  console.log(`Player A wins: $${a}`);
  console.log(`Player B wins: $${b}`);
  console.log(`Total paid out: $${a + b}`);
  console.log(`A's edge per game: ${(a - b) / rolls}`);
  console.log(`Difference: ${(a - b)}`);

Poker has much, much higher variance than dice though (or weighted coins, which is what you're actually modeling). It takes hundreds of thousands of hands to establish a statistically significant win rate.

At a common online pace of 1.5 hands per minute (live games are much slower) that's over a thousand hours of playing. I.e. even if playing for one hour every day, it takes years before a player knows whether they're profitable or not.

Seems disingenious to compare to dice when you presumably know poker belongs to that class of distributions to which the central limit theorem applies very slowly.