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Variance & bankroll

Why a winning player can lose for thousands of hands, and how big a bankroll has to be to survive the swings.

8 steps, as text. step through the interactive version →

  1. 01, open this step in the interactive version

    Meet a good player. On average they win 5 every 100 hands. Watch their first 1,000.

  2. 02, open this step in the interactive version

    Up, down, up. Over 1,000 hands, luck is still much bigger than skill.

  3. 03, open this step in the interactive version

    Now twelve players, all exactly this good. Same skill, very different results.

  4. 04, open this step in the interactive version

    Some of them are losing after 1,000 hands. They’re playing well and still behind. That’s .

  5. 05, open this step in the interactive version

    Play longer. Over 50,000 hands the luck starts to even out and the skill shows.

  6. 06, open this step in the interactive version

    But you only get to the long run if you don’t go broke on the way. Say each of them started with 5 buy-ins.

  7. 07, open this step in the interactive version

    With 5 buy-ins, some winning players go broke before their edge shows. A bigger bankroll survives the swings.

  8. 08, open this step in the interactive version

    Choose a starting bankroll. How many of these good players make it?