How many buy-ins do you need for live cash poker?

Define the roll and the buy-in.

State how much money belongs to this poker scenario, what stake you actually play and your usual buy-in. Deposits and withdrawals change the roll, while session results describe the poker played.

At USD 2/5, a USD 500 buy-in is 100 big blinds. A USD 1,000 buy-in is 200 BB. The same number of buy-ins means different money and depth.

Then state your assumed true net edge after rake and mandatory costs, standard deviation, risk target and willingness or ability to move down. Game quality, depth, straddles and room fees can change the edge and SD.

A fictional fixed-stakes example.

Use USD 2/5, a USD 500 buy-in, assumed net edge 5 BB/100 hands and assumed SD 100 BB for a 100-hand result. These are illustrative inputs, not measured live benchmarks. At an assumed 30 hands/hour, the net edge is 1.5 BB/hour.

Choose a 1% lifetime risk target in the fixed-stakes model. In the bankroll tool, enter cash, big blind 5, buy-in depth 100 BB, live win rate 1.5 BB/hour, SD 100 per 100 hands, assumed hands/hour 30 and risk tolerance 1%.

The Brownian approximation is B = −s² × ln(r) / (2w), with B in BB, w and s for the same 100-hand block, and r = 0.01 for a 1% target. It gives about 4,605.17 BB. Rounding up to whole USD 500 buy-ins gives 47 buy-ins, or USD 23,500.

At that rounded bankroll, the model’s fixed-stakes ruin estimate is about 0.91%. The formula and diffusion assumptions are described by Chin and Ingenoso, §1; their original discussion starts with limit hold’em, not a measured live-NLHE population.

What that number assumes.

The calculation keeps stakes, true edge and variance constant, treats results as independent increments and continues indefinitely. Ruin means reaching zero. Real poker has discrete losses and minimum buy-ins, so being unable to continue can happen before zero.

Moving down, topping up, withdrawing money or changing games changes the question. The 1% figure is not a forecast for your next session. An unknown or non-positive true edge does not support a positive-edge bankroll result.

A recent winning sample does not establish the edge you entered. Assess observed-rate uncertainty separately, and change the inputs in the bankroll tool rather than treating 47 as a universal minimum.

Kelly asks a different bankroll question.

Kelly targets long-run expected logarithmic wealth growth. Thorp explains that objective; Aldous discusses the mean/variance approximation and uncertain inputs.

GoodRun’s advanced live cash comparison assumes continuous proportional stake rebalancing. Enter the same example’s edge, SD and 100 BB depth in that tool to reproduce the following references; its defaults may differ:

Here, half Kelly corresponds to 2.5% of bankroll per modeled buy-in. “Half” describes the fraction of Kelly exposure; it does not mean half the bankroll or a bet in one hand.

These Kelly references do not target the fixed-stakes 1% ruin figure above. The diffusion comparison is not an exact discrete Kelly solution from mean and SD alone. Large drawdowns remain possible, and half Kelly is not a safe-stake or zero-ruin promise. Actual BB and buy-in depth remain inputs.

Keep the inputs connected to your record.

Track all sessions, net costs and bankroll movements so the next review starts from consistent data. A changed rake structure or deeper game needs fresh assumptions.

Start with fixed-stakes bankroll planning, then use Kelly only for the separate growth comparison. GoodRun’s offline bankrolls and goals can keep the history together. This guide covers live cash, not tournament bankrolls.