Bankroll Truth

Each faint line is one possible run of this exact game. The bands hold the middle half and the middle ninety percent of them. The cone is the point: the average is a line, but nobody plays the average.

The bet ramp this bankroll can carry

Generated from the measured edge at each true count and your risk tolerance — not copied from a chart. Spread 1 to 7 units · playing every hand.

The chart, re-derived for your table

Basic strategy is not a tradition and it is not a document. It is the answer to an arithmetic problem, and the answer changes when the rules change. So this does not show you a chart — it works one out for the rules you set, by pricing every option and taking the best one.

This is a correctness claim, not an advantage claim. A chart derived for your exact table is right rather than approximately right; it does not beat the house on its own, and nothing here should be read as saying it does. The improvement that actually moves the number is the count.

Trip planner

Every assumption behind these numbers

Nothing here is buried in a settings screen. Change any of it and every number above re-flows immediately.

Decks

6

Dealer on soft 17

hits

Blackjack pays

3:2

Double after split

yes

Late surrender

no

Resplit aces

no

Penetration

75%

Hands per hour dealt

100

Hands per hour played

100

Unit

$25

Bankroll

$10,000 · 400u

Bet sizing

50% Kelly, capped at 12u

Counting system

Hi-Lo, running count over decks remaining

Session length

4 hours

True count is running count divided by decks remaining, estimated from the discard tray the way a player actually estimates it.

Playing decisions come from the same strategy engine the drills and the graded test use — basic strategy for a basic player, plus the index deviations and the insurance rule for a counting player.

Your sessions against this curve

Members who log sessions can lay their real results over the expected line and its bands, and see whether a bad month is variance or a leak. The tracker answers what happened; this answers whether it was normal.

The calculator above is complete and free. This overlay needs your logged sessions, which is the only reason it sits behind an account.

How this works, and how to check it

Two independent layers compute every number on this page, and they are built to disagree if either one is wrong.

The CLOSED-FORM layer is standard applied probability. A bankroll is treated as a random walk, which over many rounds behaves like Brownian motion with drift — and that approximation is what makes exact formulas possible. Expected value is linear in the number of rounds; standard deviation grows with the square root of it; risk of ruin follows from the classical barrier problems that have been in the literature for a century; optimal bet sizing follows Kelly's growth criterion. None of this is proprietary to anyone, and every formula is derived in the comments of the source rather than asserted.

The SIMULATION layer plays actual hands. It deals seeded shoes and plays them with the same strategy engine the drills and the graded test use — the same basic strategy, the same index deviations, the same insurance rule. Nothing is imported from anyone else's software, and no reference table was copied from any source: every figure this page shows was produced by playing the hands here.

The two layers are cross-checked against each other. The simulation measures the edge and the spread of outcomes; the closed form predicts what the risk of ruin should be given those measurements; and the simulation is then run again as thousands of independent bankroll paths to see how often ruin actually happens. Where the two agree, you can trust either. Where they disagree, the simulation is the more honest one, because it made fewer assumptions — and the disagreement is reported rather than smoothed away.

The approximation is weakest over short horizons and with bets that are large relative to the bankroll. That is exactly where a session-length answer matters most, so treat short-run numbers as the roughest thing on the page.