Large-scale simulation

One million cards. OOB and Basic Strategy, compared.

Two simulated tracks of 1,000,001 cards each, dealt from the same shuffles. On the first, OddsOfBlackjack decides every hand and two bet-sizing rules are played side by side: OOB Graduated and OOB Selective. On the second, Basic Strategy plays every hand with a flat bet. Every stake uses a fixed $10 unit, and every account starts from $1,000.

1,000,001
cards on each track
187,395 OOB rounds; 187,382 Basic Strategy rounds
+$8,575
OOB Graduated — net result
main result of this comparison; 1 refill of $1,000, not counted as profit
+$1,490
OOB Selective — net result
same track and decisions; 2 refills of $1,000, not counted as profit
−$12,285
Basic Strategy — Flat Bet — net result
its own card path; 12 refills of $1,000, not counted as profit
Read these results with their limits:
Retrospective analysis Independent validation: Not yet performed.

Looking for the first one-million-card track (+$7,570) cited in Technical Whitepaper V1? It is a separate experiment, kept unchanged in the first-track archive.

The bet rules

The initial bet, in units, chosen by the pre-bet EV.

Both OOB rules read the same pre-bet EV of the shoe and play the same decisions; only the initial bet differs. Each lower bound is inclusive. Doubles and splits add the same initial bet again. In this simulation one unit was always $10.

Pre-bet EVOOB GraduatedOOB SelectiveBasic Strategy — Flat BetBS flat
Below −1.0% No bet No bet 1×
−1.0% to below +0.1% 1× 1× 1×
+0.1% to below +0.2% 2× 2× 1×
+0.2% to below +0.3% 3× 2× 1×
+0.3% to below +0.5% 4× 2× 1×
+0.5% to below +0.7% 6× 2× 1×
+0.7% to below +0.9% 8× 2× 1×
+0.9% to below +1.1% 10× 2× 1×
+1.1% and above 12× 13× 1×

Basic Strategy — Flat Bet bets 1× unit on every round, with no EV filter. The OOB track observes 51,433 rounds without a bet (pre-bet EV below −1.0%).

Card by card

Realised net result of each account across its track.

R is the realised net result: everything won minus everything staked, before any refill. Every line starts at $0. Use the buttons to show or hide each account; OOB Selective is hidden at first.

−$15,000 −$10,000 −$5,000 $0 +$5,000 +$10,000 +$15,000 +$20,000 0 200k 400k 600k 800k 1M Basic Strategy −$12,285 OOB Selective +$1,490 OOB Graduated +$8,575
All lines are hidden. Use the buttons above to show a line.
Horizontal axis: cards dealt on each account’s own track. Vertical axis: cumulative R in USD, starting at $0. Points every 2,500 cards keep the lowest, the highest and the last value of each interval, plus the exact points of each line’s lowest and highest R and of the start and end of its maximum drawdown, so no extreme or drawdown is smoothed away. Hover or tap the chart for values; on small screens the chart scrolls sideways.
Main indicators

OOB Graduated over 1,000,001 cards.

All figures in this block are for the OOB Graduated account.
OOB Graduated — net result (R)
+$8,575
final balance $10,575 − $1,000 start − $1,000 refill
OOB Graduated — model contribution (C)
+$4,089.20
sum of initial stake × pre-bet EV
OOB Graduated — maximum drawdown
$10,560
largest fall of R from a previous peak (+$18,405 to +$7,845)
OOB Graduated — initial stakes
$2,404,630
$2,663,240 staked including doubles and splits; largest initial bet $120
OOB Graduated — refills
1
$1,000 added when a stake could not be covered; funding, not profit
OOB Graduated — rounds with a bet
135,962
51,433 rounds observed without a bet
Comparison table

The three accounts, measure by measure.

MeasureOOB GraduatedOOB SelectiveBasic Strategy — Flat Bet
Net result R (USD) +$8,575 +$1,490 −$12,285
Model contribution C (USD) +$4,089.20 +$741.18 not available
Maximum drawdown of R (USD) $10,560 $8,580 $15,395
Lowest R (USD) −$1,810 −$2,190 −$12,500
Highest R (USD) +$18,405 +$7,730 +$2,895
Initial stakes (USD) $2,404,630 $1,881,710 $1,873,820
Total staked, including doubles and splits (USD) $2,663,240 $2,080,620 $2,064,520
Largest initial bet (USD) $120 $130 $10
Rounds with a bet / observed without a bet 135,962 / 51,433 135,962 / 51,433 187,382 / 0
Refills of $1,000: number / total (USD) 1 / $1,000 2 / $2,000 12 / $12,000
Final balance (USD) $10,575 $4,490 $715
Cards on the track 1,000,001 1,000,001 1,000,001

OOB Graduated ended +$8,575 and OOB Selective +$1,490 on the same OOB track; Basic Strategy — Flat Bet ended −$12,285 on its own track. C is available for the OOB accounts only: no EV model is attributed to Basic Strategy. The difference between R and C is the realised outcome minus the model contribution; it is not attributed entirely to variance.

Method, data and provenance

Everything needed to check the numbers.

Other bet-sizing variants on the OOB track

The OOB track carried three more accounts with the same decisions and the same participation; only their stakes differ. All use a constant $10 unit, start from $1,000 and receive a $1,000 refill only when a stake cannot be covered.

VariantLevelsR (USD)C (USD)Max. drawdownInitial stakesRefillsLargest bet
V1 1× to 12× unit, rising with EV (edge per unit 0.20%) +$1,535 −$136.14 $7,585 $1,863,270 1 $120
VERDE 1× / 2× / 8× unit +$1,115 −$1,284.09 $5,805 $1,745,860 1 $80
ROZ 1× / 2× / 8×–16× unit (by EV above +1.1%) +$1,295 +$804.26 $8,790 $1,869,000 2 $160

VERDE and ROZ use the same thresholds below +1.1% as OOB Selective (no bet below −1.0%, 1× to +0.1%, 2× to +1.1%). V1 has the shape of OOB Graduated with an edge per unit of 0.20%.

Methodology

Both tracks were produced by the OOB simulator from the same sequence of shuffles: an 8-deck shoe dealt to the cut card. On the OOB track every playing decision is taken by the engine from the exact remaining composition and the pre-bet EV is recorded before each round; rounds below −1.0% are observed without a bet. On the Basic Strategy track every round is played with Basic Strategy decisions and a 1× bet. Because decisions differ, the two tracks consume the cards differently and do not play identical hands.

Every account was simulated with its own balance and full accounting: each stake, double, split and payout, round by round. One unit was always $10, independent of the balance.

  • R = Σ (amount returned − amount staked) = final balance − $1,000 − refills.
  • C = Σ initial stake × pre-bet EV (OOB accounts only).
  • Maximum drawdown = largest fall of R from its previous peak (the start counts as a peak of $0).
  • Refills: $1,000 at the start; another $1,000 only when a stake could not be covered. A refill is funding, not profit.
Provenance and game rules
DatasetSecond simulation, 167 completed batches on each track, seed 20261006, completed 11 October 2026; two tracks with the same shuffles: OOB and Basic Strategy
Game rules8 decks, cut card at 208 of 416 (50% penetration), dealer stands on soft 17, no hole-card peek, double on any two cards, no double after split, up to 2 hands from a split, no resplitting aces, no hitting split aces, no surrender, blackjack pays 3:2
Engine buildOOB-ENG-b0681ede84a3 (historical; the current engine is OOB-ENG-992c737432c3)
SimulatorOOB-M6-de23a88e2d14
OOB journals (SHA-256, aggregate)2eb7700c818a7b885c0602007fad9a6a260c8239af90296b9684c6adb5ffa43a
Basic Strategy journals (SHA-256, aggregate)6e8fc60e7eb7c6bf331f2b0ac6a5e2569c0d868de028b412cf1e11b96679736c
Accounting checkFor every account and every round, R changes exactly by the round result, and the balance equals $1,000 plus refills plus R.
What this comparison does and does not show
  • It shows the realised results of three fixed-stake accounts on two simulated tracks of 1,000,001 cards, with exact accounting.
  • It is one pair of tracks, not an average: another million cards can end lower, or negative, for any account.
  • The OOB and Basic Strategy tracks share the same shuffles but follow separate card paths. Basic Strategy bets every round; the OOB accounts sit out rounds below −1.0% pre-bet EV.
  • Refills are funding, not profit; R already subtracts them.
  • It uses a fixed $10 unit. It does not test or validate the balance-based stake sizing of the current app.
  • It ran on the historical engine build OOB-ENG-b0681ede84a3; it was not rerun on the current engine OOB-ENG-992c737432c3.
  • OOB Selective was chosen after examining the first one-million-card track; this second simulation uses a different seed. It is not independent validation.
The first one-million-card track (archive)

An earlier, separate experiment reported +$7,570 for the Selective (MOV) ramp applied retrospectively to one simulated OOB track of 1,000,005 cards (seed 20261001), with no Basic Strategy track. Technical Whitepaper V1 describes that first track and cites this address for it; its chart and figures are kept unchanged at One Million Cards: First Track (Archive). Its result and this comparison come from different simulations and are not added together.