Problem → Inputs → Model → Outputs → Interpretation

Problem

Blackjack advantage play succeeds only when you understand the exact table in front of you. The usual “house edge charts” assume tidy combinations of rules, but real pits mix and match soft-17 behavior, split restrictions, surrender availability, and penetration depth. On top of that, recent cards bias the shoe’s composition and counting systems introduce true-count drift, so the betting ramp you brought from a playbook may no longer be optimal. The real question is not merely “is this game beatable?” but “how much EV per 100 hands does this precise ruleset produce, how volatile is my ramp, what bankroll do I need to keep ruin below 5%, and where does my edge actually originate?”

Inputs

The form captures the levers that matter. Bankroll and table minimum translate units into dollars and calibrate risk of ruin. Deck count, penetration fraction, and the soft-17 toggle define the structural backbone. Dropdowns for double-after-split, resplitting aces, and surrender policies encode the most impactful rule variations. Ten composition fields accept excess cards per deck so you can incorporate table-side observations like “two extra fives just left the shoe.” Counting parameters—starting true count, drift standard deviation, and betting efficiency—model how aggressively your system deploys capital.

New controls focus on execution. Hands per hour and session length convert the abstract per-hand EV into hourly dollars and session volatility. A target ruin slider solves for the bankroll required to stay under a chosen ruin probability, while the table-max field warns if your ramp ever exceeds posted limits. All inputs are mobile-friendly, labeled, and wired into a debounced recompute so the results update smoothly as you adjust the ramp.

Model

The engine layers three models. First, it computes a baseline edge using linear approximations for each rule change: decks, penetration, soft-17 behavior, surrender variants, DAS, and RSA each contribute a fractional edge shift. Composition adjustments apply a linear response model so that, for example, extra fives raise EV more than extra threes. True-count dynamics follow a Gaussian diffusion: the mean true count decays toward zero as cards are dealt, while the variance of the count grows according to the supplied standard deviation.

The expected value per hand remains the weighted sum of bucket edges times bet multiples, expressed in MathML as $E_{\text{hand}}={\displaystyle \sum _{k}P\left(k\right)·A\left(k\right)·B\left(k\right)}$. Variance uses the same summation with squared bet multiples. From these per-hand quantities the tool derives session statistics: EV, standard deviation, and the probability of finishing the session down despite a positive edge.

Risk of ruin employs the same diffusion approximation used in the poker planner, working in units of table minimum bets. The model also reports the classical $N_0=\frac{{\sigma }^2}{{\mu }^2}$, the number of hands needed for the expected edge to equal one standard deviation. Contributions from each rule and composition adjustment are tabulated so you can see precisely where the advantage originates.

Outputs

The results panel is divided into themed sections. EV & Variance lists per-100-hand EV, variance, the per-hand Sharpe ratio, and $N_0$. Session Outlook converts your ramp, hands-per-hour, and session length into session EV, session standard deviation, hourly EV, and the probability of finishing the session in the red or losing 10% of bankroll. If your ramp violates the table max, a warning appears inline.

Bankroll Planning reports the current risk of ruin and the bankroll required to satisfy the selected ruin threshold. True Count Drift offers a human-readable list of bucket probabilities, edges, and bet multiples so you can sanity-check your ramp. A new Edge Contribution Breakdown table itemizes how much each rule toggle and composition adjustment contributes to the overall edge, while the familiar heatmap shows EV swings when swapping H17/S17 and surrender policies. The CSV export now includes cumulative probabilities for each bucket to aid downstream spreadsheet analysis.

Interpretation

The expanded outputs let you interrogate a table from multiple angles. If the edge breakdown shows most of your advantage coming from late surrender, you know to abandon the shoe if the pit removes that rule. If the session outlook reports a 55% chance of a losing session despite a positive edge, you can recalibrate bankroll expectations or adjust the ramp to smooth volatility. The bankroll planner reverses the usual calculation: instead of asking “what is my ruin probability with $X,” you can solve “how deep must my bankroll be to guarantee ruin under 5%?”

Because the tool includes a table-max warning, you can verify that your top bucket fits within pit limits; if not, adjust the ramp before heat-checking a game. The shareable URL hash encodes every toggle, letting teammates audit assumptions or suggest adjustments on the fly.

Worked 6-Deck S17 DAS LS Example

Consider a $25-minimum, 6-deck shoe where the dealer stands on soft 17, DAS and RSA are allowed, and late surrender is offered. Penetration averages 75%, you log 100 hands per hour over four-hour sessions, and you run a Hi-Lo ramp of 1-2-4-6-10 units with betting efficiency 0.95. Your bankroll is $15,000 (600 units), and you log two extra fives and one extra ten per deck in the discard tray.

The calculator reports +0.68 units per 100 hands of EV and 17.9 units of variance. The per-hand Sharpe ratio is 0.16 and $N_0$ is about 700 hands. Session Outlook shows 400 hands per session, an expected profit of $680, session standard deviation around $4,400, and a 43% chance of a losing session; only 7% of sessions are expected to drop 10% of bankroll. Bankroll Planning reports a 3.1% ruin probability at your current bankroll and suggests roughly $18,800 would be required to cut ruin to 2%. The table-max warning stays silent because the top bet (10 units, $250) fits under a typical $500 max.

The contribution table highlights the sources of edge: baseline rules contribute −0.55%, S17 adds +0.20%, DAS adds +0.13%, late surrender adds +0.07%, and composition adds +0.10% thanks to the extra fives and tens. If the pit switched to H17, the heatmap confirms you would lose 0.20 percentage points of edge, and the contribution table would immediately show the penalty.

Rule & Ramp Comparison

The comparison shows that swapping S17 for H17 cuts hourly EV by $200 and more than doubles ruin risk. Dropping late surrender hurts nearly as much, so insisting on S17 or LS is justified unless penetration improves dramatically.

Assumptions, Limitations, and Practical Tips

The linear response model for composition is accurate for moderate deviations; extremely biased shoes or shuffle tracking require more detailed simulation. True-count drift is modeled as Gaussian—if you incorporate ace side counts or shuffle machines that reset the shoe unpredictably, calibrate the efficiency slider downward. Risk of ruin assumes bets can scale continuously; spreading across table-max caps or wonging out early will change the true distribution of results, so treat the ruin figure as directional.

Practical tips: (1) note the table max before you sit; the warning makes it obvious if your ramp must be toned down; (2) feed actual hands-per-hour measurements into the session outlook to set realistic expectations; (3) revisit composition inputs every shoe and watch how the contribution table responds; (4) export the CSV to monitor cumulative probabilities and verify ramp execution in post-session audits; (5) use the target-ruin slider as a team bankroll planning tool—backers can demand a bankroll consistent with the agreed ruin ceiling.

Testing Checklist

• Edge cases: zero efficiency or negative bet multiples collapse EV to zero and surface an explanatory warning.
• Validation: table-max warning fires when the ramp exceeds the limit; target ruin outside (0,1) reverts to 5%.
• Performance: cumulative bucket probabilities and session stats recompute instantly even on mid-range phones.
• Accessibility: aria-live status updates results, and helper text covers every new control.
• CSV export: includes cumulative probabilities so spreadsheet spot checks align with the on-page drift report.