To estimate your risk of ruin before you spin, define your bankroll in THB, your bet unit, your expected edge (usually negative in casino games), and your game's variance, then run a simple spreadsheet model (binomial/normal) plus a Monte Carlo check. Use the result to size bets conservatively and set hard stop-loss and stop-win rules.
Preflight checklist for estimating risk of ruin
- Bankroll is a fixed amount (in THB) you can fully lose without borrowing.
- Bet unit is consistent (one "unit" = your base bet size in THB).
- Edge is expressed per bet as a decimal (e.g., -0.027 for -2.7%).
- Variance is defined for the same unit bet (not per hour, not per session).
- You wrote down a ruin line (e.g., 0 THB, or a "stop at 30% bankroll" threshold).
- You know the number of bets you plan to make (a session horizon).
- You will verify with simulation instead of trusting a single risk of ruin calculator output.
Critical inputs: bankroll, edge, variance, and bet units
This workflow fits intermediate players doing online casino bankroll management who can track bets and accept that casino games typically have a negative edge. It's also useful for roulette bankroll management because bet sizes are discrete and session horizons are easy to define.
Skip this method (or simplify it) if you can't keep bet size consistent, you plan to chase losses, you don't know the payout structure (variance), or you're mixing multiple games without separating results. In those cases, a "one-number" bankroll management calculator tends to be misleading.
Choosing a model: Kelly, Gambler's Ruin, and binomial approximations
You only need a spreadsheet (Excel/Google Sheets) and one of these model styles:
- Binomial/normal approximation (practical default): best when you can estimate mean and variance per bet and you want "probability of dropping below a threshold within N bets."
- Gambler's Ruin (discrete win/lose steps): best when each bet has a fixed win amount and loss amount and probabilities are stable (a stylized coin-flip type game).
- Kelly framework (position sizing): best for gambling bankroll management when you have a positive edge (rare in casinos; more relevant to promotions, advantage play, or verified betting models). Fractional Kelly is still useful as a safety rule even with small/uncertain edges.
What you must have before calculating:
- Bankroll B in THB and base bet b in THB.
- Session horizon N bets (choose a number you will actually stop at).
- Per-bet expected value μ and per-bet standard deviation σ (in THB) for your chosen bet.
Spreadsheet-ready formulas and a ready-to-use table
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Lock your units (THB and one base bet)
Pick a base bet size b (THB). Convert everything to "per one bet of size b" so your risk doesn't get distorted by mixed stakes.
- Bankroll: B (THB)
- Ruin line: R (THB), often 0 or a safety floor like 0.3B
- Horizon: N bets
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Estimate edge as expected value per bet
If your game has house edge e (negative for most casino bets), set expected value per bet: μ = e × b.
- Example: b = 200 THB, e = -0.027 => μ = -5.4 THB per bet.
- If you don't know e, don't guess precision-treat it as a range and test worst-case.
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Estimate variance per bet (use outcomes, not "feelings")
Compute per-bet variance from the payout distribution of your bet type. For a simple win/lose bet: if you win +w with probability p and lose -l with probability (1-p), then:
- μ = p×w - (1-p)×l
- Var = p×(w-μ)2 + (1-p)×(-l-μ)2
- σ = SQRT(Var)
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Approximate "drop below ruin line within N bets"
For a fast, spreadsheet-friendly estimate, model the bankroll after N bets as approximately normal: SN = B + Nμ with standard deviation SDN = σ×SQRT(N).
- Approximate probability of being below R at bet N: P(SN ≤ R) ≈ NORM.DIST(R, B+Nμ, σ×SQRT(N), TRUE)
- This is a lower-bound style check for "end-of-session ruin." To approximate "any-time during the session," use simulation (next section).
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Cross-check with a discrete Gambler's Ruin when applicable
If each bet moves you up/down by a fixed amount (same w and l every time), you can also compute a discrete ruin probability against a fixed boundary. Use it as a sanity check against your risk of ruin calculator or spreadsheet normal approximation.
- Use this only when outcomes are truly step-like (not complex bonus features).
Compact comparison table (three scenarios)
Use the table as a spreadsheet template: fill your own inputs and let the formulas produce a comparable "end-of-horizon below ruin line" estimate. Values are intentionally left blank because you must use your game's true payout distribution.
| Scenario | Typical use | Inputs you enter (per base bet) | Spreadsheet outputs | Notes / when it fails |
|---|---|---|---|---|
| A: Fixed-stake even-money bet | Simple roulette outside bets; basic casino bets | B, R, N, b, p, w, l | μ, σ, P(SN ≤ R) | Fails if bet payouts change (side bets, bonuses, variable multipliers). |
| B: Volatile payout (wide outcomes) | Slots/bonus features where σ is large | B, R, N, b, outcome list {xi, qi} | μ = SUM(qixi), Var = SUM(qi(xi-μ)2) | Normal approximation gets rough; simulation becomes primary. |
| C: Positive-edge sizing check | Advantage play / promos / verified edge | B, b, edge estimate range, σ | Suggested stake via fractional Kelly; sensitivity table | Fails if edge estimate is uncertain; use conservative fractions and worst-case edge. |
Fast-track mode: the 4-step quick algorithm
- Set B, R, b, and N before playing; don't change them mid-session.
- Compute μ and σ per bet from the bet's payout distribution (or a conservative approximation).
- Calculate P(SN ≤ R) in your spreadsheet and treat it as a first-pass warning light.
- Run a Monte Carlo "any-time ruin" check; if results disagree, trust the simulation and reduce b.
Monte Carlo simulations: setup, sample size, and convergence checks
- Simulate bankroll path bet-by-bet (not only final outcome) so you capture "ruin at any time."
- Use the same stake rule you will actually follow (fixed b, fractional Kelly, or dynamic sizing).
- Hard-code a stop condition: end the run when bankroll ≤ R or when bets reach N.
- Run enough trials until the estimated ruin probability stabilizes (re-run with more trials and compare).
- Seed or randomize consistently so you can reproduce changes when you adjust inputs.
- Stress-test worst-case edge (more negative) and higher variance (more volatile) than your baseline.
- Check sensitivity: halve and double b; ruin probability should move materially-if not, your model is wrong.
- Validate the random outcome generator against your intended distribution (probabilities sum to 1, outcomes match bet rules).
Scaling bets: fractional Kelly, fixed stakes, and dynamic sizing
- Using Kelly sizing with a negative edge: it can recommend "zero" (which is correct); forcing it to bet anyway defeats the method.
- Mixing bet sizes while calculating μ and σ for a single base bet; this silently underestimates risk.
- Ignoring table limits/minimums: real-world constraints can prevent downsizing when bankroll drops.
- Confusing "per bet" edge with "per hour" results; risk of ruin is driven by the number of trials (bets).
- Using a stop-loss but still continuing to bet smaller "to win it back"; that's not a stop-loss rule.
- Assuming independence when your strategy changes after wins/losses (tilt/chasing creates dependence and worse tails).
- Estimating variance from a short, lucky session; volatility is usually undermeasured in small samples.
- Rounding errors: small μ with large σ can be sensitive-keep enough decimal precision in the sheet.
Interpreting results: thresholds, confidence levels, and stop-loss rules
Use the output to make a decision rule, not to "optimize excitement." Practical alternatives depending on your goal:
- Fixed-stake cap: choose b so that simulated "any-time ruin" to your floor R is acceptably low for your horizon N; best for casual sessions and strict limits.
- Fractional Kelly (only if edge > 0 and measured): stake = f × Kelly stake with f < 1; best when you want growth but must control drawdowns.
- Two-boundary plan: set both stop-loss (hit R) and stop-win (bankroll target); best for keeping session risk bounded in entertainment play.
- Shorter horizon: reduce N (fewer bets per session) instead of shrinking b; best when table minimums make b hard to lower.
Short clarifications on common calculation issues
Is a risk of ruin calculator accurate for roulette?
It can be directionally useful for roulette bankroll management if it matches your exact bet type and assumes fixed stakes. If it ignores table limits or you change bet sizing, the result can be overly optimistic.
What's the difference between end-of-session ruin and "ruin at any time"?
End-of-session checks only whether you're below the threshold after N bets. "Any-time ruin" is stricter and typically higher; you estimate it reliably via Monte Carlo path simulation.
Can I use a bankroll management calculator without variance?
You can, but it becomes a rough guess because variance drives drawdowns. If you can't estimate variance, use conservative assumptions and rely more on simulation with wide outcome ranges.
How do I choose N (number of bets) realistically?
Pick N as a hard session cap you will follow, not your average on a good day. If you often extend play, model the larger N because risk grows with more bets.
What bankroll number should I use for online casino bankroll management?
Use only money you pre-commit as the session bankroll, not total savings and not credit. If you top up mid-session, you're changing B and your calculated ruin probability no longer applies.
Why does my spreadsheet show a low risk but I still bust quickly sometimes?
Either the variance is higher than you modeled, or you are effectively increasing stakes (tilt, chasing, "pressing wins"). Recalculate σ and rerun the simulation with your real bet sizing behavior.
Does Kelly guarantee I won't go broke?
No. Kelly optimizes long-run growth under assumptions and can still suffer large drawdowns, especially if edge/variance estimates are wrong. Fractional Kelly and a ruin floor R reduce practical blow-ups.
