How to use simulations to test betting systems

Simulation is the best way to test an idea when an analytic formula is complex or unavailable. You simulate the same randomness as in the game (RNG), run thousands of "virtual" sessions with your betting system and see the distribution of results: average (EV), quantiles, frequency of "plus" outcomes, depth and duration of drawdowns. Below is a practical technique.

1) What exactly we model

1. Game: distribution of outcomes of one step (back/bet) - multiplier (X) to bet (0; 0. 2; 1; 5;...) or event model (hit/miss, bonuses).

2. Strategy: bet size and exit/pause rule (flat, progressions, break profit/stop loss, "break after L-streak").

3. Session: length (N) of steps or stop conditions (bank ≤ stop loss; achieved a break-profit; time limit).

The main thing: the strategy does not change the probability of outcomes, it changes the distribution of the session result (risk profile).

2) Basic simulation framework (algorithm)

1. Define a "distribution passport" for one step: values (x_j) and their probabilities (p_j) (sum (p_j=1)).

2. Initialize the bank (B_0), rate size (b_1) and counters.

3. For step (t = 1... N):

Randomly select the outcome (X_t) by (p_j).
Calculate the winnings (W_t=b_t\cdot X_t), net (R_t=W_t-b_t).
Update your bank (B_t=B_{t-1}+R_t).
According to the rules of the strategy, calculate the next (b_{t+1}) and check the stop conditions (stop loss/teak profit/break).
4. Save session metrics: total (B_T-B_0), max drawdown (max drawdown), session length, number of bonuses/significant hits.
5. Repeat M times (for example, 100,000 sessions). Plot the distribution of results.

3) Key metrics worth collecting

EV session: average total in rates or% of the bank.

Result quantiles: (Q_{50}), (Q_{75}), (Q_{90}), (Q_{95}).

Goal chance: (\mathbb {P} (\text {total }\ge 0%)), (\mathbb {P} (\ge + 20%)).

Risk of ruin: (\mathbb {P} (B_t\le 0\\text {or }\\le\text {stop loss})).

Max drawdown: median and 90th percentile of depth and duration of drawdowns.

Threshold waiting intervals (≥×10; bonus): median and 75th percentile.

Sensitivity: How metrics change with rate/session length variation.

4) How many runs do you need

For the "bodily" picture: M = 10,000 sessions by N = 1,000 steps.

For heavy tails (rare big wins): increase M to 100,000 + or use stratification/additional point scenarios (conditional simulations "if ≥×200 happened").

Rule: see stability of estimates - if EV/quantiles change noticeably when doubling M, increase M.

5) How to compare strategies correctly

Common random numbers (CRNs): Run strategies on the same sequence of random outcomes. So you reduce the spread and compare exactly the logic of the bets, and not the "luck of the noise."

Permutation test: the difference in average totals (\Delta) between A/B strategies - shuffle the A/B labels and see how often (\Delta ^	\ge	\Delta). This gives a (p) -value without assuming normality.
Bootstrap interval for (\Delta): Resample "total A, total B" pairs over sessions many times and take 2. 5–97. 5th percentile.

Important: if the expectation of the game is negative (RTP <100%), the "best" strategy is distinguished by risk and the form of distribution, and not a sign of expectation.

6) Accelerators and modeling techniques

Variation of common numbers (CRN) - must-have for comparisons.

Antithetic samples: Use pairs (U) and (1-U) to reduce variance of estimates.

Cumulative caching: Store CumP and binary search/" ≤ "for fast mapping (U\to X).

Aggregation by baskets: instead of accurate (x_j), combine payments into 4-6 intervals - a sharp increase in speed with an almost unchanged risk picture.

Markov states for sticky-mechanics and bonus-stairs: keep the state, transitions, instant rewards.

7) What is considered the "success" of the strategy

Fix the criterion in advance: for example,

"median drawdown ≤ 150 bets" and "chance of finishing ≥0% ≥ 40% per 1,000 spins," or "90th percentile of drawdown ≤ 300 bets at EV not worse than − 5% of the bank."

Without a criterion, any strategy will find a "beautiful window."

8) Type experiments

Flat vs progression (martingale, d'Alembert, build-up after hit): compare EV, (Q_{90}), risk of ruin, length of "deserts."

Break profit/stop loss: estimate the frequency of "early exit" and the price of missed tails.

Session length: how the chance changes ≥0% from 200 to 2,000 spins.

Buying a bonus: (EV_{\text{net}}=\mathbb{E}[X]-C) how dispersion and the risk of ruin are growing.

Rate size as a share of the bank: choose (f) to limit the 95th percentile of drawdown.

9) Typical mistakes and how to avoid them

After-the-fact fit: change strategy "in the course" of simulation. Fix the rules in advance.

Mix different RTP versions/slots in the same model.

Small M with heavy tails → the illusion of "strategy dragged."

Comparison on different "noises" (without CRN) - the difference is often phantom.

Stopping "by luck" - the test "to the first plus" distorts the distribution.

Ignoring time/pauses - no realistic exposure limits.

10) Mini pseudocode (understandable without language)


input: distribution {x_j, p_j}, bank B0, rate b0, N, rules of strategy S
M times:
B:= B0; b:= b0; peak:= B; maxDD: = 0 for t = 1.. N:
x: = case of {x_j, p_j}
win:= b x
B:= B + (win - b)
peak:= max(peak, B); maxDD:= max(maxDD, peak - B)
if conditions S require pause/stop → exit b: = next _ bet _ rule (B, history, S)
if b = 0 → quit (session stopped)
save total (B-B0), maxDD, length, other metrics collect distributions, EV, quantiles, risk when comparing strategies - use the same x (CRN)

11) How to document results (report template)

Game/RTP Version/Step Distribution - Short Description or Basket Table

Strategies: A (flat), B (progression k =...), exit rules
Simulation parameters: N =..., M =..., CRN = yes, antithetic = yes/no
EV (median by session): A...% (IQR... -...%); B …% (IQR …–…%)
Finish chance ≥0 %/ ≥+20%: A .../...; B …/…
Max drawdown (median/90th percentile): A .../... rates; B …/… rates
Desert length ≥×10 (median/75th percentile): A .../... spins; B …/…

A − B difference: (\Delta) EV... pp; bootstrap 95% CI [...;...]; permutation (p =)...

Conclusion: which strategy gives an acceptable risk profile for your goals; limitations and recommendations.

12) Important reminders

Simulations do not make negative expectation positive; they show the cost of risk and the sustainability of the rules.

See quantiles and drawdowns, not just the average: the player lives in the median and "bad days," not waiting.

The honesty of the experiment is more important than the result: fix the criteria in advance, use CRN and show the intervals of uncertainty.

Bottom line: A properly posed Monte Carlo simulation turns "belief in strategy" into verifiable numbers: EV, goal chance, drawdowns, and risk of ruin. This allows you to compare betting systems on the quality of the distribution of results and make decisions rationally - before you risk real money.