How to assess the risk of player bankruptcy

1) What is Risk of Ruin

Bankruptcy Risk (RoR) - The probability of dropping to zero (or a given stop loss threshold) before you reach the target (profit/spin count/end of vager). This is not a "horror story," but a practical indicator: if the RoR is high, the strategy is not viable.

2) What RoR depends on

Waiting (EV/edge): with EV <0, RoR increases with game length and turnover; at EV> 0 - drops.

Variance (volatility): wider spread ⇒ higher chance of deep drawdown.

Rate size as% of bankroll (BR): the larger the share, the higher the RoR.

Distance: more spins/bets ⇒ closer to expectation (and, with EV <0, to minus).

Limits and rules: bonus rate/exception limit, vager period, payment caps - everything affects RoR.

3) Two working ways to estimate RoR

A) Quick "stress test" without formulas

Suitable for slots and equally likely bets.

1. Rate the level of game volatility (low/medium/high).

2. Choose the "typical bad streak" you're willing to survive:

low volatility: 30-80 cons in a row;
average: 80-150;
high: 100-300 empty spins.

3. Check safety margin:

for 1:1 bids: BR/bid ≥ run length;
for slots: BR/bid ≥ series length × 1. 5-2 (wins are small and do not fully compensate for the series).
If not executed - RoR high, reduce the rate (in% of BR) or reduce the distance.

B) Approximation of the "normal" distribution (for a session of N attempts)

The total result ≈ N· EV ± σ·√N, where σ is the "standard deviation of one attempt."

Roulette 1:1: EV on bet ≈ − 2. 7% of the bet, σ one attempt ≈ 1 bet.

Slots (average volatility): oriented σ one attempt ≈ 1. 5-3 bets;

high-vol: 3-6 stakes.

The probability of breaking through the SL stop loss (for example, − 30% BR) before the end of the session is roughly estimated through the z-score:

[
z=\frac{−SL − N\cdot EV}{\sigma\sqrt{N}}\quad\Rightarrow\quad RoR\approx \Phi(z),  ]

where (\Phi) is the standard normal function. If (z) is about 1. 3 → RoR ≈ 10%; (z≈2) → ≈2. 3%; (z≈3) → ≈0. 13%.

💡 For slots, take a conservatively large σ: it is better to overestimate the risk than underestimate.

4) Classic "player ruin" (gambling problem)

For a par win/lose outcome bet with probabilities (p) and (q = 1-p) and with units (B = BR/bet):

if (p\le q) (EV≤0) and there is no horizon, RoR → 1;
if (p> q) (EV> 0), RoR at "infinite" horizon (\approx (q/p) ^ B).
This is useful in plus sports betting (where (p> q)) to understand how many units are needed for a small RoR. In casino games with EV <0, the formula only confirms: without limiting turnover, bankruptcy is a matter of time.

5) How to estimate RoR in slots

Hit Frequency (h): The lower the h, the more often long empty series. Probability of k empty in a row (\approach (1-h) ^ k).

Before bonus: if average distance to bonus (B) spins, survival check:

[
BR/rate ;\ge; 2 {-} 3\times B\quad (\text {for high-vol games - closer to} 3).
]

Buying a bonus: Consider the "seriality" of unsuccessful purchases (5-10 in a row is a normal stress test), and so that 10 "empty" purchases do not break through your stop loss.

6) Vager and RoR: "the cost of living to the end"

Wagering = huge turnover ⇒ tax from edge:

[
\ text {Cost }\approach\text {Bonus }\times\text {Wager }\times\text {edge (of allowed games)}.
]

Even if the math is close to zero, the variance can "kill" the bankroll before the end. Therefore, for a wager:

choose allowed games with lower volatility and high RTP;
hold bet 0. 25–0. 5% BR;
strictly observe the bet limit and the list of games (otherwise progress will not be counted - the actual RoR rises sharply).

7) Practical presets that reduce RoR

Rate from BR:

high-vol slots: 0. 25–0. 75%;
average volatility: ~ 1%;
low/rates 1:1: 1-2%.

Stop losses/teik profits:

high-vol: SL 30-40% of session budget, TP 60-150%;
mean: SL 20%, TP 30%.
Turnover/time limit: less turnover ⇒ lower expected "price" minus ⇒ below RoR per session.
Speed: fewer auto-spins → slower turnover/hour → lower RoR per hour.
Diversification: "core" (moderate games) 70-90% of the time; high-vol "hunting" - 10-30%.

8) Clear examples

Example A - Average Volatility Slot

BR = 200 cu, rate = 1% = 2 cu, N = 800 spins, RTP = 96% (edge 4%).

Waiting for session (EV_{tot}\approx -0. 04\times (2\times 800) = -64) c.u.

Take conservatively (\sigma) one attempt = 2 bets = 4 cu.

Then (\sigma _ {tot }\approx 4\sqrt {800 }\approx 113) c.u.

We want to understand the risk of breaking through SL = − 40 cu. (20% BR).

(z = \frac{-40 - (-64)}{113} \approx 0. 21 \Rightarrow RoR \approx 58%).

Conclusion: with this length and SL 20%, the risk is high - reduce the N or bet to 0. 5–0. 75% BR, or raise SL (aware of budget risk).

Example B - high-vol slot (stress test)

BR = 200, bid = 0. 5% = 1 unit

Stock for 200 empty: BR/rate = 200 ≥ 200 → basic stress is sustained.

Add a factor of 1. 5-2 for small winnings → the stock is close to the lower limit; better than 0. 25–0. 4% (0. 5–0. 8 y. e.) .

Example C - wager × 35, bonus 100, edge 4%

The cost of the game ≈ 100 × 35 × 0. 04 = 140 cu.

If BR = 300, the rate is 0. 5% = 1. 5 cu., moderate volatility → a higher chance of "surviving" than at 1-2%.

9) RoR at EV> 0 (sports): fractional Kelly

If you have a confirmed advantage, use fractional Kelly to contain the RoR:

[
f ^ =\frac {k p - 1} {k - 1} ,\quad\text {but real - }\tfrac {1} {4 }\text {- }\tfrac {1} {2 }\cdot f ^.
]

So you reduce the depth of drawdowns with a slight loss of growth rate.

10) Frequent errors that explode RoR

Rate in cu, not% of current BR. After drawdown, the proportion grows imperceptibly.

Progressions/dogons. Accelerate turnover and bring bankruptcy closer with EV <0.

Ignoring the actual RTP/slot version. 96% versus 92% is almost twice the edge.

Too high speed. Fast auto-spin = high RoR "per hour."

Play on high-vol games. High dispersion "breaks" the game to the finish.

11) RoR assessment checklist (in 60 seconds)

1. Target and horizon: How many spins/bets, is there a stop loss/deadline?

2. RTP/edge and game volatility known?

3. Rate as% BR selected by volatility?

4. Batch stress test: BR/bid ≥ stock required?

5. For the vager: calculated Bonus × Vager × edge, the game is allowed, the bet is in the limit?

6. Speed/auto-backs limited? Is there a turnover and time limit?

7. Diary of sessions: fix turnover, total, drawdown - adjust shares?

The RoR estimate is a combination of simple stress tests and conservative approximations. By reducing the share of the bankroll bet, reducing turnover/speed, choosing cheaper games and reasonable stop levels, you dramatically reduce the likelihood of bankruptcy. At EV> 0, scale the preponderance with fractional Kelly; with EV <0 - let mathematics work to control costs, not against your bankroll.