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How to calculate the optimal rate
1) "Optimal" depends on the goal
First, honestly state why you put:- Long and even game (entertainment, cost control): the goal is to minimize drawdowns for a given time budget.
- Bonus/wager wagering: The goal is to make it to the end with acceptable variance.
- Profit maximization at EV> 0 (sports/rare games by a margin): the goal is to grow the bankroll with risk control.
The method of choosing the size of the bet depends on the goal.
2) Base values
Bankroll (BR) - the amount that can be lost without harming the budget.
Volatility - scatter of results (the higher, the deeper and longer the drawdown).
Expected "price of the game" at a distance: 'Total ≈ Turnover × (− edge)', where Turnover = bet × the number of rounds.
3) Simple and reliable base: fixed percentage of BR
Fixed Fraction method: For each round, you bet a fraction of the'f' of the current bankroll.
Recommendations on f taking into account volatility
Low volatility (frequent small wins): 'f = 1-2%'
Average volatility: 'f = 0. 5–1. 5%`
High volatility (rare major hits): 'f = 0. 25-1% '(more often closer to the bottom of the range)
Example: BR = 200 cu.
Low volatility → rate 2 cu. (1%)
High volatility → rate 0. 5-1 y. e. (0. 25–0. 5%)
Pros: simple, automatically reduces the risk of drawdown. Cons: When you win, the bet grows - emotions can interfere with discipline.
4) "Units" and session budget
If it is more convenient to think in "units," select N attempts in session and protection against drawdown in 3 σ (large margin rule).
Algorithm:1. Decide how many tries you want (like 500 spins).
2. Set the stop loss of the session (say, 20% BR).
3. Take conservatively for high volatility: rate = BR × 0. 25–0. 5%.
4. Check: "If the first 100-200 spins are empty, will I live to see the end of the session?" If not, reduce the rate.
Example: BR = 300 cu, target 600 spins on a high-volatility slot.
We take 0. 4% → rate 1. 2 cu. Turnover ≈ 720 cu. If the edge ≈ 4%, the "price" of the session ~ 28. 8 cu. With a stop loss of 60 CU, there is a risk margin.
5) When EV> 0: Kelly criterion (and why "Kelly share" is better)
For a binary outcome (sport/arbitration) with decimal coefficient 'k', your probability 'p' and 'q = 1 − p': Full Kelly:- 'b = k − 1 '(net payout),' f = (b· p − q )/b = (k· p − 1 )/( k − 1) '- bankroll share of the rate.
In practice, fractional Kelly (½, ¼) is used to reduce volatility.
Example: k = 2. 10, p = 0. 52
`k·p − 1 = 2. 10×0. 52 − 1 = 0. 092` (edge 9. 2%)
`b = 1. 10` → `f ≈ 0. 092 / 1. 10 ≈ 8. 36%`
We play ½ Kelly ≈ 4. 2% of BR. If BR = 1000 cu. → rate ~ 42 cu.
Important comments:- Kelly cannot be applied to games with negative EV (classic casino) - it will speed up drawdown.
- The sensitivity to error in'p 'is high: it is better to underestimate the share (½ - ¼ Kelly).
6) The size of the bet under the bonus and vager
The goal is to live to the end of the game, minimizing the likelihood of bankruptcy before the conditions are met.
1. Calculate the cost of the game: 'Cost ≈ Bonus × Wager × edge (allowed games)'.
2. Match games with lower volatility (if allowed).
3. Keep the bet closer to 0. 25–0. 75% BR - long empty batches are less dangerous.
4. Watch rate limits and term - violation of conditions kills EV.
7) Rapid guidelines for drawdown risk
The higher the volatility and the higher the rate in% BR, the higher the chance of deep drawdown.
Conservative approach: plan so that a typical series of failures (for high-volatility slots of 100-300 empty spins in a row is not uncommon) does not eat up more than 30-40% of the session budget.
8) Practical preset sets
A. Long, calm session (entertainment)
BR 200 cu; low/medium volatility: rate 1-2% (2 cu); stop loss 20%; teik profit 30%.
B. High volatility (hit hunt)
BR 200 cu; bet 0. 25–0. 75% (0. 5–1. 5 cu.); stop loss 30-40%; teik profit 60-150%; fewer auto-spins, more pauses.
C. Bonus with a large vager
BR 300 cu; bet 0. 25–0. 5% (0. 75–1. 5 cu.); low/medium volatility games; rate limit control according to the rules; monitoring wagering progress.
D. Plus sport (there is a model)
Fractional Kelly ¼ - ½ from 'f'; daily risk limit (for example, ≤5 -8% BR in total); not chasing express trains.
9) Frequent errors when choosing the size of the bet
The rate is too high for volatility. Rapid deep drawdowns → loss of discipline.
Progressions (martingale). Accelerate turnover growth and approach limits/bankruptcy with EV <0.
Ignoring bonus rules. Bet limit, excluded games, term - break the math, even if the bet is "correct."
Lack of stop loss/teik profit. No framework - no risk control.
10) Algorithm "in 60 seconds"
1. Define the goal: playtime/wagering/EV> 0.
2. Rate the volatility of the game.
3. Select fixed percentage (for casino) or fractional Kelly (only for confirmed EV> 0).
4. Assign a rate:- low volatility: '1-2% BR';
- average: '0. 5–1. 5% BR`;
- high: '0. 25–1% BR`;
- Sport EV> 0: '½ Kelly' (or less).
- 5. Put a frame: stop loss, break profit, time limit.
- 6. Check bonus rules (if relevant): does the rate fit into the limit? is the game allowed? is the term sufficient?
- 7. Keep a diary: turnover, total, drawdown depth - adjust f according to the results.
The optimal bet size is the balance between your goal, product volatility and acceptable risk. For most scenarios, a fixed small percentage of the bankroll, adapted to volatility, wins in the casino. When you have a confirmed advantage, use a fractional Kelly - neatly and disciplined. This approach makes the game predictable in risk, and solutions - systemic.