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Why an increase in the bet does not guarantee a win
1) The main idea in one sentence
An increase in the rate does not change the probability of the outcome and does not create + EV. It only accelerates the growth of turnover, which means that it realizes mathematical expectation faster (in a casino it is negative).
2) Independence of outcomes and RNG without memory
In slots and roulette, each spin/spin is independent: the chance of winning does not depend on previous results.
After a series of setbacks, the next outcome is not "obliged" to be a win. Doubling the bet does not increase the chance - it only increases the size of the possible loss.
3) Expected value and "price" of the game
Denote edge = 1 − RTP (in fractions). Then at any distance:- Expected total ≈ − edge × Sales volume, where Sales volume = bid × number of attempts.
- Upping the ante, you... increase turnover - and the rate of expected losses at EV <0.
4) Why "to fight back" progressions don't work
Martingale and similar schemes promise to cap a losing streak with one bigger bet. Problems:1. The expectation is negative at every step - the progression does not change it.
2. Exponential growth of the risk amount: after n losses, the bet is ~ (2 ^ n), the total risk is already (2 ^ {n + 1} -1).
3. Table limits and ultimate bankroll: a long streak inevitably comes - and one "tail" eats up dozens of small victories.
5) Volatility: more rate → deeper drawdown
Even with constant RTP, the rate increase increases the scope of the result fluctuations:- On highly volatile slots, a series of 100-300 empty spins are normal.
- With a large bet, they turn into a quick and deep drawdown, increasing the risk of ruin long before the "very" drift.
6) Case studies
Roulette (European, bet 1:1):- p (gain) = 18/37, q = 19/37, EV ≈ − 2. 70% of the rate.
- Increased the rate from 5 to 20 cu? Your expected minus per spin 100 has grown 4 times. The probability of winning has not changed.
- edge=4%. 500 spins of 1 cu. → Turnover 500, waiting − 20 cu.
- 500 spins of 3 cu. → Turnover 1500, waiting − 60 cu.
- The chance to catch the bonus is the same, but the risk of draining and the amplitude of drawdown is higher.
- EV of single bet: EV = k· p − 1.
- If EV ≤ 0, increasing the bet size only scales the expected loss; The "good" of the sum does not change the mathematics.
7) Psychological traps
Gambler's fallacy: "after 10 minuses, it's time to win" - no, the probability is the same.
The illusion of control - "I drive the bet means I influence the outcome" - you influence risk, not probability.
Tilt and escalation: the rise of the "to return" rate is a hidden progression leading to rapid collapse.
8) How to properly scale your bid
If EV <0 (classic casino games): Keep the rate as% of the current bankroll:- High-vol slots: 0. 25–0. 75% BR;
- Average volatility: ~ 1% BR;
- Low/rates 1:1: 1-2% BR.
- Limit the time/number of spins (sales control).
- Enter stop loss/teik profit: for example, − 20... − 40% and + 30... + 150% (wider for high-vol).
[
f=\frac{k p - 1}{k - 1}\times {\tfrac{1}{4}\text{ или }\tfrac{1}{2}}
]Consider correlations, commissions, and errors in p.
9) Mini calculators "on the fingers"
Price per hour: less auto-spins ⇒ less turnover/hour ⇒ lower expected minus/hour.
A series of empty spins: with hit-frequency (h), the probability of k empty consecutive ≈ ((1-h) ^ k). The lower the h and the higher the rate, the more painful the series.
Bonus and vager: the cost of the game ≈ Bonus × Vager × edge (allowed games). A large bet here increases the risk of not "surviving" to the finish line.
10) Checklist before "raising bid"
1. Why do I raise? If "to fight back" - stop.
2. RTP/edge and game volatility known?
3. Rate as% of current BR, not fixed amount?
4. Is there a stop loss/break profit and a time limit?
5. For the bonus: the bet does not break the limit according to the rules and does not raise the RoR until the end of the vager?
The rate increase is a scaling of risk, not probability of victory and not expectation. In games with EV <0, it simply speeds up the implementation of the mathematical minus and brings you closer to limits and drawdowns. If you want to play longer and calmer - keep the bet as a percentage of the bankroll, take into account volatility, limit turnover and use strict stop rules. And increasing the rate makes sense only where you have a provable advantage, and then - carefully and according to the formula.