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How the progression betting strategy works
1) What is "rate progression"
Progression is a predetermined change in the size of the bet depending on the result of a past attempt.
The goal is to change the trajectory of the results (as the balance fluctuates), but not the average outcome of the game itself.
The key truth: if the game has EV <0 (edge> 0), any progression does not make it positive. At a distance, the result stretches to:[
\ text {Expected Total }\approach - ,\text {edge }\times\text {Turnover} ,\quad
\ text {where Turnover} =\sum\text {rates}.
]2) Why they are used at all (and for what they scold)
Why they pull: a sense of control, rhythm and "plans for getting out of the series."
Why criticize: progressions more often accelerate turnover and variance without improving expectation; rest on the limits of the table and the final bankroll.
3) The main types of progressions and their logic
A) Martingale (double after loss)
Bets: (1,2,4,8 ,\dots, 2 ^ n) to win first.
Bank for experiencing (n) cons + next step: (\displaystyle BR_{\min}=2^{n+1}-1).
Plus: quickly "closes" short episodes.
Cons: exponential rate/bank growth; a high chance of a "fatal" series; expectation does not change.
B) D'Alembert (step forward/back)
After losing + 1 to the base bet, after winning − 1 (without falling below the minimum).
Plus: softer than martingale; psychologically easier.
Cons: with long clusters of losses, the bank "crawls" down; EV former.
C) Fibonacci
Sequence: (1,1,2,3,5,8 ,\dots). Losing → forward by one, winning → back by two.
Total risk before step (n): (\sum _ {k = 1} ^ {n} F _ k = F_{n+2}-1).
Plus: rate increases slower than doubles.
Cons: With "untimely" wins, the series does not close; risk and turnover accumulate.
D) Labouchere (cancellation)
Set a series of numbers, bet = sum of extreme. We won - "crossed out" the extreme, lost - added the amount to the end.
Plus: a sense of "plan."
Cons: In protracted series, the numbers inflate, as does the bank required; high operational complexity.
E) Reverse Martingale (Paroli)
Increase in bet after winning, reset to base after losing; usually a 2-3 victory cap.
Pros: limited loss per cycle (usually ≈ − 1 base rate), "positive asymmetry."
Cons: rarity of long winning streaks; EV does not change, the discipline of fixation is critical.
4) How progressions affect risk and variance
↑ variance: Variable rate size expands the spread of results relative to the flat rate.
Risk of Ruin (RoR) ↑: especially in aggressive schemes (martingale, Labouchere) due to the rapid growth of bets.
↑ loss rate at EV <0: the higher the turnover/hour, the higher the expected loss/hour:[
\ text {Loss} _ {hour }\approach\text {edge }\times\text {average rate }\times\text {attempts/min }\times 60.
]5) Why "series" break progressions
Let the probability of losing in betting be 1:1 - (q). The probability of (k) cons in a row is (q ^ k).
Even if (q) is just over 0. 5 (roulette with zero), an 8-10 losing streak is not as rare over long distances.
Any progression that "puts everything on the experience of the series" ends up running into a limit or bank.
6) Mini-examples (intuition by numbers)
Martingale, base 1 cu, target to survive 8 cons:- Need (BR_{\min}=2^{9}-1=511) c.u.; maximum rate up to the limit - 256 cu.
- One "tail" eats dozens of successful short cycles.
- Total nested series (\approach F_{12}-1=143) c.u.; winning the "bad" step does not easily overlap the tail.
- Probability of 3 consecutive wins (p ^ 3). In roulette (p\approx0. 4865) → ~11. 5%.
- Success gives ~ 14 cu., other cycles more often − 2 cu. Or about 0 (with free-bet after the first victory).
7) When progressions "make sense"
Only as a tool of psychology and rhythm, and not "a way to beat mathematics."
Paroli may be suitable for those who prefer a small fixed risk per cycle and rare "upside" (strict cap is required).
All others are options for controlling trajectory and emotions. The average wait is not improving.
8) When progressions definitely harm
With narrow table limits and a small bankroll, aggressive schemes quickly break down.
In highly volatile games (slots with rare large payments) - progressions dramatically increase the chance of deep drawdown.
In a vager, progressions accelerate turnover and the risk of "not living" to the end of the conditions.
9) Safe alternatives to progressions
Flat rate as% of current bankroll:- high-vol: 0. 25–0. 75% BR, average volatility: ~ 1% BR, low/1: 1: 1-2% BR.
- Play in series: record the time, number of attempts and SL/TP (for example, − 20... − 40 %/+ 30... + 150%).
- Speed control: less auto-attempts/min → lower "price of the hour."
- Choice of "cheap" games/bets: European roulette, blackjack with basic strategy, slots with high actual RTP.
- Bonus hygiene: count "wager tax" = Bonus × wager × edge (allowed games).
10) Checklist before using progression
Does the game give EV> 0? If not, progression will not make it positive.
I know the limit of the table and how many steps can I really stand?
Did the minimum bank count (for martingale (2 ^ {n + 1} -1); for Fibonacci (F_{n+2}-1))?
Is the rate expressed as% of the current BR and not as a fixed amount?
Are there hard SL/TP and time/pace limit?
Ready to interrupt the strategy in the series without "catching up"?
Rate progressions are about the form of risk, not plus-expectation. They can discipline and set the rhythm, but with negative EV they only redistribute how you come to the average minus, and not change the fact itself. If your goal is to control the budget and nerves, choose a flat rate as a percentage of the bankroll, short sessions, reasonable stop levels and "cheap" edge games. Leave progressions as an educational tool for understanding variance - without illusions to "break" mathematics.