1–3–2–6 Betting System: Rules and Blackjack Examples

The 1–3–2–6 betting system uses a four-stage starting-stake sequence: one unit, three units, two units and six units. Advance after a win, then reset after a loss or the fourth winning stage. The sequence changes the amount exposed; it does not make the next wager more favourable.

Four ordinary wins complete the full sequence with twelve units of profit. Other endings matter too: losing the third stage still leaves two units of cycle profit, while losing the fourth stage returns that ordinary even-money cycle to break-even. Those figures require the precise assumptions set out below.

This guide follows every terminal path, illustrates repeated cycles and explains how pushes, naturals, doubles and splits complicate the arithmetic. All Canadian-dollar amounts, budgets and limits are invented teaching examples, not recommended stakes or available casino terms.

What the four numbers mean

The method is usually grouped with positive progressions because wins move it forward. That does not mean every successive stake rises, nor does the label describe a positive expected return.

Our betting systems guide compares other starting-stake rules. Keep the progression separate from the decisions made after cards appear: none of its four numbers tells a blackjack player whether to hit, stand, double or split. The comparison with basic strategy separates those hand decisions from starting-stake rules.

The ordinary settlement model used here

First assume one starting wager per round. An ordinary win earns profit equal to that wager, a full loss costs the wager, and a push returns it without profit. W, L and P refer to those outcomes only.

Advance one stage after W. Reset after L. After the fourth W, end the cycle and reset before any further bet. After P, repeat the same stage and stake. A session can end at a separate money or time boundary even when the cycle is unfinished.

We use a $5 base unit for the main dollar examples, giving starting stakes of $5, $15, $10 and $30. These amounts do not establish what any real table permits. Other units scale the money figures but leave the stated multipliers unchanged.

Returned stakes are excluded from profit. A $15 even-money win returns $30 in total, of which $15 is profit. The payouts guide explains that distinction before naturals and extra wagers are added.

The four stages with a $5 unit

The cycle-profit column below shows the position before the next wager is placed, assuming all earlier stages were ordinary wins. It is not the total account balance or a prediction that the next bet will win.

Starting with $100, four ordinary wins settle the balance at $105, $120, $130 and $160. The cycle earns $60 on $60 of total starting stakes. The next cycle’s starting amount is $5, not another $30 or a newly enlarged unit.

That full winning path is one possibility, not a representative session. Showing only its final $160 balance would conceal both the $100 opening money and the three earlier wins required to reach the last stage.

Every way an ordinary cycle can end

A cycle stops at its first loss or its fourth win. That gives five terminal paths. Pushes can appear between these outcomes without changing the stage under our convention, so the table initially omits them.

The third-stage loss is profitable because the first two wins earn four units and the third stake loses two. The fourth-stage loss breaks even because the earlier three wins earn six units and the last stake loses six.

The largest ordinary terminal-cycle loss is two units, but the largest individual starting stake is six. Those measure different things. Neither is a general session loss limit, and the two-unit statement does not include extra blackjack commitments.

Cycle loss and a fall from the highest balance

With the $100 opening balance and $5 unit, three ordinary wins raise the balance to $130. Losing the $30 final bet brings it back to $100. The cycle breaks even relative to its opening money, but the balance has fallen $30 from its highest point.

That fall is a drawdown. It is different from the terminal loss measured against the start of the cycle. Describing the outcome only as “nothing lost” hides the fact that $30 of previously held winnings was exposed and lost.

A record can show both measures without contradiction: zero cycle profit and a $30 fall from the peak. The earlier winnings were money under the player’s control, not a separate risk-free fund. Labelling the last stage “house money” does not change its value.

Keep the session peak separate from the cycle peak as well. A new cycle can start after an earlier loss, so breaking even in that new cycle may still leave the whole session below its opening balance and below a previous high.

Repeated cycles need one continuous session total

Consider a deliberately selected five-cycle exercise starting at $100 with the $5 unit. Its cycles end L, W–L, W–W–L, W–W–W–L and W–W–W–W. There is one of each terminal path; this is not their expected frequency.

The settled balances are $95, $85, $95, $95 and $155. Net cycle results of −$5, −$10, +$10, $0 and +$60 combine to a $55 session profit. Total starting stakes are $175 across fourteen ordinary rounds.

A fresh cycle label does not restart the actual balance. Three W–L cycles lose $30 altogether. A later W–W–L cycle earns $10, leaving the combined exercise $20 down despite that last cycle being positive.

Keep the running total from the first bet, including interrupted cycles. A report that counts only full four-win completions cannot describe the whole method because most terminal paths contain a loss.

Resetting the sequence is not recovering a loss

After W–L, the ordinary cycle is two units down and the next proposed stake returns to one unit. The reset changes the next stake; it does not replace the money lost. A later successful cycle may offset earlier results, but it is not guaranteed to occur.

Doubling the base unit after a failed cycle creates a different, combined progression. It also invalidates comparisons that assume the same unit throughout. Record that change instead of presenting the later result as evidence for the original rule.

A separate stopping boundary can interrupt a winning sequence too. Ending after two ordinary wins leaves four units of cycle profit without playing the third stage. That is an incomplete cycle with a stated stop, not the W–W–L terminal result.

Likewise, substituting a smaller final bet because the six-unit stake is unavailable changes the ledger. The new result must be calculated from the actual amount, not copied from the original terminal table.

Available money matters at every stage

In the ordinary model, stage two exposes more than the first win. With a $5 unit and only $5 opening money, a first win leaves $10, which cannot fund the proposed $15 second bet. A winning first round is not sufficient by itself to continue.

For comparison, $10 opening money can fund every path of one ordinary cycle by reusing returned stakes and winnings. After the first win the balance is $15, enough for stage two. After the second it is $30, enough for stage three; after the third it is $40, enough for stage four.

That is a narrow funding calculation, not a recommended budget. A W–L result would exhaust that invented $10 opening balance, and extra wagers or other settlements change the calculation. It does not supply money for indefinite repeated cycles.

Three W–L cycles at a $5 unit can exhaust an invented $30 allowance. The session budget calculator helps keep a money and time boundary separate from the desired sequence.

Table limits can block the six-unit step

With a $5 unit, the last starting stake is $30. An invented table maximum of $25 would block it. The $30 of ordinary cycle profit already earned after three wins does not override a posted maximum.

If a $25 replacement bet then wins ordinarily, the cycle earns $55 instead of $60. If it loses, the cycle ends $5 ahead instead of breaking even. These are different results because the actual last stake was changed.

Minimums and permitted increments can matter too. The two-unit third stage must still be a valid bet. MGM GameSense explains that table minimums and maximums are posted; check the actual table rather than assuming the teaching unit fits.

Check all four amounts before a paper comparison. A base unit that fits the minimum can still produce a three-unit or six-unit stake outside an allowed range. Rounding one stage to a permitted amount changes that stage’s payoff and requires a new calculation.

Splitting the amount across boxes or moving tables is another modification. It can change the number of hands, available decisions and relationship between results. It should not be treated as the original single-wager example.

Pushes repeat a stage

For W–P–W–L at a $5 unit, the starting stakes are $5, $15, $15 and $10. The push repeats stage two. Net profit is $5 + $0 + $15 − $10 = $10, matching the W–W–L terminal amount.

Total starting stakes are now $45 rather than $30 because another $15 bet was placed and returned. Four actual rounds were needed to obtain the three decisive results. This is why a four-stage system does not necessarily finish within four elapsed rounds.

Repeated pushes could extend a cycle further. A time boundary can end the exercise before the next decisive result. Keep that stopping reason in the record rather than advancing the sequence merely because another round has passed.

Real account reports may define turnover differently. In this guide’s exercises, action means the sum of amounts placed before settlement, including pushed wagers. Use the relevant definition when comparing a report or an expected-return calculation.

A fair probability model does not produce an advantage

For a mathematical illustration, assume independent rounds with a 50% chance of an ordinary win and a 50% chance of a full loss. There are no pushes, naturals or additional wagers. This is a fictional even-money game, not blackjack data.

The terminal probabilities are one-half for L, one-quarter for W–L, one-eighth for W–W–L, and one-sixteenth each for W–W–W–L and W–W–W–W. Together they account for every path.

Weighting their net unit results gives −1 × 1/2 − 2 × 1/4 + 2 × 1/8 + 0 × 1/16 + 12 × 1/16 = zero. The twelve-unit completed win is balanced by the other possible outcomes.

The expected amount wagered is 1 + 3 × 1/2 + 2 × 1/4 + 6 × 1/8 = 3.75 units per cycle. Different paths place different total stakes, so this weighted average is not the amount every cycle costs.

What happens in an unfavourable model?

Change the fictional win probability to 49%, with losses at 51% and ordinary even-money payouts unchanged. Each dollar wagered has a two-cent expected loss. Keep the same progression, caps and independent-round assumptions.

The probability of four wins is 0.49 to the fourth power, or 0.05764801: about 5.76%. The profitable W–W–L path has probability 0.49² × 0.51 = 0.122451, about 12.25%. Four wins are not the only profitable terminal result.

Enumerating all five endings gives an expected result of −0.07312188 units on 3.656094 expected units of action. At a $5 unit the expected cycle loss is about $0.37. Dividing expected loss by expected action retains the same 2% disadvantage.

Those figures describe the invented model, not the outcome or likelihood of a real session. The odds and house edge guide explains the difference between expectation and an individual result.

Blackjack information and playing strategy are separate

Actual shoe blackjack is not the independent game above. OLG PlaySmart explains that removed cards change the remaining composition. The round labels W and L do not contain all that information.

Moving from one stage to another therefore does not establish a better next-hand expectation. Two previous wins tell the system to move from three units to two; they do not prove which card comes next or whether the table rules have become more favourable.

The basic strategy guide and cheat sheet state their playing assumptions. Their hand decisions address a different question from the sequence’s starting amounts.

Under a condition where the next wager still has a negative expected return per dollar, changing the stake does not change that sign. This statement does not equate actual card-composition analysis with a progression based only on previous results.

Naturals and partial losses change cycle profit

Blackjack can pay a natural at 3:2 or 6:5 according to the posted rules. A $5 natural earns $7.50 or $6, rather than the $5 ordinary profit assumed in the terminal table.

Suppose the first result is a $5 natural paid 3:2, followed by an ordinary $15 loss at stage two. The actual cycle result is $7.50 − $15 = −$7.50, not the ordinary W–L result of −$10.

A half-stake surrender loss changes the amount too. A $5 ordinary first win followed by surrender of a $15 second-stage bet loses $7.50 on that bet and ends the cycle $2.50 down, assuming the stated surrender conditions permit it.

For a practice ledger, one explicit convention is to advance after a positive net main-round result, reset after a negative result and repeat after zero. Record the actual settlement separately. That convention defines a practice variant; it does not make the ordinary terminal amounts apply unchanged.

Doubles and splits can exceed the ordinary loss figure

Three ordinary wins at the $5 unit earn $30 before stage four. If the $30 fourth-stage hand is doubled to $60 and loses, the cycle ends $30 down. It does not break even and does not stay within the ordinary two-unit maximum terminal loss.

The additional stake is the reason. The double down guide explains that a starting amount is not necessarily the entire round commitment. Funding a six-unit starting bet does not automatically fund every possible additional action.

Splitting the $10 third-stage hand creates two $10 hands before further permitted additions. One ordinary win and one loss produce a zero combined result on $20 of action. Under the explicit net-round convention above, the next round repeats the two-unit stage.

Use the splitting guide for separate-hand accounting. Keep insurance and side wagers in their own columns instead of letting one wager’s outcome silently determine the other’s stage.

Compared with flat stakes, Martingale and Paroli

On W–L at a $5 base, 1–3–2–6 loses $10 on $20 of action. Flat $5 starting stakes break even on $10 of action. Three-win Paroli loses $5 on $15 of action. The larger second stake changes this selected result.

On W–W–L, 1–3–2–6 earns $10 on $30 of action, flat stakes earn $5 on $15, and three-win Paroli loses $5 on $35. The deliberate reduction from three units to two matters at the third stage.

Our flat betting guide gives full fixed-stake ledgers, while Martingale versus Paroli compares the two doubling methods. These outcome examples are illustrations, not evidence that one selected path is typical.

Martingale increases after ordinary losses; this sequence resets after them. Combining the two rules by increasing the base after a failed cycle creates another system with different possible exposure.

Account conditions and other game formats

A permitted initial unit does not establish that the six-unit stage is eligible under every account condition. Read the applicable stake and game restrictions, especially if a restricted balance is involved. The bonus terms guide explains those distinctions.

Nor do the ordinary terminal amounts transfer unchanged to slots or side bets with varied prizes. A result that pays less than the stake back is a net loss even if an animation celebrates it. A larger prize needs its actual profit recorded.

Define what a win, loss or zero result means before running any variant. Otherwise the stage rule can change from round to round without the record revealing it.

A practice record that keeps the stages clear

Record the cycle number, stage, opening balance, starting stake, extra stakes, net result, ending balance and proposed next stage. Include a reason whenever the exercise stops before its usual terminal point.

Separate money added or withdrawn from game results. Opening with $100, depositing another $50 and ending with $120 means a $30 loss if there are no other adjustments. It is not a $20 profit simply because the displayed balance exceeds the opening $100.

Keep failed cycles and unavailable bets in a comparison. A demonstration that restarts the balance after every difficult result has changed its funding assumptions. A screenshot of one completed four-win run cannot establish typical performance.

If modelling randomly, disclose probabilities, payouts, trial count, push treatment and stopping rules. Include all five terminal paths and identify any additional blackjack settlement types excluded from the model.

The gambling help page provides support information, and the guides directory connects the related rules and calculations.

Common 1–3–2–6 questions

Why does the stake fall from three units to two?

That reduction is part of this sequence. It leaves two units of ordinary profit if the third stage loses after two wins. Replacing it with another increase changes the terminal results.

Do four wins have to be consecutive?

Four winning stages complete the full ordinary cycle. A loss resets it, while a push repeats the current stage. Consecutive decisive wins can therefore contain pushed rounds between them.

Is two units the most that can be lost?

It is the largest terminal loss for one cycle in the stated ordinary model. Repeated cycles accumulate losses, and doubles, splits or separate wagers can increase exposure within a cycle.

Does completing a cycle mean the session is profitable?

No. Include earlier results, money movements and the actual settlement. Keep spending boundaries independent of a wish to recover. Our gambling help page provides support information, and the guides directory connects the related rules and calculations.

Do the 49% win probability and 2% disadvantage describe blackjack?

No. They belong to the fictional independent even-money model used to demonstrate the calculation. Real blackjack includes pushes, naturals, extra stakes and changing shoe composition. The example’s expected loss is not a measured blackjack result or a prediction of one session.

Can I stop after two ordinary winning stages?

Yes. A separate time or spending boundary can end the exercise before the cycle’s usual endpoint. Two ordinary wins earn four units of profit, and no third-stage bet has been made. Record that as an interrupted cycle with its actual result; do not label it as the three-result W–W–L path.

Does winning the first bet fund the three-unit second stage?

Not necessarily. In the $5-unit example, starting with only $5 and winning leaves $10, while stage two requires $15. Funds already committed or unavailable cannot be counted as usable balance. The guide’s separate $10 opening-balance illustration covers one ordinary cycle only, not extra blackjack wagers or repeated play.

What happens if the six-unit final hand is doubled and loses?

The actual result can exceed the ordinary cycle-loss figures. With a $5 unit, three ordinary wins earn $30. A $30 fourth-stage hand doubled to $60 and lost then leaves the cycle $30 down. Record both the initial and added stake; the ordinary fourth-stage-loss result of zero no longer applies.

References

Sources and calculations reviewed November 1, 2026. The dollar ledgers and fictional probability models are original calculations. Other games’ published probabilities are not treated as blackjack probabilities. Ontario and US references explain game mechanics, not current Alberta table rules or availability.

1. Wizard of Odds: 1–3–2–6 Betting System — progression structure, ties and terminal-path analysis.
2. Wizard of Odds: The Truth about Betting Systems — expected results relative to the amount wagered.
3. OLG PlaySmart: Blackjack Odds — changing card composition and rule-dependent expectations.
4. OLG PlaySmart: Blackjack Strategies — playing decisions under stated rules.
5. MGM GameSense: Guide to Blackjack — limits, payouts and additional wagers.