The 1-3-2-6 sequence changes bet size after wins; it does not overcome the house edge. It can produce a 12-unit gain after four consecutive even-money wins, but many cycles end earlier with a loss or smaller result.
The sequence
Choose one affordable unit. Bet 1 unit. After a win, bet 3 units; after another win, bet 2; after a third win, bet 6. Reset to 1 unit after a loss or after completing the four bets. Decide in advance how pushes and blackjack payouts affect your reset rule.
Cycle arithmetic
For a simplified even-money model with no pushes or blackjacks, the possible completed cycle results are:
- Loss on bet 1: −1 unit.
- Win 1, then lose 3: −2 units.
- Win 1 and 3, then lose 2: +2 units.
- Win 1, 3 and 2, then lose 6: 0 units.
- Win all four bets: +12 units.
At $10 per unit, four wins produce +$120. Losing the 6-unit fourth bet after winning the first three returns that simplified cycle to $0, not a profit.
The probability-weighted result
If q is the probability of an even-money win and losses occur with probability 1 − q, the simplified expected cycle result is:
−(1 − q) − 2q(1 − q) + 2q²(1 − q) + 12q⁴
When q = 0.5, that expression equals zero, as it must in a fair even-money game. When the underlying wager has negative expected value, changing stakes according to prior independent outcomes does not make the total expectation positive.
How often does each cycle finish?
Keep the same simplified model and set q = 0.5, with independent even-money outcomes. The size of a winning cycle is only half the comparison; the other half is how often each outcome occurs.
| Cycle path | Probability | Net result |
|---|---|---|
| L | 1/2 = 50% | −1 unit |
| W–L | 1/4 = 25% | −2 units |
| W–W–L | 1/8 = 12.5% | +2 units |
| W–W–W–L | 1/16 = 6.25% | 0 units |
| W–W–W–W | 1/16 = 6.25% | +12 units |
Thus 75% of cycles lose money, 6.25% break even and 18.75% finish ahead in this fair illustration. Multiplying each result by its probability gives −0.5 − 0.5 + 0.25 + 0 + 0.75 = 0 units. These are model probabilities, not promised frequencies over your next 16 cycles and not real blackjack win rates.
The average initial action per cycle is 1 + 3q + 2q² + 6q³, or 3.75 units at q = 0.5. Some cycles contain one wager and others four, so compare both total initial action and net results rather than the cycle count alone. See Shackleford’s primary betting-system analysis for the wider distinction between winning sessions and expected return.
Real blackjack is more complicated
Blackjack includes pushes, 3-to-2 or other blackjack payouts, doubles, splits and rule-dependent strategy. Treating every hand as a simple even-money win or loss is only an illustration. If each round has the same modeled negative return per initial-wager dollar, increasing initial-wager volume increases expected loss. Conventional blackjack house edge uses initial wagers as its denominator and already reflects modeled doubles and splits; do not apply it a second time to those added stakes.
What the system changes
The progression concentrates more money in some winning sequences, so session results and volatility can feel different from flat betting. The highlighted 12-unit cycle does not erase the more frequent cycles that stop before four wins. There is no recovery guarantee, loss-minimization proof or reliable income mechanism.
Risk controls
Use a unit small enough that the 6-unit bet is affordable, set a total loss limit and time limit, and never chase a cycle. Flat betting is simpler if your goal is to limit stake variation.
The 6-unit figure is the largest opening wager, not necessarily the largest amount committed during a round. If doubling is available, doubling that hand commits 12 units; splitting into two hands and doubling both commits 24, before any further resplits. Check the actual rules and leave room for correct decisions. Do not mistake a small base unit for a small maximum exposure.
Further reading
Use 1-3-2-6 only as a staking pattern; it cannot change the mathematical expectation of the underlying bets.
