Does the 1-3-2-6 system work?

How 1-3-2-6 is played

1. Stakes follow 1, 3, 2, 6 units on an even-money bet.
2. After a win, move to the next stake. After the fourth win, start again at 1.
3. After any loss, start again at 1.

What 20,000 sessions show

Sessions that finished ahead were up $177.65 on average; sessions that finished behind were down $282.31. Almost no session ran out of money or hit the table limit; the losses came from steady erosion instead. 70.8% reached the 500-spin cap without hitting the target or busting.

A full four-win sequence nets 12 units, and a loss on the second bet costs only 2 net. The sequence completes on four straight even-money wins, roughly 5.6% of attempts on a single-zero wheel, so the system is mostly a slow series of small losses between rare completions.

The median session lasted 500 spins. The median longest losing run was 8 spins in a row (the worst of 20,000 was 22), and one session in ten put at least $30 on the table in a single spin.

European versus American wheel

The same 20,000 seeds, replayed on a double-zero wheel. The second zero roughly doubles the edge to $5.26 per $100 wagered. Measured return goes from −$2.71 to −$5.33 per $100, and the mean session from −$111 to −$231.

The code that produced these numbers

This Lua is the strategy as Engineer mode runs it, inside the same sandbox and kernel. A test in the repository replays it against the bulk generator on fixed seeds and fails the build if the two ever disagree by a single dollar.

-- 1-3-2-6: stake 1, 3, 2, then 6 units across a winning run; reset on any loss.
-- Session rules shared by every 0xroulette.com/systems page:
-- $5 unit, $500 table max, walk away at +$200, and stop the moment
-- the next stake can't be covered by the bankroll or the table limit.
local UNIT, TABLE_MAX, TARGET = 5, 500, 200

local seq, i = { 1, 3, 2, 6 }, 1

local function reset() i = 1 end

local function place(ctx)
  return { { type = "red", amount = UNIT * seq[i] } }
end

local function settle(result)
  if result.net > 0 then i = i % 4 + 1 else i = 1 end
end

-- Shared wrapper: enforces the session rules around place/settle.
strategy = {}
local start, stopped

function strategy.setup(ctx)
  start, stopped = ctx.bankroll, false
  reset()
end

function strategy.bet(ctx)
  if stopped or ctx.bankroll >= start + TARGET then
    stopped = true
    return {}
  end
  local bets, stake = place(ctx), 0
  for _, b in ipairs(bets) do
    if b.amount > TABLE_MAX then stopped = true end
    stake = stake + b.amount
  end
  if stake > ctx.bankroll then stopped = true end
  if stopped then return {} end
  return bets
end

function strategy.on_spin(ctx, result)
  if not stopped then settle(result) end
end

Session rules

Limitations

One bankroll, one unit size, one table limit, and one walk-away target. A bigger bankroll or a higher limit moves where a progression breaks; it does not change the return per dollar wagered. Spins are fair and independent, as on a correctly functioning wheel or a certified RNG. Physical wheel bias is a separate question, covered on Physics.

Related

• Does the Paroli system work?
• Does the Reverse Martingale system work?
• Does the Contra D’Alembert system work?
• All 20 systems, compared on the same seeds