Does the Reverse Labouchère system work?

How Reverse Labouchère is played

1. Write the line 1, 2, 3, 4 and stake the first plus last number, in units.
2. On a win, add the stake to the end of the line.
3. On a loss, cross off the first and last numbers.
4. If the line empties or the next stake would exceed the table maximum, start a new line.

What 20,000 sessions show

Sessions that finished ahead were up $269.80 on average; sessions that finished behind were down $999.91. 28.5% of sessions ended because the next stake no longer fit the bankroll or the table limit.

The reverse version accepts many small cycle losses (each cleared line costs 10 units) in exchange for occasional long winning runs where the stake grows. It turns Labouchère’s rare large loss into frequent small ones.

The median session lasted 50 spins. The median longest losing run was 5 spins in a row (the worst of 20,000 was 21), and one session in ten put at least $285 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 −$2.66 to −$5.44 per $100, and the mean session from −$92 to −$199.

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.

-- Reverse Labouchère: Labouchère inverted: append the stake on a win, cross off two numbers on a 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 line

local function reset() line = { 1, 2, 3, 4 } end

local function stake_units()
  if #line == 1 then return line[1] end
  return line[1] + line[#line]
end

local function place(ctx)
  return { { type = "red", amount = UNIT * stake_units() } }
end

local function settle(result)
  local units = stake_units()
  if result.net > 0 then
    table.insert(line, units)
  else
    table.remove(line, 1)
    table.remove(line)
  end
  if #line == 0 or UNIT * stake_units() > TABLE_MAX then reset() 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 Labouchère system work?
• Does the Reverse Martingale system work?
• Does the Paroli system work?
• All 20 systems, compared on the same seeds