Does the Fibonacci roulette system work?

How Fibonacci is played

1. Stakes follow 1, 1, 2, 3, 5, 8, 13… units, starting at the first 1.
2. After a loss, move one step forward in the sequence.
3. After a win, move two steps back (never below the start).

What 20,000 sessions show

Sessions that finished ahead were up $200 on average; sessions that finished behind were down $681.44. 30.9% of sessions ended because the next stake no longer fit the bankroll or the table limit.

Fibonacci escalates more slowly than doubling, so sessions last longer before they break. But a win only cancels the last two losses, not the whole run, so the player can be several wins away from recovery while stakes are still climbing.

The median session lasted 192 spins. The median longest losing run was 7 spins in a row (the worst of 20,000 was 11), and one session in ten put at least $275 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 −$2.78 to −$5.39 per $100, and the mean session from −$72 to −$155.

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.

-- Fibonacci: move one step up the Fibonacci sequence after a loss, two steps back after a win.
-- 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 i

local function fib(n)
  local a, b = 1, 1
  for _ = 1, n do a, b = b, a + b end
  return a
end

local function reset() i = 0 end

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

local function settle(result)
  if result.net > 0 then i = math.max(0, i - 2) else i = 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 Martingale system work?
• Does the D’Alembert system work?
• Does the Labouchère system work?
• Study: Five strategies on the same seeds
• All 20 systems, compared on the same seeds