Does betting on two dozens work?

How Two Dozens is played

1. Each spin: one unit on 1–12 and one unit on 13–24.
2. A hit on either dozen pays 2:1 on that bet and loses the other: net +1 unit.
3. Anything in 25–36 or a zero loses both bets: net −2 units.

What 20,000 sessions show

Sessions that finished ahead were up $101.71 on average; sessions that finished behind were down $190.89. Almost no session ran out of money or hit the table limit; the losses came from steady erosion instead. 94.5% reached the 500-spin cap without hitting the target or busting.

Covering 24 of 37 numbers hits about 65% of the time, but each win nets one unit and each miss costs two. The win rate looks favourable; the payout ratio is what makes the expectation negative.

The median session lasted 500 spins. The median longest losing run was 5 spins in a row (the worst of 20,000 was 16), and one session in ten put at least $10 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 −$2.72 to −$5.30 per $100, and the mean session from −$133 to −$264.

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.

-- Two Dozens: one unit each on the first and second dozens, every spin.
-- 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 function span(a, b)
  local t = {}
  for n = a, b do t[#t + 1] = n end
  return t
end
local FIRST, SECOND = span(1, 12), span(13, 24)

local function reset() end
local function settle(result) end

local function place(ctx)
  return {
    { type = "dozen", pockets = FIRST, amount = UNIT },
    { type = "dozen", pockets = SECOND, amount = UNIT },
  }
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 Romanosky roulette system work?
• Does a Martingale on dozens work?
• Does the James Bond roulette strategy work?
• All 20 systems, compared on the same seeds