Walkthrough: A $100 Evening on Red

The plan

Budget $100, which is money we can lose. Stake $5, 5% of the budget, which gives us about twenty losing bets in hand. Stop-lossstrategyStop-lossA pre-set amount of loss at which you end the session.Read full → at −$50 and stop-winstrategyStop-winA pre-set profit target at which you end the session.Read full → at +$50, decided now. Expected lossmathExpected lossExpected value times total amount wagered; the average amount lost over a session or a period.Read full → over 60 spins is 60 × $5 / 37 = $8.11. We expect to leave with about $92 and to be anywhere between $20 and $170 with reasonable probabilitymathProbabilityChance of an outcome, from 0 to 1 or 0% to 100%. One number: 1/37 = 2.70%.Read full →.

Spins 1–20

R B B R R 0 B R R B R B B B R R B R B R. Ten redsbetRedEven-money bet on the 18 red numbers. French: rouge.Read full →, nine blacksbetBlackEven-money bet on the 18 black numbers. French: noir.Read full →, one zerowheelZeroThe single green pocket that no even-money, dozen or column bet covers; the source of the house edge. Also: single zero, 0.Read full →: +$50 − $45 − $5 = $0. Balance $100. The zero at spin 6 cost a chipmoneyChipA token representing a fixed amount, placed on the layout to make a bet. Also: check.Read full → and was, at 1/37, a little early. Nothing here is unusual. We are level after twenty spins.

Spins 21–36

B B B B B R B B R B B R B B B B. Five blacks to open, thirteen in all: three reds, thirteen blacks, +$15 − $65 = −$50. Balance $50. This is the stretch that makes people change their bet, double up or switch colors. The probability of 13 or more blacks in 16 spins is under 1%; it was going to happen to somebody tonight. We are down $50 from the start, the stop-loss fires at spin 36, and we stand up.

Spins 37–60, without us

R B R B, then R R B R 0 R B R R B R R B B R R B R B R. Fourteen reds, nine blacks, one zero: had we stayed, +$70 − $45 − $5 = +$20 and a balance of $70 at spin 60. Thirty-six spins at a live table is about 45 minutes. We left with $50, down $50, against an expected −$4.86 for 36 spins. Thirteen reds, twenty-two blacks, one zero.

What happened

We paid about $5 for 45 minutes of roulette, plus $45 of bad luck. Thirteen reds in 36 spins is well below the expected 17.5, and nine reds short of the blacks is −$45 before the zero. The evening was decided by variancemathVarianceA measure of how widely results spread around the expected value. High for straight up, low for even-money bets.Read full →; the price was decided by the stake and the spins; the stop-loss decided when it ended. Staying would have recovered $20 by spin 60, and that is not a reason to stay: the recovery was variance too, and so was the black run that came before it.

What we did not do

Change the stake after a loss (that is a progressionstrategyProgressionAny rule that changes the stake based on previous results. Negative progressions raise it after losses, positive after wins.Read full →, and it raises turnovermoneyTurnoverThe total amount wagered over a session or period, counting re-bet winnings. Also: handle, action.Read full →). Switch colors after the black run (identical odds). Stay past 60 spins because we were “nearly even” (that is the stop-loss being renegotiated). Bet the dozenbetDozen1–12, 13–24 or 25–36, pays 2:1.Read full → that “hadn’t come up” (same edge, different shape). Every one of these would have changed the shape of the evening and none would have changed its expected cost.

Questions