Problem: Two Dozen and One Chip
Two dozen dey cover 24 numbers. Add one chip on zero and you go cover 25. Di insurance dey pay?
No. Every part na −2.70% of im stake, so di combination na −2.70% of di total. Di problem dey show why, e dey calculate di exact distribution, and e dey show wetin dey change (di shape) and wetin no dey change (di price).
Di Problem
You stake $10 on di first dozenbetDozen1–12, 13–24 or 25–36, e dey pay 2:1.Read di whole tin →, $10 on di second dozen and $1 on zerowheelZeroDi one green pocket wey no even-money, dozen or column bet dey cover; na im be di source of di house edge. Dem also dey call am: single zero, 0.Read di whole tin →. (a) Wetin be di outcomes wey fit happen and dia probabilities? (b) Wetin be di expected valuemathsExpected valueDi average result for each bet for di long run. −1/37 of di stake for every standard European bet.Read di whole tin →? (c) Di zero chipmoniChipToken wey stand for one fixed amount, wey you put on top di layout to make bet. Dem also dey call am: check.Read di whole tin → dey make di bet better?
Answer (a) and (b)
Outcomes: ballequipmentBallDi small ball wey dem dey throw for di track against di rotor. Modern balls na ivorine or Teflon, 18–21 mm.Read di whole tin → for 1–24 (24 pocketsequipmentPocketOne of di 37 small boxes wey get number for di rotor. Dem also dey call am: slot, cup.Read di whole tin →): one dozen dey pay $20, di oda one lose $10, zero lose $1: net +$9. Ball for 25–36 (12 pockets): both dozens lose, zero lose: −$21. Ball on zero (1 pocket): di dozens lose $20, zero pay $35: +$15. EV = (24 × 9 + 1 × 15 − 12 × 21)/37 = (216 + 15 − 252)/37 = −21/37 ≈ −$0.57 for every spin on $21 wey you stake: 2.70%.
Answer (c)
Without di zero chip: (24 × 10 − 13 × 20)/37 = (240 − 260)/37 = −20/37 ≈ −$0.54 on $20 wey you stake, also 2.70%. Di zero chip don turn di −$20 zero outcome to +$15 (improvement of $35 one time out of 37, wey worth $0.95 for every spin) and e cost $1 for di oda 36 spins (wey worth $0.97 for every spin). Di net change: −$0.03 for every spin, wey be 2.70% of di extra dollar. Dem price di insurance exactly like everytin else.
Why E Dey Apply Everywhere
Expected values dey add up. Any set of bets wey you put di same time get EV wey equal di sum of di EVs of di parts, and each one of dem na −1/37 of im stake. So any combination na −1/37 of di total stake. No arrangement of chips for di layoutequipmentLayoutDi betting grid wey dem print for di table. Dem also dey call am: table, felt, cloth.Read di whole tin →, no matter how many, fit escape dis; di Bet Builder tool go confirm am for any set wey you fit put. Wetin combinations dey change na di distribution: how often you dey win, how much, and how bad di worst case go be.
Harder Question Wey Follow
Find combination of standard bets wey go cover all 37 numbers. Three dozen ($10 each) plus $1 on zero: any of 1–36 go bring −$1 (one dozen go pay $20, di oda two go lose $20, zero go lose $1), and zero go bring +$35 − $30 = +$5. EV = (36 × (−1) + 5)/37 = −31/37 on $31 wey you stake: 2.70%. You fit guarantee sey notin go ever surprise you, and you still dey pay di same price for dat privilege.
Formula
Questions wey pipo dey ask
No, for European table. For French table, even-money betsbetEven-money betRed/black, odd/even, high/low. 18 numbers, e dey pay 1:1.Read di whole tin → alone na 1.35%; if you add anytin else, di blended edge go rise.
E dey lose $1 for every $1 only on zero, and e no dey win anytin oda time. EV −2.70% with no upside: di one combination wey no get any point at all.
To choose shape of session wey you go enjoy. Dat one na correct reason and na di only one.
Small laugh
Insurance for roulette table dey cost exactly wetin e dey save.
Sources
- Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling.