Problem: two dozen an a chip

Di problem

Yuh stake $10 pon di fus dozenbet demDozen1–12, 13–24 or 25–36, pay 2:1.Read di whole ting →, $10 pon di second dozen an $1 pon zeropon di wheelZeroDi one green pocket weh no even-money, dozen or column bet nuh cover; a weh di house edge come fram. Nex name: single zero, 0.Read di whole ting →. (a) Wah di result dem weh can happen, an wah dem probability? (b) Wah a di expected valuemathsExpected valueDi average result pon evry bet inna di long run. −1/37 a di stake fi evry standard European bet.Read di whole ting →? (c) Di zero chipmoney mattaChipA token weh stand fi a fix amount, weh yuh put pon di betting layout fi mek a bet. Nex name: check.Read di whole ting → mek di bet betta?

Solution (a) an (b)

Result dem: ballgearBallDi likkle ball weh di dealer fling roun di track di opposite way to di rotor. Modern ball mek outta ivorine or Teflon, 18–21 mm.Read di whole ting → inna 1–24 (24 pocketgearPocketOne a di 37 compartment wid numba pon di rotor. Nex name: slot, cup.Read di whole ting →): one dozen pay $20, di odda one lose $10, zero lose $1: net +$9. Ball inna 25–36 (12 pocket): both dozen lose, zero lose: −$21. Ball pon zero (1 pocket): di dozen dem lose $20, zero pay $35: +$15. EV = (24 × 9 + 1 × 15 − 12 × 21)/37 = (216 + 15 − 252)/37 = −21/37 ≈ −$0.57 evry spin pon $21 stake: 2.70%.

Solution (c)

Widout di zero chip: (24 × 10 − 13 × 20)/37 = (240 − 260)/37 = −20/37 ≈ −$0.54 pon $20 stake, 2.70% too. Di zero chip tun di −$20 zero result inna +$15 (a improvement a $35 one time outta 37, worth $0.95 evry spin) an cost $1 pon di odda 36 spin (worth $0.97 evry spin). Net change: −$0.03 evry spin, weh a 2.70% a di extra dolla. Di insurance price exactly like evryting else.

Wah mek dis work fi evryting

Expected value add up. Any set a bet weh yuh put dung same time have EV equal to di sum a di piece dem EV, an each one a dem a −1/37 a it stake. Suh any combination a −1/37 a di total stake. Nuh way nuh deh fi lay out chip pon di betting layoutgearBetting layoutDi bettin grid weh print pon di table. Nex name: table, felt, cloth.Read di whole ting →, nuh matta ow much, weh escape dis; di Bet Builder tool wi confirm it fi any set yuh can put dung. Wah combination change a di distribution: ow often yuh win, ow much, an ow bad di wors case be.

A harda follow-up

Find a combination a standard bet weh cova all 37 numba. Tree dozen ($10 each) plus $1 pon zero: any a 1–36 net −$1 (one dozen pay $20, di odda two lose $20, zero lose $1), an zero net +$35 − $30 = +$5. EV = (36 × (−1) + 5)/37 = −31/37 pon $31 stake: 2.70%. Yuh can mek sure seh nutten neva surprise yuh, an yuh still pay di same price fi dat privilege.

Formula

Question dem