Let-It-Ride and Jackpot Bets
Bets that run over several spins: a stake left to ride on a repeat, or a small charge every spin toward a jackpot. Both are priced by where they end.
Alphabetic Roulette’s Bonus Box lets a winning stake ride on the same letter: collecting after two repeats costs 11.84%, riding on to the third 7.83%. Pro-Aggressive Roulette charges a unit every spin toward a jackpot for three spins in a line on the layout, which comes about once in 185 spins. Whether that is a fair price depends on the jackpot, which the bet does not fix.
Bets that last more than one spin
Most roulette bets are settled by one spin. A few run across several: the stake rides on a repeat, as in WINGO, or a small stake goes in on every spin toward a jackpot, as in Roulette Royale. The house edgemathHouse edgeThe share of each stake the casino keeps on average: 2.70% in European roulette.Read full → of such a bet depends on where it ends, and often the player chooses that. Two games described by Bollman (2021) show the two kinds at their clearest.
Alphabetic Roulette’s Bonus Box
Alphabetic Roulette, at Fitzgerald’s in downtown Las Vegas, put letters in place of numbers: 25 pocketsequipmentPocketOne of the 37 numbered compartments on the rotor. Also: slot, cup.Read full →, A to X and one YZ pocket that the payoutsmoneyPayoutWhat a winning bet returns, quoted as “X to 1” on top of the returned stake.Read full → ignore. Bets on 1, 2, 3, 4, 6 or 12 letters paid (24 − n)/n to 1, an edge of 4%. The Bonus Box bet was on a repeat: $1 that the letter just spun would come up again. A repeat paid $23, the ordinary 23 to 1. The player could collect, or let it ride for a second repeat, which paid $550, and then for a third, which paid $14,400.
Collecting early is the dear choice
The middle step is priced worst. A player who collects after two repeats pays 11.84%; one who rides on to the third pays 7.83%, because $14,400 is closer to a fair payout than $550 is. Most players would call taking the money the careful choice. On this bet it is the expensive one. Bollman’s own advice was simpler: skip the bet.
Words as bets
Two spaces on the Alphabetic layoutequipmentLayoutThe printed betting grid on the table. Also: table, felt, cloth.Read full → could be named by the casino, and the defaults were “Party Pit” and “Roulette”. Any word works on the same rule as long as the rule gives a payout a casino can pay. TROPICAN has eight different letters and pays 2 to 1, at the usual 4%. A five-letter word such as LUXOR does not fit: the rule asks for 3.8 to 1, and at 3½ to 1, the nearest half unitmoneyUnitThe base stake a system or a player works in. Progressions are described in units so they apply at any table.Read full → below it, the bet would cost 10%.
Pro-Aggressive Roulette: a line in three spins
Pro-Aggressive Roulette, patented in 2004 for the American wheel, adds a progressive side betbetSide betAn optional extra wager attached to the main game, usually on a streak, a bonus event or a jackpot. Almost always dearer than the standard bets.Read full → made on every spin. It pays when three spins in a row land on a line of three on the layout: a row, three in a columnbetColumnTwelve numbers in one vertical column of the layout, pays 2:1.Read full →, or a diagonal of a three-by-three block, in any order. Spins of 24, 30 and 27 would do. A larger jackpot pays for 0, 00 and 2, which form a V at the top of the layout. You need no chipsmoneyChipA token representing a fixed amount, placed on the layout to make a bet. Also: check.Read full → on the numbers, only the side bet on each of the three spins. A spin that cannot continue the current line starts a new one.
What the jackpots would have to be
Each $1 spin buys 1/185 of a small jackpot and 1/9,936 of the large one, so the return on a dollar is about S/185 + L/9,936, where S and L are the two jackpots in dollars. With the small one at $100 and the large one at $2,500, the bet returns about 79 cents on the dollar, an edge near 21%. The small jackpot alone would have to reach about $185 for the bet to break even. The book gives the probabilities but not the jackpots, so the edge is for you to work out at the table.
The common thread
A bet that lasts several spins has more than one price. Find them all before you play.
- A bet that runs over several spins is priced by where it stops.
- Collecting early is not always cheaper: on the Bonus Box it is the dearest choice.
- A charge every spin toward a jackpot is a long run of small losses paid for by one rare win. Divide the jackpot by its odds to see what each spin buys.
- The same reasoning prices WINGO, Roulette Rage and Roulette Royale on the side-bets page.
Questions
If you play it at all, riding to the third repeat is cheaper than stopping at the second. Not playing is cheaper still.
The line jackpot about once in 185 spins, the V jackpot about once in 9,900.
Only when each jackpot divided by its odds adds up to more than the stake. Check before you play.
Fun with Math
Try these yourself first. Each solution is folded; open it when you are ready.
On Alphabetic Roulette, 25 pocketsequipmentPocketOne of the 37 numbered compartments on the rotor. Also: slot, cup.Read full → with every bet paying (24 − n)/n to 1, a casino names a layoutequipmentLayoutThe printed betting grid on the table. Also: table, felt, cloth.Read full → space LUXOR. What is the most it can pay, in whole or half unitsmoneyUnitThe base stake a system or a player works in. Progressions are described in units so they apply at any table.Read full →, and still keep an edge? What does that cost?
Show the solution
Answer 3½ to 1, which costs 10%.
LUXOR has five different letters, so the rule asks for 19/5 = 3.8 to 1. At 3.8 the bet would cost the usual 4%.
The whole and half payoutsmoneyPayoutWhat a winning bet returns, quoted as “X to 1” on top of the returned stake.Read full → nearest 3.8 are 3½ and 4. At 4 to 1 the bet wins 5 times in 25 and brings back 25 units: no edge at all, a fair gamemathFair gameA game in which neither side has an edge: every bet has an expected value of zero.Read full →. So 3½ to 1 is the most that keeps an edge. It brings back 5 × 4.5 = 22.5 units for every 25 staked: 10%.
A word with eight different letters, like TROPICAN, needs 2 to 1, exactly what the rule gives. LUXOR is simply the wrong length.
Comic relief
On the Bonus Box, stopping at two is the dearest choice.
Sources
- Bollman, M. Mathematics of the Big Four Casino Table Games: Blackjack, Baccarat, Craps, & Roulette.