Mathematical Analysis of
Bonus Box (Side Bet)
For " 00" Roulette
The “Bonus Box Side Bet” is an optional side bet for
the player who is playing double-0 roulette. This bet
allows the player to wager that the number just rolled
will repeat 1, 2, or 3 times. The purpose of this side bet
is to encourage players to go for a large payout, with
odds equal to normal roulette odds for 1 repeat, and
with odds better than normal roulette for repeating 2
or 3 times.
This wager appears on the layout as the “Bonus Box.”
The rules and payouts of the Bonus Box wager are as
follows:
1. Player places $1 wager in “Repeat” area of Bonus
Box.
2. If the previous number repeats, the player has the
option of either taking a $35 payoff, or moving his
chip to the next location, “2-nd time.” If the previous
number does not repeat, the player loses his original $1
wager.
3. If the previous number repeats again, the player has
the option of either taking a $1,350 payoff, or moving
his chip to the next location, “3-rd time.” If the
previous number does not repeat, the player loses his
original $1 wager.
4. If the previous number repeats again, the player
receives a $50,000 payoff. If the
previous number does not repeat, the player loses his
original $1 wager.
5. The house edge and payoff tables for three possible
player strategies are given in
Appendix A. The house edge for Player 1 (playing for
first repeat only) is 5.26%.
The house edge for Player 2 (playing for first and
second repeats) is 6.44%. The
house edge for Player 3 (playing for all repeats) is 8.88%






Progressive
Bonus Box (Side Bet)
For Alphabetic Roulette
1. Player Places $1 wager in " Repeat " area of Bonus
Box.
2. If previous letter repeats, the player has the option of
either taking a $23 payoff, or moving his chip to the next
location ," 2-nd time". If the previous letter does not
repeat, the player loses his original $1 wager.
3. If the previous letter repeats again, the player has the
option of either taking a $550 payoff, or moving his
chip to the next location, " 3-rd time." If the previous
letter does not repeat, the player loses his original
$1 wager.
4. If the previous letter repeats again, the player
receives a $14,400 payoff. If the previous letter does
not repeat, the player loses his original $1 wager.
5. The payoff tables for three possible players are given
below. The house edge for Player 1 is 4.00%. The
house edge for player 2 is 11.84%. The house edge for
player 3 is 7.83%
Progressive
Progressive
Progressive