Repeater Bets Plus

Introduction

Repeater Bets Plus is a table game version of the craps Repeater repeater side bets. They throw in some extra bets and a surrender option to some bets. The game began a field trial at the Linq in Las Vegas on July 16, 2021.

Rules

1. Two ordinary six-side dice are used.
2. There are many bets available. The commonality to all bets is that all unresolved bets lose on a total of seven. To win, the player must roll other totals a specified number of times before rolling a total of seven.
3. The player may make place bets at any time on any total that has not already been rolled.
4. Table 1 below shows the bets available, what they pay, and a brief description of what is required to win. All wins are on a "for one" basis.
5. Bets on a specific total have a surrender option if the total bet on has already been rolled at least so-many times, according to the specific bet. The surrender values are shown in Table 2 below.

The following table shows the available bets, what they pay, and a brief description of what is required to win.

Table 1 — List of Bets

Bet Pays Description
2 or 12 before 7 3 2 or 12 before 7
3 or 11 before 7 2 3 or 11 before 7
2 40 2 before 7, 2x
3 50 3 before 7, 3x
4 65 4 before 7, 4x
5 80 5 before 7, 5x
6 90 6 before 7, 6x
8 90 8 before 7, 6x
9 80 9 before 7, 5x
10 65 10 before 7, 4x
11 50 11 before 7, 3x
12 40 12 before 7, 2x
2, 3, 11, or 12 100 Any 2, 3, 11 or 12, 7x
Updown 15 A win on the 2, 3, 4, 5, or 6 bet
Downtown 15 A win on the 8, 9, 10, 11, or 12 bet
Even 12 A win on the 2, 4, 6, 8, 10, or 12 bet
Odd 18 A win on the 3, 5, 9, or 11 bet
Horn 12 A win on the 2, 3, 11 or 12 bet
Citywide 9 A win on the 2, 3, 4, 5, 6, 8, 9, 10, 11, or 12 bet

The following table shows the full and surrender values for the bets on 2 to 12, according to the number of times the given total has already been rolled before a seven.

Table 2 — Surrender Values

Bet 6x 5x 4x 3x 2x 1x
6 or 8 90 40 18 8
5 or 9   80 30 12
4 or 10     65 21 7
3 or 11       50 12
2 or 12         40 6

Analysis

The following table 3 shows the probability of winning and expected return of all available bets. The average house edge is 19.99%, with a low of 17.80% on Citywide to a high of 24.65% on the Horn.

Table 3 — Analysis

Bet Pays Prob. Win Exp. Value
2 40 0.020408 -0.183673
3 50 0.015625 -0.218750
4 65 0.012346 -0.197531
5 80 0.010240 -0.180800
6 90 0.008820 -0.206209
8 90 0.008820 -0.206209
9 80 0.010240 -0.180800
10 65 0.012346 -0.197531
11 50 0.015625 -0.218750
12 40 0.020408 -0.183673
Even 12 0.065395 -0.215265
Odd 18 0.043176 -0.222839
Downtown 15 0.054592 -0.181121
Uptown 15 0.054592 -0.181121
Horn 12 0.062789 -0.246528
Citywide 9 0.091330 -0.178032

Table 4 below shows the probability of reaching mid-state probabilities for bets on a 2 to 12 (except 7) that have a surrender value or a full win.

Table 4 — Mid-State Probabilities

Bet 6x 5x 4x 3x 2x 1x
6 or 8 0.008820 0.019404 0.042688 0.093914
5 or 9   0.010240 0.025600 0.064000
4 or 10     0.012346 0.037037 0.111111
3 or 11       0.015625 0.062500
2 or 12         0.020408 0.142857

Table 5 below shows the expected value of the 2 to 12 bets (except 7) according to the available surrender points.

Table 5 — Surrender Expected Values

Bet 6x 5x 4x 3x 2x 1x
6 or 8 -0.206209 -0.223848 -0.231610 -0.248685
5 or 9   -0.180800 -0.232000 -0.232000
4 or 10     -0.197531 -0.222222 -0.222222
3 or 11       -0.218750 -0.250000
2 or 12         -0.183673 -0.142857

My surrender advice is that if you are looking to maximize expected value per initial bet made, then going for the full win is the best strategy on all bets, except the 2 and 12, where the player should surrender after one win.

However, an argument could be made the player should keep going after achieving one 2 or 12 on those bets. If we look at risking the equity after one 2/12 win as a separate bet, it would have a house edge of 4.76%. This is less than any initial bet in the game. The way I typically give gambling advice to to maximize return per the initial wager. Looking at it that way, the player should surrender after one 2 or 12.

Strategy

As mentioned earlier, the average house edge in this game, is 19.99%. This sounds high, but keep in mind most bets will take many rolls of the dice to resolve. If you do play, the best bet, before considering the surrender option, is on Citywide at 17.80%. However, you can cut down the house edge to 14.29% by betting on a 2 or 12 and surrendering for a win of 6 for 1 after rolling the target total once.

Methodology

The math for most of the bets was rather easy. However, for the following were bets were more complicated to analyze: Even, Odd, Uptown, Downtown, Horn, and Citywide. For these, I think most people use use a random simulation, but I try to get a closed-form solution wherever I can. For these bets, I used integral calculus. Here is a short document explaining How to Analyze the Even, Odd, Uptown, Downtown, Horn, and Citywide bets in Repeater Bets Plus (PDF).

I would like to thank Ace2 for verifying the answer for the Even bet and for his general help with this method of analyzing craps side bets.