# Bet the Set Progressive

## Introduction

I noticed this variation of Bet the Set on April 19, 2013 at the Red Rock casino in Las Vegas. It was dealt from a six-deck game. The bet wins if the player has a pair for his initial two cards, more if they are suited. Unlike the normal Bet the Set, if the player has a pair he has a chance for big wins if the dealer also has a pair of the same rank.

If the player gets a colored four of a kind not only is he paid 250 to 1, but also wins a progressive jackpot. In addition, there are envy bonuses if another player gets a colored four of a kind. The minimum bet to qualify for the jackpot and envy bonuses is \$1.

## Rules

1. The following analysis is based on six decks. I suppose any number could be used.
2. If the four cards, consisting of the player's and dealer's initial two cards, consist of a colored four of a kind, then the player's wager shall win 250 to 1, plus the amount in the progressive jackpot.
3. Otherwise, if the four cards, consisting of the player's and dealer's initial two cards, consist of a four of a kind of both red and black, then the player's wager shall pay 100 to 1.
4. Otherwise, if the player's two cards form a suited pair, then the player's wager shall pay 20 to 1.
5. Otherwise, if the player's two cards form a non-suited pair, then the player's wager shall pay 5 to 1.
6. Otherwise, the player must have two cards of different ranks, which loses.
7. If any player gets a colored four of a kind then every other player at the table who made the Bet the Set wager shall win an envy bonus of \$50.

Rack card. Click on either image for a larger version.

## Analysis

The following table shows the odds for a six-deck game, before considering the jackpot and envy bonuses. The lower right cell shows a house edge of 27.74%.

### Bet the Set — Progressive — Six Decks

Event Pays Combinations Probability Return
Colored four of a kind 250 77,220 0.000033 0.008308
Four of a kind 100 751,608 0.000323 0.032346
Suited pair 20 37,177,920 0.016000 0.319993
Pair 5 133,840,512 0.057599 0.287993
Loser -1 2,151,826,560 0.926045 -0.926045
Total   2,323,673,820 1.000000 -0.277405

The following table shows the expected value per each \$1,000 in the meter and each additional player by the bet amount. Remember that the progressive and envy bonuses are flat awards, thus the benefit is inversely proportional to bet size.

### Value per \$1000 in Meter and Additional Players

Wager Value per
\$1000 in Meter
Value per
\$1 3.323% 0.166%
\$5 0.665% 0.033%
\$10 0.332% 0.017%
\$25 0.133% 0.007%

The following table shows the expected value per each \$1,000 in the meter and each additional player by the bet amount. Remember that the progressive and envy bonuses are flat awards, thus the benefit is inversely proportional to bet size.

### Value per \$1000 in Meter and Additional Players

Wager Breakeven
Point
\$1 \$8,347.58
\$5 \$41,737.88
\$10 \$83,475.76
\$25 \$208,689.39

When I saw this bet on April 20, 2013 the meter was at \$7,817.44.