# Dakota Duel Draw

## Introduction

Dakota Duel Draw is a poker variant where the player has two chances to win. At the time of this writing (Feb. 1, 2023), it can be played at the Lodge casino in Deadwood, South Dakota.

## Rules

1. A single 52-card deck is used. All hands scored according to conventional poker rules.
2. Player starts with the player making the Ante bet and/or Big 8 bet at this time.
3. The dealer shall deal each player two hole cards and two sets of three community cards, also known as the flop. All community cards are dealt face down.
4. After examining his cards, the player must either make a Play bet, equal to his Ante bet, or fold.
5. The dealer shall turn over the three community cards.
6. Two poker hands shall be formed. Hand 1 using the player's hole cards and the first flop. Hand 2 using the player's hole cards and the second flop.
7. The wager on Hand 1 shall be the Play bet. The wager on Hand 2 shall be the Ante bet.
8. Both hands shall pay according to the pay table below.
9. If the player's two hole cards form a pair of 9's or higher, then he will win a bonus equal to 8x the Ante wager.
10. The Big 8 wager shall pay according to the highest five-card hand that can be created using all eight cards (both flops and the player's community cards. Even if the player folds his Ante wager, he still will have action on the Big 8. The pay table for the Big 8 is below.

The following table shows the pay table for the Ante and Play bets. Wins are on a "to one" basis.

### Ante and Play Pay Table

Hand Pays
Royal flush 100
Straight flush 50
Four of a kind 30
Full house 8
Flush 6
Straight 4
Three of a kind 3
Two pair 2
Nine of nines or better 2
All other Loss

The following table shows the pay table for the Big 8 bet. Wins are on a "to one" basis.

### Big 8 Pay Table

Hand Pays
Royal flush 150
Straight flush 70
Four of a kind 30
Full house 5
Flush 3
Straight 1

## Strategy

According to the math report by GLI, kindly provided to me by the game creator and owner, the player should raise if at least one of the follow are true about the player's hole cards.

• At least one card is a 9 or higher.
• The cards form a pair.
• The cards are suited, except with 2-7, 2-8 and 3-8.

## Analysis

Following the strategy above, the house edge on the Ante wager is 3.02%. The player will make the Play wager 80.1% of the time, for an average total wager of 1.801 units. This makes the Element of Risk, defined as the ratio of the expected player loss to total amount bet, 0.0302/1.801 = 1.68%.

The following table shows my analysis of the Big 8 bet. The lower right cell shows a house edge of 1.87%.

### Big 8 Return Table

Hand Pays Combinations Probability Return
Royal flush 150 64,860 0.000086 0.012928
Straight flush 70 546,480 0.000726 0.050833
Four of a kind 30 2,529,262 0.003361 0.100829
Full house 5 45,652,128 0.060664 0.303321
Flush 3 50,850,320 0.067572 0.202715
Straight 1 67,072,620 0.089129 0.089129
All other -1 585,822,480 0.778462 -0.778462
Total   752,538,150 1.000000 -0.018707