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Last Updated: March 20, 2007

Wan Doy Pairs Poker

Introduction

Wan Doy is a unique poker-based game using seven cards, with no straights or flushes. Although the rules are unconventional the optimal strategy is simple and the element of risk is 1.94%. The game is available to play at online casinos using Wager Works software.

Rules

  1. The game is played with a single 52-card deck, which is shuffled before every hand. All cards are ranked as in poker, except aces are always high.
  2. Play starts with the player making an ante and Bonus Wager of exactly the same amount. In addition there is an optional side bet.
  3. After all wagers have been made each player and the dealer shall receive seven cards dealt face down. The player may look at his own cards but may not share information with other players.
  4. After examining his own cards the player has the choice to either raise or fold. If the player raises he must make a raise wager exactly equal to the ante wager. If the player folds he forfeits the ante, Bonus Wager, side bet (if made), and his cards.
  5. The dealer will flip over his cards.
  6. Both player and dealer hands will be ranked according to the Bonus Wager pay table. Note that there are no straights or flushes. Only pairs and higher shall count for purposes of breaking a tie. For example QQ66J83 would beat QQ44K97. Singletons are not considered in the ranking of hands. For example KKQ9753 would push against KKJ9753. Any two hands of less than a pair would push.
  7. If the player hand outranks the dealer hand then the ante and raise bets shall pay even money.
  8. If the player has at least a three of a kind then the bonus hand shall pay according to Bonus Wager Pay Table below, regardless of the value of the dealer hand.
  9. If the player has less than a three of a kind and the player beats the dealer then the Bonus Wager shall push. Otherwise if the player has less than a three of a kind and ties or loses to the dealer's hand then the bonus bet shall lose.
  10. The side bet shall pay according to both the value of player's and dealer's hands. If both hands qualify for a win then the player will be paid for both. If one hand qualifies for a win the player's original side shall be returned, if both qualify the player shall get his original side bet back twice.

The following pay table is for the Bonus Wager.

Bonus Wager Pay Table

Hand Pays
Four of a kind plus Three of a kind 100
Four of a kind plus pair 80
2 Three of a kinds 50
Three of a kind plus 2 pairs 25
Four of kind 10
3 pairs 5
Three of a kind plus pair 3
Three of a kind 2
2 pair or less, player beats dealer 0
2 pair or less, dealer ties or beats player -1

The following pay table is the last known confirmed one for the side bet, which pays based on both the player's and dealer's hand. The original bet is returned once for each win.

Side Bet Pay Table

Hand Pays
4 of a kind + 3 of a kind 5000
4 of a kind + pair 150
3 of a kind + 3 of a kind 75
3 of a kind + pair + pair 50
4 of a kind 20
Pair + pair + pair 15
All other Loss

House Edge

The following table shows all possible outcomes under optimal player strategy, the win (positive) or loss (negative) to the player, the probability, and contribution to the total return.

Wan Doy Return Table

Player Hand Winner Pays Combinations Probability Return
4 of a kind + 3 of a kind Player 102 28316700000 0.000005 0.000476
4 of a kind + pair Player 82 1868460000000 0.000308 0.025237
3 of a kind + 3 of a kind Player 52 2489930000000 0.00041 0.021327
3 of a kind + pair + pair Player 27 5597370000000 0.000922 0.024893
4 of a kind Player 12 8280440000000 0.001364 0.016367
Pair + pair + pair Player 7 110621000000000 0.018221 0.127546
3 of a kind + pair Player 5 143704000000000 0.02367 0.118351
3 of a kind Player 4 276136000000000 0.045484 0.181935
Pair + pair Player 2 1061320000000000 0.174815 0.34963
Pair Player 2 1272310000000000 0.209568 0.419136
No pair Player 2 0 0 0
4 of a kind + 3 of a kind Dealer 98 137280 0 0
4 of a kind + pair Dealer 78 458172000 0 0.000006
3 of a kind + 3 of a kind Dealer 48 1953220000 0 0.000015
3 of a kind + pair + pair Dealer 23 9372650000 0.000002 0.000036
4 of a kind Dealer 8 25731000000 0.000004 0.000034
Pair + pair + pair Dealer 3 1513750000000 0.000249 0.000748
3 of a kind + pair Dealer 1 5809190000000 0.000957 0.000957
3 of a kind Dealer 0 22890200000000 0.00377 0
Pair + pair Dealer -3 284047000000000 0.046787 -0.14036
Pair Dealer -3 1569260000000000 0.25848 -0.775441
No pair Dealer -3 0 0 0
4 of a kind + 3 of a kind Tie 100 0 0 0
4 of a kind + pair Tie 80 0 0 0
3 of a kind + 3 of a kind Tie 50 0 0 0
3 of a kind + pair + pair Tie 25 0 0 0
4 of a kind Tie 10 115150000 0 0
Pair + pair + pair Tie 5 96370600 0 0
3 of a kind + pair Tie 3 0 0 0
3 of a kind Tie 2 0 0 0
Pair + pair Tie -1 252254000000 0.000042 -0.000042
Pair Tie -1 29086800000000 0.004791 -0.004791
No pair Tie -1 0 0 0
Player folds -2 1275850000000000 0.210151 -0.420303
Total 6071102437399880 1 -0.054243

The lower right cell shows that for two initial bets of 1 unit each the player can expect to lose 0.054243 units. For example if the player bet $100 on the ante and Bonus Wager he could expect to lose $5.42. The house edge is traditionally defined as the expected loss to the initial wager. In this case two initial wagers are required so the house edge would be 5.4243%/2 = 2.7122%. After considering raise bets the average total wager is 2.79 units. Thus the element of risk is 5.4243%/2.79 = 1.94%.

Originally, three pairs paid 6 to 1, as opposed to the current 5 to 1. I think most, if not all Wager Works casinos now pay 5 to 1, so I indicate 5 as the win for three pairs in the pay table above. However, should you see a game that pays 6 to 1 the house edge would be lowered to 3.58%.

The next table shows how the return of the side bet is determined. The side bet is actually two side bets, half on the player's hand and half on the dealer's hand. So for a loss I show only half a unit. Normally the return column is the product of the probability and the win. However in this case it is double that, because there are two hands the bet is based on.

Side Bet Return Table

Hand Pays Combinations Probability Return
4 of a kind + 3 of a kind 5000 624 0.000005 0.046642
4 of a kind + pair 150 41184 0.000308 0.092351
3 of a kind + 3 of a kind 75 54912 0.00041 0.061568
3 of a kind + pair + pair 50 123552 0.000924 0.092351
4 of a kind 20 183040 0.001368 0.054727
Pair + pair + pair 15 2471040 0.01847 0.554109
All other -0.5 130910208 0.978515 -0.978515
Total 133784560 1 -0.076767

Strategy

The strategy is simple, the player should raise on any pair or higher.


Written by: Michael Shackleford

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