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Rabbit Hunter

Rules

 

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Sunset Station Pay Table

Hand Pays
Royal Flush 500
Straight Flush 100
Four of a Kind 50
Full House 30
Flush 9
Straight 7
Three of a Kind 5
Two Pairs 2
Pair of Tens or Better 1

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  1. Rabbit Hunter is a house-banked poker game played heads up against the dealer. The object of the game is to win by having a better five-card poker hand than the dealer.
  2. The game is played using one standard 52-card deck. The game uses standard poker rules for scoring and comparing hands.
  3. To begin, the player makes an Ante wager and an optional Bonus Bet equal to his Ante.
  4. The dealer deals five cards face down to the player and to himself. The player then examines his cards and must exercise one of the following options:
    • Fold, forfeiting his Ante and Bonus Bet (if made).
    • Play by making a Play Bet equal to his Ante.
    • Play and buy a card. The player must make a Play Bet equal to his Ante and pay a fee equal to his Ante to receive a sixth card. This amount is not a wager, but rather payment for the sixth card that goes directly into the chip rack. With the card, the player’s hand is comprised of the best five out of six cards.
  5. Once all players have acted, the dealer reveals his five cards and compares his hand to the player’s hand. The dealer must qualify with ace-high or better. If the dealer does not qualify, then the Player’s Ante is a push and only the Play Bet is in action. Otherwise, both the player’s Ante and Play Bet are in action.
    • If player’s hand beats the dealer’s hand, the player is paid 1 to 1 on all bets in action.
    • If the dealer’s hand beats the player’s hand, then the player loses all bets in action.
    • In the event of a tie, all bets in action push.
  6. The Bonus Bet pays based on the player’s best five-card hand and is not affected by the value of the dealer’s hand (the player may lose against the dealer but still be paid for a winning Bonus Bet hand). Literature from Shufflemaster, the game's distributor, indicates six different pay tables. The one used at the Sunset Station in Las Vegas was as follows.
  7. There is also a Bad Beat side bet that pays 10 to 1 if both the player and dealer have a pair of tens or better, thus causing one of them to have a "bad beat."
 

Strategy

The next table shows the probability of any given hand beating the dealer's hand.
 

Player's Hand Ranking

Hand Probability of Winning
Royal Flush 0.99999923
Straight Flush 0.99999154
4 of a Kind 0.99986456
Full House 0.99902423
Flush 0.99732124
Straight 0.99437621
3 of a Kind 0.98184966
2PR – A up 0.96762859
2PR – K up 0.96061963
2 PR – Q up 0.95422015
2 PR – J up 0.94843014
2 PR – 10 up 0.94324961
2 PR – 9 up 0.93867855
2 PR – 8 up 0.93471696
2 PR – 7 up 0.93136485
2 PR – 6 up 0.92862222
2 PR – 5 up 0.92648906
2 PR – 4 up 0.92496537
2 PR – 3 up 0.92405116
PR A 0.90749377
PR K 0.87498846
PR Q 0.84248315
PR J 0.80997784
PR 10 0.77747253
PR 9 0.74496722
PR 8 0.71246191
PR 7 0.6799566
PR 6 0.64745129
PR 5 0.61494598
PR 4 0.58244067
PR 3 0.54993536
PR 2 0.51743005
AK High 0.46899529
AQ High 0.41326531
AJ High 0.37323391
A10 High 0.34576138
A9 High 0.32790424
A8 High 0.31711146
A7 High 0.31122449
A6 High 0.30847724
KQ High 0.26236264
KJ High 0.23076923
K10 High 0.20918367
K9 High 0.19525118
K8 High 0.18681319
K7 High 0.18210361
K6 High 0.14717425
K5 High 0.15678964
QJ High 0.14854788
Q10 High 0.12715856
Q9 High 0.11322606
Q8 High 0.10478807
Q7 High 0.10007849
Q6 High 0.04866562
Q5 High 0.06966248
J High 0.05867347
10 High 0.02845369
9 High 0.01216641
8 High 0.0043171
7 High 0.00078493


Based on the probabilities in the table above, the following is the strategy recommend by Elliot Frome, based on the player making the Bonus Bet.

Play and Buy the Card when:
  • Player has a Straight Flush that is a 4-Card Royal
  • Player has a Flush that is a 4-Card Straight Flush or 4-Card Inside Straight Flush
  • Player has a Straight that is a 4-Card Straight Flush or 4-Card Inside Straight Flush
  • Player has Three of a Kind
  • Player has Two Pair
  • Player has a Pair
  • Player has nothing, but a 4-Card Straight Flush, 4-Card Inside Straight Flush, 4-Card Flush, 4-Card Straight or 4-Card Inside Straight


Fold when:
Player has A-8 or less and is not a Play/Buy hand

Play and not Buy when:
Any other hand
 

Odds

The math report by Elliot Frome indicates the Overall Payback is 98.89%. I assume he means the return relative to the total amount bet. Thus, the element of risk is 100%-98.89%=1.11%. He also indicates the average number of units wagered is 3.2411. This would make the expected loss relative to a single unit 1.11%×3.2411 = 3.61%. If we define the house edge as the expected loss compared to the sum of the Ante and Bonus wagers then it would be 3.61%/2 = 1.80%.

Elliot never mentions the odds if the player doesn't make the Bonus bet. However, Discount Gambling says that the Bonus Bet carries a 136% player advantage, so the player should always make it.

Bad Beat

 

Elliot's report doesn't mention the Bad Beat bet, so I had to do the math on that myself. I calculate the odds of a pair of tens or better are 23.878% with five cards, and 38.104% with six. According to Discount Gambling, the player makes the raise bet 47% of the time. This results in a probability of winning the Bad Beat bet of 7.2981%. The following return table for the Bad Beat shows a house edge of 19.72%. This admittedly is a rough estimate, but good enough to show it is a bad bet.

Bad Beat

Event Pays Probability Return
Win 10 0.072981 0.729812
Loss -1 0.927019 -0.927019
Total   1.000000 -0.197206

Acknowledgement

Normally I like to do my own math. However, a combinatorial analysis would have required looping through 167,439,136,344,480 poker hands. This would have taken either a lot of computer and/or programming time. Shufflemaster kindly provided their math report by mathematician Elliot Frome to save me the trouble. This report is based on Elliot's report.

Outside Links

Discount Gambling has a page on the game, although based on a different pay table.