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Last Updated: May 1, 2001

Bonus Six

Introduction

Bonus Six is a poker based game card game, popular in the casinos of Black Hawk, Colorado. As in five-card stud the player gets cards gradually and must keep raising to stay in or fold. The twist in this game is that if the player buys insurance initially he has the option to buy a sixth card if he needs one. Following are the specifics.

The Rules

  1. The game is played with a single deck of cards, which is shuffled after every hand.
  2. The player begins by placing an ante bet. The player may also buy insurance at the cost of half the ante bet. The cost of the insurance policy is never returned.
  3. Each player receives two cards face down and one community card dealt face up. All players may use the community card as part of their hand.
  4. After looking at his cards the player must decide to either bet or fold. If the player folds he forfeits his ante. If player bets he must add to his wager an amount equal to the ante.
  5. All players who raised receive a fourth card.
  6. Again, all players still in must either bet or fold. If the player folds he loses both his ante and previous bet. If player bets he must add to wager an amount equal to the ante.
  7. All players still in receive a fifth card.
  8. If the player initially purchases insurance and does not have a paying hand he has the option to buy a sixth card. The cost of the card is equal to the ante. If the player buys the sixth card he may make the best five-card hand among his six cards. The fee for the sixth card is never returned.
  9. All players still in are paid according to the pay table below.

Pay Table for Bonus Six

Hand Payoff
Royal flush 1000 to 1
Straight flush 100 to 1
Four of a kind 50 to 1
Full house 20 to 1
Flush 6 to 1
Straight 4 to 1
Three of a kind 3 to 1
Two pair 2 to 1
High pair (6-ace) 1 to 1

Strategy

The player should never buy insurance.

With three cards, bet with any of the following hands, otherwise fold. A "high card" is a six or greater.

  1. Any pair, three of a kind
  2. Any 3 to a flush
  3. 3 to a straight with at least 2 high cards
  4. Any 3 high cards

With four cards, bet with any of the following hands, otherwise fold.

  1. Any pair, two pair, three of a kind
  2. Four to a straight, flush, or straight flush
  3. Any 3 high cards

Note that this strategy does not apply if the player buys insurance, which he shouldn't do in the first place.

House Edge

The house edge is 10.42%. To be exact it is 5,417,544/51,979,200. The average bet size is 1.93 units which makes the element of risk 5.41%. If the player buys insurance and plays the appropriate insurance strategy the house edge is 23.83%, with an average bet size of 3.71 units, for an element of risk of 6.42%.

Statistics

The following table shows the number of times in each combination 51,979,200 hands that each event is expected to happen, the probability, and the contribution to the player's return when the player does not buy insurance.

Statistics Table for Bonus Six - No Insurance

Outcome Number Pays Probability Return
Nothing 11312304 0.217631 -1 to 1 -0.652894
High pair 9369504 0.180255 1 to 1 0.540765
Two pair 1839240 0.035384 2 to 1 0.212305
Three of a kind 887640 0.017077 3 to 1 0.153691
Straight 140640 0.002706 4 to 1 0.032468
Flush 102160 0.001965 6 to 1 0.035377
Full house 74880 0.001441 20 to 1 0.086435
Four of a kind 12480 0.00024 50 to 1 0.036014
Straight flush 720 0.000014 100 to 1 0.004156
Royal flush 80 0.000002 1000 to 1 0.004617
Fold on 3 cards 27518400 0.529412 -1 to 1 -0.529412
Fold on 4 cards 721152 0.013874 -1 to 1 -0.027748
Total 51979200 1 -0.104225

The next table shows statistics if the player buys insurance.

Statistics Table for Bonus Six - With Insurance

Outcome Number Probability Pays Return
Nothing 903692688 0.369908 -1 to 1 -1.109723
High pair 887837964 0.363418 1 to 1 1.090254
Two pair 155762244 0.063758 2 to 1 0.382548
Three of a kind 59688144 0.024432 3 to 1 0.219889
Straight 23771328 0.00973 4 to 1 0.116764
Flush 16178336 0.006622 6 to 1 0.119201
Full house 3519360 0.001441 20 to 1 0.086435
Four of a kind 586560 0.00024 50 to 1 0.036014
Straight flush 87744 0.000036 100 to 1 0.010775
Royal flush 3760 0.000002 1000 to 1 0.004617
Fold on 3 cards 287856576 0.117828 -1 to 1 -0.117828
Fold on 4 cards 104037696 0.042586 -1 to 1 -0.085171
Total 2443022400 1 0.753773

The cost of insurance is 0.5 units and the cost of extra cards is 0.492059 units, for a total return of -0.238286 units.
Written by: Michael Shackleford

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