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.

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.

 

 

 

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.

 

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%.

 

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.

 

 

The next table shows statistics if the player buys insurance.

 

 

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