Bonus Six

Last Update: May 01, 2001

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.

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

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.

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.