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I first noticed Big Raise Stud Poker at the Golden Nugget in Las Vegas on January 9, 2014. Before that it was known to be at the Venetian. It is a simple poker-based game based on the player's five-card hand only. It is similar to Mississippi Stud, but the player has one raise opportunity only, and can do so up to four times his Ante. Following are the complete rules.
Hand | Pays |
---|---|
Royal flush | 500 to 1 |
Straight flush | 100 to 1 |
Four of a kind | 40 to 1 |
Full house | 8 to 1 |
Flush | 6 to 1 |
Straight | 4 to 1 |
Three of a kind | 3 to 1 |
Two pair | 2 to 1 |
High pair (10-ace) | 1 to 1 |
Medium pair (6-9) | Push |
All other | Loss |
For purposes of the strategy I shall use the following notation:
Make a 4x raise with:
Make a 1x raise with:
The following table shows all possible outcomes for the game. The lower right cell shows a house edge of 2.58%.
Hand | Raise | Pays | Combinations | Probability | Return |
---|---|---|---|---|---|
Royal flush | 4 | 2500 | 40 | 0.000002 | 0.003848 |
Straight flush | 4 | 500 | 168 | 0.000006 | 0.003232 |
Four of a kind | 4 | 200 | 5,088 | 0.000196 | 0.039154 |
Full house | 4 | 40 | 27,072 | 0.001042 | 0.041666 |
Flush | 4 | 30 | 5,012 | 0.000193 | 0.005785 |
Straight | 4 | 20 | 3,120 | 0.000120 | 0.002401 |
Three of a kind | 4 | 15 | 284,052 | 0.010929 | 0.163942 |
Two pair | 4 | 10 | 516,348 | 0.019867 | 0.198675 |
High pair (10-ace) | 4 | 5 | 1,295,304 | 0.049839 | 0.249197 |
Medium pair (6-9) | 4 | 0 | 1,031,136 | 0.039675 | 0.000000 |
Loser | 4 | -5 | 78,420 | 0.003017 | -0.015087 |
Royal flush | 1 | 1000 | - | 0.000000 | 0.000000 |
Straight flush | 1 | 200 | 192 | 0.000007 | 0.001478 |
Four of a kind | 1 | 80 | 1,152 | 0.000044 | 0.003546 |
Full house | 1 | 16 | 10,368 | 0.000399 | 0.006383 |
Flush | 1 | 12 | 46,068 | 0.001773 | 0.021271 |
Straight | 1 | 8 | 64,320 | 0.002475 | 0.019799 |
Three of a kind | 1 | 6 | 179,748 | 0.006916 | 0.041497 |
Two pair | 1 | 4 | 463,212 | 0.017823 | 0.071292 |
High pair (10-ace) | 1 | 2 | 1,891,896 | 0.072794 | 0.145589 |
Medium pair (6-9) | 1 | 0 | 1,135,584 | 0.043694 | 0.000000 |
Loser | 1 | -2 | 7,802,820 | 0.300229 | -0.600457 |
Fold | -1 | 11,148,480 | 0.428959 | -0.428959 | |
Total | 25,989,600 | 1.000000 | -0.025751 |
On average, the player will make a 4x raise 12.49% of the time, a 1x raise 44.62%, and fold 42.90%. This makes the average final wager 1.95 units. Thus, the element of risk is 1.32%.
The 3 Card Bonus is a side bet that pays based on the player's initial three cards only. Mathematically, it is exactly like the Pairplus bet in Three Card Poker.
The following return table shows a house edge of 7.28%.
Hand | Pays | Combinations | Probability | Return |
---|---|---|---|---|
Straight flush | 40 | 48 | 0.002172 | 0.086878 |
Three of a kind | 30 | 52 | 0.002353 | 0.070588 |
Straight | 6 | 720 | 0.032579 | 0.195475 |
Flush | 3 | 1096 | 0.049593 | 0.148778 |
Pair | 1 | 3744 | 0.169412 | 0.169412 |
Loser | -1 | 16440 | 0.743891 | -0.743891 |
Total | 22100 | 1.000000 | -0.072760 |
The Progressive is $1 side bet based on the player's final five-card hand. A royal flush pays a progressive jackpot and a straight flush pays 10% of the jackpot. There are also envy bonuses if another player has a straight flush or higher.
The following table shows the return based on a hypothetical jackpot of $100,000. All wins are on 'for one' basis. The lower right cell shows a return of 82.30%, which equates to a house edge of 17.70%.
Hand | Pays | Combinations | Probability | Return |
---|---|---|---|---|
Royal flush | 100000 | 4 | 0.000002 | 0.153908 |
Straight flush | 10000 | 36 | 0.000014 | 0.138517 |
Four of a kind | 300 | 624 | 0.000240 | 0.072029 |
Full house | 50 | 3,744 | 0.001441 | 0.072029 |
Flush | 40 | 5,108 | 0.001965 | 0.078616 |
Straight | 30 | 10,200 | 0.003925 | 0.117739 |
Three of a kind | 9 | 54,912 | 0.021128 | 0.190156 |
All other | 0 | 2,524,332 | 0.971285 | 0.000000 |
Total | 2,598,960 | 1.000000 | 0.822994 |
Overall, the return of the progressive jackpot is 53.06% plus 2.92% for each $10,000 in the meter and 0.57% for each extra player at the table. The break-even jackpot, when no other players are at the table is $160,530.53.
My thanks to Stephen How of Discount Gambling for his help with the strategy.