BIG TIMES DRAW POKER - Special Straight Flush

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QuadGod
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BIG TIMES DRAW POKER - Special Straight Flush

Post by QuadGod »

At one of the casinos I frequent, there are a couple of "Big Times Draw Poker" games, where a multiplier is awarded based on the highest card in your dealt hand, if you pay more than 5 credits per hand; if the highest card is a King or Queen, there is no multiplier. The lower the highest card, the bigger the multiplier (for example, if you get dealt a hand with only 2's and Aces' and playing 10 credits, the multiplier is 10X.

Although I play the Double Double Bonus version, I noticed on the other offerings (Regular Draw Poker, Bonus Poker and Double Bonus) that there is a special straight flush (A2345) that is paid the same as a Royal Flush (4,000 credits), if the highest card in the dealt hand is a 4 or less. [You can see the explanation of the "special straight flush" on the "Help Page" where the game is listed on this website (videopoker.com).] I realize that this is an extremely unlikely event, but I would like to know what the probability is of getting that hand, and how much that hand increases the payback for the game. The Wizard of Odds website discusses the game and gives the returns for each game, but does not appear to include the special straight flush. (I presume that there are also some strategy adjustments for this hand).

New2vp
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Post by New2vp »

There was some discussion in the forum about this subject 12 and a half years ago:

https://www.videopoker.com/forum/viewto ... ight+flush

If this link doesn't work, search with the words special straight flush and my nickname as the author, and scroll down until you find some references to this game.

I think that the odds of getting dealt a hand suggesting a draw to this special straight flush are about 6369 to 1. About 12% of these hands give you a 1 in 47 chance of hitting when you are drawing to a 432A 4-card straight flush. The remainder give you only a 1 in 1081 chance of hitting while drawing to a 3-card straight flush (432, 43A, 42A, or 32A). You would not want to hold a 3-card straight flush if you had a pair or aces, two pair, or trips. So, overall, your chances of hitting the special straight flush are 1 in 1,919,041 on any single hand. Since this game is offered in Triple Play, Five Play, and Ten Play, your chances per deal go up to once in 650,186 hands, 396,442 hands, or 206,188 dealt hands, respectively.

The additional payback is dependent on the actual pay schedule that you are playing and also how many coins per hand you are playing (since you can get the special straight flush when playing as few as 6 coins per hand). My answer is based on playing 10 coins and the pay schedules on this site: 9-6 Jacks or Better, 7-5 Bonus Poker, or 9-6-5 Double Bonus.

I may not be accounting for every nuance but it looks to me like the add-on EVs are 0.1043% for Double Bonus, 0.1187% for Bonus Poker, and 0.1564% for Jacks or Better. The difference in magnitude is chiefly due to the multiplier when the high card in the dealt hand is a 4: 6x for Double Bonus, 7x for Bonus Poker, 9x for Jacks or Better. In two of those games the multiplier for a dealt hand with a high card of 3 is higher; however, you would never hold a 3-card straight flush in such a hand.

I noticed on the Wizard of Oz's website that he discussed a Deuces Wild game of this type. That game is not on this website and you didn't mention it. It would be interesting to know if that game also has a special straight flush, particularly since it would include a deuce, which is generally used as a wild card.

QuadGod
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Post by QuadGod »

Many thanks for your excellent and thorough response. I sensed that the odds of hitting that hand was extremely remote, but I really had no idea what a long shot it was nor the add-on EV—so I appreciate very much you pointing that out.

For the game I play, there is no offering for deuces wild, so I don’t know if it is offered there or not.

QuadGod
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Posts: 30
Joined: Sun Jul 05, 2015 12:28 pm

Post by QuadGod »

Many thanks for your excellent and thorough response, New2vp. I sensed that the odds of hitting that hand was extremely remote, but I really had no idea what a long shot it was nor the add-on EV—so I appreciate very much you pointing that out.

For the game I play, there is no offering for deuces wild, so I don’t know if it is offered there or not.

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