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Double Draw Poker

Introduction

Double Draw Poker is a variation of video poker designed by Bally, which I first encountered at the Suncoast on November 7, 2006. This game is similar to traditional video poker but includes a unique element: players who are dealt three of a kind or a full house receive two opportunities to draw new cards.

When dealt a three of a kind or a full house, the optimal strategy is to preserve the three of a kind, even if it means letting go of a full house. After the second draw, if a four of a kind is achieved, it should be retained. If the first draw results in a full house, it's wise to keep that as well; however, if it involves three aces, the pair should be discarded. Following the first draw, a player should always discard any two unmatched cards if they still hold a three of a kind.

In the 7/5 Double Bonus variant, three of a kind and full house draws account for 14.325% of the game's overall return. Conversely, in 7/5 Double Draw Poker (the version offered at the Suncoast), these draws contribute 19.450% to the return. Thus, the second draw enhances the return by an additional 5.125%.

The subsequent two tables illustrate the returns of various hands, categorized by whether they were achieved through standard play or as a result of being dealt a three of a kind or full house. When contrasting 7/5 Double Draw with 10/7, it's notable that the former yields 43.4% more four of a kinds. The pay table at the Suncoast supports the 7/5 configuration. Double Bonus Analyzing the standard deviation for n-play video poker.

"6/5\" Double Draw PokerExpand

Hand Payoff Single
Draw
Combinations
Double
Draw
Combinations
Total
Combinations
Probability Return
Royal Flush 800 3001849488 0 3001849488 0.000025 0.020079
Straight Flush 50 12991323672 0 12991323672 0.000109 0.005431
Four A 160 17788263048 17670977280 35459240328 0.000296 0.047437
Four 2-4 80 38204132256 51321029760 89525162016 0.000749 0.059883
Four 5-K 50 120893159088 153963089280 274856248368 0.002298 0.114907
Full House 6 981094949784 300467914560 1281562864344 0.010715 0.064293
Flush 5 1304164271160 0 1304164271160 0.010904 0.054522
Straight 4 1569996955512 0 1569996955512 0.013127 0.052509
Three of a kind 3 6682645102680 2175818768640 8858463871320 0.074068 0.222203
Two pair 1 14672503914840 0 14672503914840 0.12268 0.12268
Pair 1 25815621160728 0 25815621160728 0.215851 0.215851
Nonpaying hand 0 65681236241424 0 65681236241424 0.549177 0
Total   116900141323680 2699241779520 119599383103200 1 0.979796

"7/5\" Double Draw PokerExpand

Hand Payoff Single
Draw
Combinations
Double
Draw
Combinations
Total
Combinations
Probability Return
Royal Flush 800 2989174464 0 2989174464 0.000025 0.019995
Straight Flush 50 12960258408 0 12960258408 0.000108 0.005418
Four A 160 17956635912 17670977280 35627613192 0.000298 0.047663
Four 2-4 80 38215184976 51321029760 89536214736 0.000749 0.059891
Four 5-K 50 120923196480 153963089280 274886285760 0.002298 0.11492
Full House 7 981767475288 300467914560 1282235389848 0.010721 0.075048
Flush 5 1305867219768 0 1305867219768 0.010919 0.054593
Straight 4 1566886317624 0 1566886317624 0.013101 0.052404
Three of a kind 3 6690119992200 2175818768640 8865938760840 0.07413 0.222391
Two pair 1 14681104026984 0 14681104026984 0.122752 0.122752
Pair 1 25766618360040 0 25766618360040 0.215441 0.215441
Nonpaying hand 0 65714733481536 0 65714733481536 0.549457 0
Total   116900141323680 2699241779520 119599383103200 1 0.990516

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