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Last Updated: February 28, 2017

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Ultimate X Bonus Streak -- Jacks or Better Strategy

Introduction

Below you will find single strategies for the Jacks or Better game in Ultimate X Bonus Streak. Optimal strategy would depend on not just the cards on the deal but the current multiplier and future multipliers as well. However, the good news is that in 10-play the multipliers tend to average out somewhat and a single strategy can be used with a cost in errors of only 0.08%.

This strategy was specifically made for 8/6 Jacks or Better, with the follow pay table and multiplier table.

8/6 Jacks or Better Pay Table

Hand Pays Multipliers
Royal flush 800 2-3-4-7-12
Straight flush 50 2-3-4-7-12
Four of a kind 25 2-3-4-7-12
Full house 8 2-3-4-7-12
Flush 6 2-3-4
Straight 4 2-3-4
Three of a kind 3 2-3-4
Two pair 2 1
Jacks or Better 1 1


Basic Strategy



The following strategy was created using our video poker strategy maker. I fudged the value of each hand to show its value including both the immediate win and the multiplier string.

Basic Strategy
Type of Play Play Details
4 of a Kind 2222; 3333; 4444; 5555; 6666; 7777; 8888; 9999; TTTT; JJJJ; QQQQ; KKKK; AAAA
Pat Hand Full House; Straight Flush; Royal Flush
4 to a Royal Flush TJQA; TJQK; TJKA; TQKA; JQKA
3 of a Kind 222; 333; 444; 555; 666; 777; 888; 999; TTT; JJJ; QQQ; KKK; AAA
Pat Hand Straight; Flush
2 Pair 2233; 2244; 2255; 2266; 2277; 2288; 2299; 22TT; 22JJ; 22QQ; 22KK; 22AA; 3344; 3355; 3366; 3377; 3388; 3399; 33TT; 33JJ; 33QQ; 33KK; 33AA; 4455; 4466; 4477; 4488; 4499; 44TT; 44JJ; 44QQ; 44KK; 44AA; 5566; 5577; 5588; 5599; 55TT; 55JJ; 55QQ; 55KK; 55AA; 6677; 6688; 6699; 66TT; 66JJ; 66QQ; 66KK; 66AA; 7788; 7799; 77TT; 77JJ; 77QQ; 77KK; 77AA; 8899; 88TT; 88JJ; 88QQ; 88KK; 88AA; 99TT; 99JJ; 99QQ; 99KK; 99AA; TTJJ; TTQQ; TTKK; TTAA; JJQQ; JJKK; JJAA; QQKK; QQAA; KKAA
4 to a Straight Flush A234; A235; A245; A345; 2345; 2346; 2356; 2456; 3456; 3457; 3467; 3567; 4567; 4568; 4578; 4678; 5678; 5679; 5689; 5789; 6789; 678T; 679T; 689T; 789T; 789J; 78TJ; 79TJ; 89TJ; 89TQ; 89JQ; 8TJQ; 9TJQ; 9TJK; 9TQK; 9JQK
1 Pair JJ; QQ; KK; AA
4 to a Flush 2347; 2348; 2349; 234T; 234J; 234Q; 234K; 2357; 2358; 2359; 235T; 235J; 235Q; 235K; 236A; 2367; 2368; 2369; 236T; 236J; 236Q; 236K; 237A; 2378; 2379; 237T; 237J; 237Q; 237K; 238A; 2389; 238T; 238J; 238Q; 238K; 239A; 239T; 239J; 239Q; 239K; 23TA; 23TJ; 23TQ; 23TK; 23JA; 23JQ; 23JK; 23QA; 23QK; 23KA; 2457; 2458; 2459; 245T; 245J; 245Q; 245K; 246A; 2467; 2468; 2469; 246T; 246J; 246Q; 246K; 247A; 2478; 2479; 247T; 247J; 247Q; 247K; 248A; 2489; 248T; 248J; 248Q; 248K; 249A; 249T; 249J; 249Q; 249K; 24TA; 24TJ; 24TQ; 24TK; 24JA; 24JQ; 24JK; 24QA; 24QK; 24KA; 256A; 2567; 2568; 2569; 256T; 256J; 256Q; 256K; 257A; 2578; 2579; 257T; 257J; 257Q; 257K; 258A; 2589; 258T; 258J; 258Q; 258K; 259A; 259T; 259J; 259Q; 259K; 25TA; 25TJ; 25TQ; 25TK; 25JA; 25JQ; 25JK; 25QA; 25QK; 25KA; 267A; 2678; 2679; 267T; 267J; 267Q; 267K; 268A; 2689; 268T; 268J; 268Q; 268K; 269A; 269T; 269J; 269Q; 269K; 26TA; 26TJ; 26TQ; 26TK; 26JA; 26JQ; 26JK; 26QA; 26QK; 26KA; 278A; 2789; 278T; 278J; 278Q; 278K; 279A; 279T; 279J; 279Q; 279K; 27TA; 27TJ; 27TQ; 27TK; 27JA; 27JQ; 27JK; 27QA; 27QK; 27KA; 289A; 289T; 289J; 289Q; 289K; 28TA; 28TJ; 28TQ; 28TK; 28JA; 28JQ; 28JK; 28QA; 28QK; 28KA; 29TA; 29TJ; 29TQ; 29TK; 29JA; 29JQ; 29JK; 29QA; 29QK; 29KA; 2TJA; 2TJQ; 2TJK; 2TQA; 2TQK; 2TKA; 2JQA; 2JQK; 2JKA; 2QKA; 3458; 3459; 345T; 345J; 345Q; 345K; 346A; 3468; 3469; 346T; 346J; 346Q; 346K; 347A; 3478; 3479; 347T; 347J; 347Q; 347K; 348A; 3489; 348T; 348J; 348Q; 348K; 349A; 349T; 349J; 349Q; 349K; 34TA; 34TJ; 34TQ; 34TK; 34JA; 34JQ; 34JK; 34QA; 34QK; 34KA; 356A; 3568; 3569; 356T; 356J; 356Q; 356K; 357A; 3578; 3579; 357T; 357J; 357Q; 357K; 358A; 3589; 358T; 358J; 358Q; 358K; 359A; 359T; 359J; 359Q; 359K; 35TA; 35TJ; 35TQ; 35TK; 35JA; 35JQ; 35JK; 35QA; 35QK; 35KA; 367A; 3678; 3679; 367T; 367J; 367Q; 367K; 368A; 3689; 368T; 368J; 368Q; 368K; 369A; 369T; 369J; 369Q; 369K; 36TA; 36TJ; 36TQ; 36TK; 36JA; 36JQ; 36JK; 36QA; 36QK; 36KA; 378A; 3789; 378T; 378J; 378Q; 378K; 379A; 379T; 379J; 379Q; 379K; 37TA; 37TJ; 37TQ; 37TK; 37JA; 37JQ; 37JK; 37QA; 37QK; 37KA; 389A; 389T; 389J; 389Q; 389K; 38TA; 38TJ; 38TQ; 38TK; 38JA; 38JQ; 38JK; 38QA; 38QK; 38KA; 39TA; 39TJ; 39TQ; 39TK; 39JA; 39JQ; 39JK; 39QA; 39QK; 39KA; 3TJA; 3TJQ; 3TJK; 3TQA; 3TQK; 3TKA; 3JQA; 3JQK; 3JKA; 3QKA; 456A; 4569; 456T; 456J; 456Q; 456K; 457A; 4579; 457T; 457J; 457Q; 457K; 458A; 4589; 458T; 458J; 458Q; 458K; 459A; 459T; 459J; 459Q; 459K; 45TA; 45TJ; 45TQ; 45TK; 45JA; 45JQ; 45JK; 45QA; 45QK; 45KA; 467A; 4679; 467T; 467J; 467Q; 467K; 468A; 4689; 468T; 468J; 468Q; 468K; 469A; 469T; 469J; 469Q; 469K; 46TA; 46TJ; 46TQ; 46TK; 46JA; 46JQ; 46JK; 46QA; 46QK; 46KA; 478A; 4789; 478T; 478J; 478Q; 478K; 479A; 479T; 479J; 479Q; 479K; 47TA; 47TJ; 47TQ; 47TK; 47JA; 47JQ; 47JK; 47QA; 47QK; 47KA; 489A; 489T; 489J; 489Q; 489K; 48TA; 48TJ; 48TQ; 48TK; 48JA; 48JQ; 48JK; 48QA; 48QK; 48KA; 49TA; 49TJ; 49TQ; 49TK; 49JA; 49JQ; 49JK; 49QA; 49QK; 49KA; 4TJA; 4TJQ; 4TJK; 4TQA; 4TQK; 4TKA; 4JQA; 4JQK; 4JKA; 4QKA; 567A; 567T; 567J; 567Q; 567K; 568A; 568T; 568J; 568Q; 568K; 569A; 569T; 569J; 569Q; 569K; 56TA; 56TJ; 56TQ; 56TK; 56JA; 56JQ; 56JK; 56QA; 56QK; 56KA; 578A; 578T; 578J; 578Q; 578K; 579A; 579T; 579J; 579Q; 579K; 57TA; 57TJ; 57TQ; 57TK; 57JA; 57JQ; 57JK; 57QA; 57QK; 57KA; 589A; 589T; 589J; 589Q; 589K; 58TA; 58TJ; 58TQ; 58TK; 58JA; 58JQ; 58JK; 58QA; 58QK; 58KA; 59TA; 59TJ; 59TQ; 59TK; 59JA; 59JQ; 59JK; 59QA; 59QK; 59KA; 5TJA; 5TJQ; 5TJK; 5TQA; 5TQK; 5TKA; 5JQA; 5JQK; 5JKA; 5QKA; 678A; 678J; 678Q; 678K; 679A; 679J; 679Q; 679K; 67TA; 67TJ; 67TQ; 67TK; 67JA; 67JQ; 67JK; 67QA; 67QK; 67KA; 689A; 689J; 689Q; 689K; 68TA; 68TJ; 68TQ; 68TK; 68JA; 68JQ; 68JK; 68QA; 68QK; 68KA; 69TA; 69TJ; 69TQ; 69TK; 69JA; 69JQ; 69JK; 69QA; 69QK; 69KA; 6TJA; 6TJQ; 6TJK; 6TQA; 6TQK; 6TKA; 6JQA; 6JQK; 6JKA; 6QKA; 789A; 789Q; 789K; 78TA; 78TQ; 78TK; 78JA; 78JQ; 78JK; 78QA; 78QK; 78KA; 79TA; 79TQ; 79TK; 79JA; 79JQ; 79JK; 79QA; 79QK; 79KA; 7TJA; 7TJQ; 7TJK; 7TQA; 7TQK; 7TKA; 7JQA; 7JQK; 7JKA; 7QKA; 89TA; 89TK; 89JA; 89JK; 89QA; 89QK; 89KA; 8TJA; 8TJK; 8TQA; 8TQK; 8TKA; 8JQA; 8JQK; 8JKA; 8QKA; 9TJA; 9TQA; 9TKA; 9JQA; 9JKA; 9QKA
3 to a Royal Flush TJA; TJQ; TJK; TQA; TQK; TKA; JQA; JQK; JKA; QKA
4 to a Straight 9TJQ; TJQK
1 Pair 22; 33; 44; 55; 66; 77; 88; 99; TT
3 to a Straight Flush A23; A24; A25; 9JQ
4 to a Straight 2345; 3456; 4567; 5678; 6789; 789T; 89TJ; JQKA
3 to a Straight Flush A34; A35; A45; 234; 235; 245; 345; 346; 356; 456; 457; 467; 567; 568; 578; 678; 679; 689; 789; 78T; 79T; 89T; 89J; 8TJ; 8JQ; 9TJ; 9TQ; 9JK; 9QK
4 to a Straight 9JQK; TQKA
4 to a Straight 89JQ; 8TJQ; 9TJK; 9TQK; TJQA; TJKA
3 to a Straight Flush 78J; 79J; 7TJ; 89Q; 8TQ; 9TK
3 to a Flush 2TK; 2JA; 2JK; 2QA; 2QK; 2KA; 3TK; 3JA; 3JK; 3QA; 3QK; 3KA; 4TK; 4JA; 4JK; 4QA; 4QK; 4KA; 5TK; 5JA; 5JK; 5QA; 5QK; 5KA; 6JA; 6JK; 6QA; 6QK; 6KA; 7JA; 7JK; 7QA; 7QK; 7KA; 8JA; 8JK; 8QA; 8QK; 8KA; 9JA; 9QA; 9KA
2 to a Royal Flush JA; JQ; JK; QA; QK; KA
4 to a Straight A234; A235; A245; A345; 789J; 78TJ; 79TJ; 89TQ
3 to a Straight TJQ; JQK
2 to a Royal Flush TJ
3 to a Straight Flush 236; 246; 256; 347; 357; 367; 458; 468; 478; 569; 579; 589; 67T; 68T; 69T
4 to a Straight 2346; 2356; 2456; 3457; 3467; 3567; 4568; 4578; 4678; 5679; 5689; 5789; 678T; 679T; 689T
3 to a Flush 28J; 28Q; 29J; 29Q; 29K; 2TA; 2TQ; 38J; 38Q; 39J; 39Q; 39K; 3TA; 3TQ; 48J; 48Q; 49J; 49Q; 49K; 4TA; 4TQ; 58J; 58Q; 59J; 59Q; 59K; 5TA; 5TQ; 68J; 68Q; 69J; 69Q; 69K; 6TA; 6TQ; 6TK; 78Q; 79Q; 79K; 7TA; 7TQ; 7TK; 89A; 89K; 8TA; 8TK; 9TA
2 to a Royal Flush TQ
3 to a Flush 23K; 24K; 25K; 26A; 26K; 27A; 27K; 28A; 28K; 29A; 34K; 35K; 36A; 36K; 37A; 37K; 38A; 38K; 39A; 45K; 46A; 46K; 47A; 47K; 48A; 48K; 49A; 56A; 56K; 57A; 57K; 58A; 58K; 59A; 67A; 67K; 68A; 68K; 69A; 78A; 78K; 79A
2 to a Straight JQ
3 to a Flush 23J; 23Q; 24J; 24Q; 25J; 25Q; 26J; 26Q; 27J; 27Q; 34J; 34Q; 35J; 35Q; 36J; 36Q; 37J; 37Q; 45J; 45Q; 46J; 46Q; 47J; 47Q; 56J; 56Q; 57J; 57Q; 67J; 67Q
2 to a Royal Flush TK
Single Card a Jack
2 to a Straight JK; QK
Single Card a Queen
Single Card a King
2 to a Royal Flush TA
Single Card an Ace
3 to a Flush 237; 238; 239; 23T; 247; 248; 249; 24T; 257; 258; 259; 25T; 267; 268; 269; 26T; 278; 279; 27T; 289; 28T; 29T; 348; 349; 34T; 358; 359; 35T; 368; 369; 36T; 378; 379; 37T; 389; 38T; 39T; 459; 45T; 469; 46T; 479; 47T; 489; 48T; 49T; 56T; 57T; 58T; 59T
2 to a Straight Flush 78; 9T
2 to a Straight Flush 45; 56; 67; 89
Garbage Discard everything

The return table below shows the expected win before considering the multiplier feature.

Basic Strategy Return Table

Hand Pays Combinations Probability Return
Royal Flush 800 397,850,916 0.000020 0.015967
Straight Flush 50 2,244,794,280 0.000113 0.005631
Four of a Kind 25 46,661,815,500 0.002341 0.058523
Full House 8 225,889,691,580 0.011332 0.090659
Flush 6 304,072,896,024 0.015255 0.091527
Straight 4 311,989,648,212 0.015652 0.062607
Three of a Kind 3 1,444,288,929,288 0.072456 0.217369
Two Pair 2 2,486,272,990,464 0.124730 0.249460
Jacks or Better 1 3,668,661,489,600 0.184048 0.184048
Nothing 0 11,442,750,411,336 0.574054 0.000000
Totals 19,933,230,517,200 1.000000 0.975790


The lower right cell shows a pre-multiplier return of 97.58%. The average multiplier using this strategy is 2.021899. Considering the player must double his bet to invoke the feature, the overall return using the basic strategy is 0.975790 × 2.021899 / 2 = 0.986475. This is only 0.09% less than the optimal strategy return of 98.74%.

In case you were wondering, following is the value of both multiplier chains, according to my calculations. This is what you should add to the win in the pay table to create a strategy for the game. In other words, this is the value of the two different multiplier chains in this game as measured by the amount bet per hand, not counting the additional amount bet to invoke the feature.

  • The 2-3-4 multiplier chain is worth 6.137727.
  • The 2-3-4-7-12 multiplier chain is worth 23.113457.

Advanced Strategy



In the very unlikely event you want to shave another 0.01% off the house edge, you can learn the exceptions listed below. This will change the return, before considering the multipliers, to 0.976002. The average multiplier will be 2.021620. The overall return would thus be 0.976002 × 2.021620 / 2 = 98.66%, which is only 0.08% lower than the optimal return of 98.74%.

Basic Strategy Exceptions
Right Play Wrong Play Pattern(s)
2 to a Straight: JK Single Card: a Jack
(more) 2♣ 3♣ 4♦ J♦ K♥
Single Card: an Ace Single Card: a King
(more) 2♣ 3♣ 6♦ K♦ A♥
Single Card: an Ace Single Card: a Queen
(more) 6♣ 7♣ 8♦ Q♦ A♥
Single Card: a Queen 2 to a Straight: QK
(more) 2♣ 3♣ 10♣ Q♦ K♥
2 to a Straight Flush: 9J Single Card: a Jack
(more) 2♣ 3♣ 9♦ J♦ A♥
2 to a Straight Flush: 8T Garbage: Discard everything
(more) 2♣ 3♣ 4♦ 8♥ 10♥
2 to a Royal Flush: TQ 3 to a Flush: 2TQ
(more) 2♣ 3♦ 4♦ 10♣ Q♣
2 to a Royal Flush: TQ 3 to a Flush: 3TQ
(more) 2♣ 3♦ 4♣ 10♦ Q♦
2 to a Royal Flush: TQ 3 to a Flush: 4TQ
(more) 2♣ 3♣ 4♦ 10♦ Q♦
2 to a Royal Flush: TQ 3 to a Flush: 5TQ
(more) 2♣ 3♣ 5♦ 10♦ Q♦
2 to a Royal Flush: TQ 3 to a Flush: 6TQ
(more) 2♣ 3♣ 6♦ 10♦ Q♦
2 to a Royal Flush: TQ 3 to a Flush: 7TQ
(more) 2♣ 3♣ 7♦ 10♦ Q♦
2 to a Royal Flush: TA Single Card: a King
(more) 2♣ 9♦ 10♥ K♣ A♥
Single Card: a Ten Garbage: Discard everything
(more) 2♣ 3♣ 5♦ 7♥ 10♠
2 to a Straight: JQ 3 to a Flush: 28J
(more) 2♣ 3♦ 8♣ J♣ Q♦
2 to a Straight: JQ 3 to a Flush: 38J
(more) 2♣ 3♦ 8♦ J♦ Q♣
2 to a Straight: JQ 3 to a Flush: 48J
(more) 2♣ 4♦ 8♦ J♦ Q♣
2 to a Straight: JQ 3 to a Flush: 58J
(more) 2♣ 5♦ 8♦ J♦ Q♣
2 to a Straight: JQ 3 to a Flush: 68J
(more) 2♣ 6♦ 8♦ J♦ Q♣
2 to a Straight: JQ 3 to a Flush: 28Q
(more) 2♣ 3♦ 8♣ J♦ Q♣
2 to a Straight: JQ 3 to a Flush: 38Q
(more) 2♣ 3♦ 8♦ J♣ Q♦
2 to a Straight: JQ 3 to a Flush: 48Q
(more) 2♣ 4♦ 8♦ J♣ Q♦
2 to a Straight: JQ 3 to a Flush: 58Q
(more) 2♣ 5♦ 8♦ J♣ Q♦
2 to a Straight: JQ 3 to a Flush: 68Q
(more) 2♣ 6♦ 8♦ J♣ Q♦
2 to a Straight: JQ 3 to a Flush: 78Q
(more) 2♣ 7♦ 8♦ J♣ Q♦
2 to a Straight Flush: 35 Garbage: Discard everything
(more) 3♣ 5♣ 7♦ 8♥ 10♠
2 to a Straight Flush: 79 Garbage: Discard everything
(more) 2♣ 3♣ 4♦ 7♥ 9♥
Single Card: an Ace Single Card: a Jack
(more) 6♣ 9♦ 10♣ J♦ A♥
2 to a Royal Flush: TQ 4 to a Straight: 678T
(more) 6♣ 7♣ 8♦ 10♥ Q♥
2 to a Royal Flush: TQ 4 to a Straight: 679T
(more) 6♣ 7♣ 9♦ 10♥ Q♥
3 to a Flush: 23J 2 to a Straight: JQ
(more) 2♣ 3♣ 9♦ J♣ Q♦
3 to a Flush: 24J 2 to a Straight: JQ
(more) 2♣ 4♣ 9♦ J♣ Q♦
3 to a Flush: 34J 2 to a Straight: JQ
(more) 3♣ 4♣ 9♦ J♣ Q♦
3 to a Flush: 25J 2 to a Straight: JQ
(more) 2♣ 5♣ 9♦ J♣ Q♦
3 to a Flush: 35J 2 to a Straight: JQ
(more) 3♣ 5♣ 9♦ J♣ Q♦
3 to a Flush: 45J 2 to a Straight: JQ
(more) 4♣ 5♣ 9♦ J♣ Q♦
3 to a Flush: 26J 2 to a Straight: JQ
(more) 2♣ 6♣ 9♦ J♣ Q♦
3 to a Flush: 36J 2 to a Straight: JQ
(more) 3♣ 6♣ 9♦ J♣ Q♦
3 to a Flush: 46J 2 to a Straight: JQ
(more) 4♣ 6♣ 9♦ J♣ Q♦
3 to a Flush: 56J 2 to a Straight: JQ
(more) 5♣ 6♣ 9♦ J♣ Q♦
3 to a Flush: 27J 2 to a Straight: JQ
(more) 2♣ 7♣ 9♦ J♣ Q♦
3 to a Flush: 37J 2 to a Straight: JQ
(more) 3♣ 7♣ 9♦ J♣ Q♦
3 to a Flush: 47J 2 to a Straight: JQ
(more) 4♣ 7♣ 9♦ J♣ Q♦
3 to a Flush: 57J 2 to a Straight: JQ
(more) 5♣ 7♣ 9♦ J♣ Q♦
3 to a Flush: 67J 2 to a Straight: JQ
(more) 6♣ 7♣ 9♦ J♣ Q♦
3 to a Flush: 23Q 2 to a Straight: JQ
(more) 2♣ 3♣ 9♦ J♦ Q♣
3 to a Flush: 24Q 2 to a Straight: JQ
(more) 2♣ 4♣ 9♦ J♦ Q♣
3 to a Flush: 34Q 2 to a Straight: JQ
(more) 3♣ 4♣ 9♦ J♦ Q♣
3 to a Flush: 25Q 2 to a Straight: JQ
(more) 2♣ 5♣ 9♦ J♦ Q♣
3 to a Flush: 35Q 2 to a Straight: JQ
(more) 3♣ 5♣ 9♦ J♦ Q♣
3 to a Flush: 45Q 2 to a Straight: JQ
(more) 4♣ 5♣ 9♦ J♦ Q♣
3 to a Flush: 26Q 2 to a Straight: JQ
(more) 2♣ 6♣ 9♦ J♦ Q♣
3 to a Flush: 36Q 2 to a Straight: JQ
(more) 3♣ 6♣ 9♦ J♦ Q♣
3 to a Flush: 46Q 2 to a Straight: JQ
(more) 4♣ 6♣ 9♦ J♦ Q♣
3 to a Flush: 56Q 2 to a Straight: JQ
(more) 5♣ 6♣ 9♦ J♦ Q♣
3 to a Flush: 27Q 2 to a Straight: JQ
(more) 2♣ 7♣ 9♦ J♦ Q♣
3 to a Flush: 37Q 2 to a Straight: JQ
(more) 3♣ 7♣ 9♦ J♦ Q♣
3 to a Flush: 47Q 2 to a Straight: JQ
(more) 4♣ 7♣ 9♦ J♦ Q♣
3 to a Flush: 57Q 2 to a Straight: JQ
(more) 5♣ 7♣ 9♦ J♦ Q♣
3 to a Flush: 67Q 2 to a Straight: JQ
(more) 6♣ 7♣ 9♦ J♦ Q♣
2 to a Straight Flush: 34 Garbage: Discard everything
(more) 3♣ 4♣ 8♦ 9♥ 10♦
2 to a Straight Flush: 45 2 to a Straight Flush: 89 4♣ 5♣ 8♦ 9♦ 10♥
2 to a Straight Flush: 45 2 to a Straight Flush: 9T 4♣ 5♣ 8♦ 9♥ 10♥
3 to a Straight Flush: 67T 3 to a Straight: TJQ 6♣ 7♣ 10♣ J♦ Q♥
3 to a Straight Flush: 458 2 to a Royal Flush: TJ 4♣ 5♣ 8♣ 10♦ J♦
3 to a Straight Flush: 468 2 to a Royal Flush: TJ 4♣ 6♣ 8♣ 10♦ J♦
3 to a Straight Flush: 569 2 to a Royal Flush: TJ 5♣ 6♣ 9♣ 10♦ J♦

3-Play and 5-Play



I also analyzed the Jacks or Better game of Ultimate X Bonus Streak. Obviously, the multipliers do not average out as much over 3 or 5 hands, compared to 10. My best single strategies have the following error rates compared to optimal strategy:

  • 3-play: 0.40%
  • 5-play: 0.30%
  • 10-play: 0.08%


Methodology



Analyzing this game with a single strategy makes for a great exercise in matrix algebra. What makes it a difficult analysis is one hand doesn't just affect that hand but up to five hands in the future. The rule about earned multipliers changing future multipliers to 12 makes this all the more challenging.

Briefly, I used matrix algebra to calculate the value of the next 13 hands for both multiplier streams. I then subtracted 13 as the cost to invoke the feature for 13 hands. This gave me the values of 6.137727 for the 2-3-4 multiplier stream and 23.113457 for 2-3-4-7-12. I then projected the whole game 32 games into the future to get an average multiplier, assuming the player played forever.

Excel, conveniently, can do matrix multiplication. For instructions on how to do that, look up the MMULT function. Don't forget to do a cntl-shift-enter over the region you want to put the product of the two matrices, starting in the upper left cell, you are multiplying.


Written by: Michael Shackleford

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