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Last Updated: September 21, 2009

World Series of Poker

Introduction

World Series of Poker (subtitled "Final Table Bonus") is a video poker variation by WMS. I have seen the game at Bally's, Caesars Palace, and Harrah's in both Vegas and Laughlin. The game plays like ordinary video poker, except the player can make an extra bet to qualify for the "Final Table Bonus." Following are the specific rules.

Rules

  1. Player starts by making two separate but equal bets. One bet bet I'll call the "video poker" bet and the other the "bonus" bet.
  2. The video poker bet shall play the same as standard video poker.
  3. After the draw in video poker a "Bonus Hand" consisting of two additional cards shall be dealt from a separate 52-card deck.
  4. If there is exactly one ace in the bonus hand, any winnings from the video poker hand will be tripled.
  5. If there are two aces in the bonus hand, any winnings from the video poker hand will be multiplied by nine.
  6. If the bonus hand is a pair of jacks or better then the player will play the Final Table Bonus. If the bonus hand is less than a pair of jacks it is still possible to play the bonus (see rule 16).
  7. In the Final Table Bonus the player will face up to nine opponents, one at a time. The player will start out in tenth place. For each opponent the player beats he shall move up one place. The player shall win according to the place he attains at the end of the bonus round.
  8. In double bonus, any four of a kind in the video poker hand win will be doubled if the player also attains the bonus round. In double double bonus, any four of a kind in the video poker hand win will be quadrupled if the player also attains the bonus round.
  9. The player's bonus hand shall be the player's hole cards against the first opponent. The player may choose to accept these cards or replace them with two random cards from a fresh deck. The player may also trade in his second hand but the third hand shall be final. In other words the player may trade in his hole cards up to two times.
  10. After the player has accepted his initial two-card hand, the opponent will be given two cards from the same deck.
  11. Three community cards (known as the "flop") will be dealt, then a fourth (called the "turn"), and then a fifth called the "river." As this happens, the game will update the probability of winning for both of the two participants.
  12. Both player and opponent will make the best five card poker hand using any combination of his own two hole cards and the five community cards. The higher poker hand wins.
  13. If the player beats or ties the opponent he will advance to the next opponent. With all subsequent opponents the first set of hole cards will be dealt from a freshly shuffled deck.
  14. The player will keep playing until he beats nine opponents or loses trying.
  15. If the player's bonus hand is less than a pair of jacks he may earn a "free seat" in the bonus round. The probability of a free seat bonus round depends on the particular game. As in an earned bonus, the player's first set of hole cards will carry over from the bonus hand.
  16. If the player loses with a four of a kind or higher the player shall win a "Bad Beat Bonus" of 10,000 times the bonus bet. It is my interpretation of the game rules that use of the two hole cards is not required for the bad beat bonus.

Pay Table for Final Table Bonus. All wins are multiplied by the Bonus Bet.

Final Table Bonus Pay Table

Place Pays
1 650
2 350
3 225
4 150
5 100
6 50
7 25
8 15
9 10
10 5

The player may choose from a menu of six games. Five are indicated below. These pay tables are based on those observed at Harrah's in Laughlin. Other pay tables are available from WMS, the game maker.

Pictures

In this picture I bet 10 coins, the 5-coin win for the pair of kings is tripled to 15 because I got an ace in the bonus hand.

In this picture I face my first opponent in the bonus round. My pair of jacks in the bonus hand carries over as my first starting hand. The lower right corner of the screen shows I can accept this hand (which I should) or trade it in for a random two-card hand.

Return

Jacks or Better

In the 97.30% version of Jacks or Better the probability of a free seat is 1 in 850, as told to me by WMS gaming.

The following is the return table for the video poker bet.

Jacks or Better - Video Poker Bet

Hand Pays Combinations Probability Return
Royal flush 800 496224876 0.000025 0.019915
Straight flush 50 2146096656 0.000108 0.005383
Four of a kind 25 47100003732 0.002363 0.059072
Full house 8 229504776948 0.011514 0.092109
Flush 5 217303355868 0.010902 0.054508
Straight 4 223952329860 0.011235 0.044941
Three of a kind 3 1484283075660 0.074463 0.223388
Two pair 2 2577335006268 0.129298 0.258597
Pair 1 4287052708344 0.215071 0.215071
Nothing 0 10864056938988 0.545022 0
Total 19933230517200 1 0.972984

The following table shows the return for the various components of the overall game.

Jacks or Better Total Return

Feature Return
Base game 0.972984
Ace multiplier 0.31699
Four of a kind multiplier 0
Earned Final Table Bonus 0.628826
Random Final Table Bonus 0.030172
Total bonus bet 0.975988
Overall game 0.974486

Bonus Poker

On the menu this game is titled "Four of a Kind Poker," although the pay table was the same as that of Bonus Poker. I was not told the free seat probability but based on WMS literature on the game I estimate the probability to be 1 in 700.

The following is the return table for the video poker bet.

Bonus Poker - Video Poker Bet

Hand Pays Combinations Probability Return
Royal flush 800 495430236 0.000025 0.019884
Straight flush 50 2132733288 0.000107 0.00535
4 aces 80 3903635460 0.000196 0.015667
4 2-4 40 10509856008 0.000527 0.02109
4 5-K 25 32673298536 0.001639 0.040978
Full house 7 229459754916 0.011511 0.08058
Flush 5 216946473756 0.010884 0.054418
Straight 4 224617025580 0.011268 0.045074
3 of a kind 3 1483756110144 0.074436 0.223309
Two pair 2 2576626215768 0.129263 0.258526
Jacks or better 1 4291056995796 0.215272 0.215272
Nothing 0 10861052987712 0.544872 0
Total 19933230517200 1 0.980147

The following table shows the return for the various components of the overall game.

Bonus Poker Total Return

Feature Return
Base game 0.980147
Ace multiplier 0.319324
Four of a kind multiplier 0
Earned Final Table Bonus 0.628826
Random Final Table Bonus 0.036637
Total bonus bet 0.984787
Overall game 0.982467

Double Bonus

On the menu this game is titled "2X Four of a Kind." I was not told the free seat probability but based on WMS literature on the game I estimate the probability to be 1 in 950.

The following is the return table for the video poker bet. The probabilities do not match those for conventional 7/5 Double Bonus because the four of a kind multiplier would cause the optimal strategy player to put a greater weighting on the four of a kinds. The strategy used for the table below is based on four of a kind pays of 162.90, 81.45, and 50.90.

Double Bonus - Video Poker Bet

Hand Pays Combinations Probability Return
Royal Flush 800 487780284 0.000024 0.019577
Straight Flush 50 2166021444 0.000109 0.005433
Four A 160 4466806116 0.000224 0.035854
Four 2-4 80 10456994388 0.000525 0.041968
Four 5-K 50 32300004528 0.00162 0.08102
Full House 8 214536782664 0.010763 0.086102
Flush 6 221042483832 0.011089 0.066535
Straight 5 309237383472 0.015514 0.077568
Three of a kind 3 1476526866480 0.074074 0.222221
Two pair 1 2413173539520 0.121063 0.121063
Pair 1 4185138187692 0.209958 0.209958
Nonpaying hand 0 11063697666780 0.555038 0
Total 19933230517200 1 0.967299

The following table shows the return for the various components of the overall game.

Double Bonus Total Return

Feature Return
Base game 0.980147
Ace multiplier 0.319324
Four of a kind multiplier 0
Earned Final Table Bonus 0.628826
Random Final Table Bonus 0.036637
Total bonus bet 0.984787
Overall game 0.982467

Double Double Bonus

On the menu this game is titled "4X Four of a Kind." I was not told the free seat probability but based on WMS literature on the game I estimate the probability to be 1 in 900.

The following is the return table for the video poker bet. The probabilities do not match those for conventional 8/5 Double Double Bonus because the four of a kind multiplier would cause the optimal strategy player to put a greater weighting on the four of a kinds. The strategy used for the table below is based on four of a kind pays of 421.72, 168.69, 84.34, and 52.71.

Double Double Bonus - Video Poker Bet

Hand Pays Combinations Probability Return
Royal flush 800 497598732 0.000025 0.019971
Straight flush 50 2115135072 0.000106 0.005306
4 aces + 2-4 400 1230139404 0.000062 0.024685
4 2-4 + A-4 160 2854746732 0.000143 0.022914
4 aces + 5-K 160 3465586500 0.000174 0.027818
4 2-4 + 5-K 80 7662852888 0.000384 0.030754
4 5-K 50 32534631276 0.001632 0.081609
Full house 8 216665304336 0.01087 0.086956
Flush 5 218462346576 0.01096 0.054799
Straight 4 257769810228 0.012932 0.051727
3 of a kind 3 1502032120572 0.075353 0.22606
Two pair 1 2455095285108 0.123166 0.123166
Jacks or better 1 4227723252828 0.212094 0.212094
Nothing 0 11005121706948 0.552099 0
Total 19933230517200 1 0.967858

The following table shows the return for the various components of the overall game.

Double Double Bonus Total Return

Feature Return
Base game 0.967858
Ace multiplier 0.315320
Four of a kind multiplier 0.000139
Earned Final Table Bonus 0.628826
Random Final Table Bonus 0.028495
Total bonus bet 0.972781
Overall game 0.970319

Deuces Wild

I was not told the free seat probability but based on WMS literature on the game I estimate the probability to be 1 in 627. Deuces are only wild in the video poker game, not the bonus hand or bonus.

Deuces Wild - Video Poker Bet

Hand Pays Combinations Probability Return
Natural royal flush 800 451792236 0.000023 0.018132
Four deuces 200 3863424612 0.000194 0.038764
Wild royal flush 25 38143832304 0.001914 0.04784
Five of a kind 12 60543033648 0.003037 0.036447
Straight flush 9 92059493940 0.004618 0.041566
Four of a kind 4 1234339050060 0.061924 0.247695
Full house 4 526041410976 0.02639 0.105561
Flush 2 352578561264 0.017688 0.035376
Straight 2 1176657577728 0.05903 0.11806
Three of a kind 1 5395672259556 0.270687 0.270687
Nothing 0 11052880080876 0.554495 0
Total 19933230517200 1 0.960127

The following table shows the return for the various components of the overall game.

Deuces Wild Total Return

Feature Return
Base game 0.960127
Ace multiplier 0.312802
Four of a kind multiplier 0
Earned Final Table Bonus 0.628826
Random Final Table Bonus 0.040903
Total bonus bet 0.982531
Overall game 0.971329

Joker Poker

I was not told the free seat probability but based on WMS literature on the game I estimate the probability to be 1 in 504. I assume that there are no jokers in the bonus hand or bonus game.

Joker Poker - Video Poker Bet

Hand Pays Combinations Probability Return
Natural royal flush 800 615552540 0.000025 0.020043
Five of a kind 200 2281952316 0.000093 0.018576
Wild royal flush 100 2574016404 0.000105 0.010477
Straight flush 50 14652758076 0.000596 0.02982
Four of a kind 16 208844242500 0.0085 0.136006
Full house 6 383739274548 0.015619 0.093714
Flush 5 390323606100 0.015887 0.079435
Straight 3 414947030400 0.016889 0.050667
Three of a kind 2 3272889107892 0.133213 0.266426
Two pair 1 2717828263404 0.110621 0.110621
Kings or better 1 3462869564496 0.140945 0.140945
Nothing 0 13697300152524 0.557506 0
Total 24568865521200 1 0.956729

The following table shows the return for the various components of the overall game.

Joker Poker Total Return

Feature Return
Base game 0.956729
Ace multiplier 0.311695
Four of a kind multiplier 0
Earned Final Table Bonus 0.628826
Random Final Table Bonus 0.050885
Total bonus bet 0.991406
Overall game 0.974067

Strategy

Except for double bonus and double double bonus the video poker strategy is the same as conventional video poker. In the two games with a four of a kind multiplier the player should play slightly more aggressively to get four of a kinds than the pay table suggests. The real for of a kind values are indicated above for both of those games.

The bonus round strategy changes as the player moves up through the opponents. This is because the player is conflicted between advancing to the next opponent and attaining the bad beat jackpot. The earlier in the bonus round the greater the relative value of the bad beat bonus. Thus, earlier in the bonus the player will be slightly more inclined to keep marginal hands.

The following table shows the bonus round strategy when in 10th place.

The following table shows the bonus round strategy when in 9th place.

The following table shows the bonus round strategy when in 8th place.

The following table shows the bonus round strategy when in 7th place.

The following table shows the bonus round strategy when in 2nd to 6th place.

Bad Beat Probabilities

The following table shows the probability of a bad beat for any given starting hand.

Bad Beat Probability Table

Staring Hand Bad Beat
Combinations
Total
Combinations
Bad Beat
Probability
2/3 suited 323562 2097572400 0.000154
2/4 suited 319091 2097572400 0.000152
2/5 suited 314993 2097572400 0.00015
2/6 suited 307598 2097572400 0.000147
2/7 suited 295788 2097572400 0.000141
2/8 suited 280598 2097572400 0.000134
2/9 suited 256912 2097572400 0.000123
2/T suited 223704 2097572400 0.000107
2/J suited 184028 2097572400 0.000088
2/Q suited 134808 2097572400 0.000064
2/K suited 75020 2097572400 0.000036
2/A suited 6540 2097572400 0.000003
3/4 suited 321985 2097572400 0.000154
3/5 suited 315135 2097572400 0.00015
3/6 suited 307613 2097572400 0.000147
3/7 suited 295800 2097572400 0.000141
3/8 suited 278542 2097572400 0.000133
3/9 suited 256882 2097572400 0.000123
3/T suited 223674 2097572400 0.000107
3/J suited 183998 2097572400 0.000088
3/Q suited 134778 2097572400 0.000064
3/K suited 74990 2097572400 0.000036
3/A suited 3758 2097572400 0.000002
4/5 suited 318029 2097572400 0.000152
4/6 suited 307755 2097572400 0.000147
4/7 suited 295815 2097572400 0.000141
4/8 suited 278554 2097572400 0.000133
4/9 suited 254824 2097572400 0.000122
4/T suited 223642 2097572400 0.000107
4/J suited 183966 2097572400 0.000088
4/Q suited 134746 2097572400 0.000064
4/K suited 74958 2097572400 0.000036
4/A suited 3599 2097572400 0.000002
5/6 suited 310649 2097572400 0.000148
5/7 suited 295957 2097572400 0.000141
5/8 suited 278569 2097572400 0.000133
5/9 suited 254836 2097572400 0.000122
5/T suited 221584 2097572400 0.000106
5/J suited 183934 2097572400 0.000088
5/Q suited 134714 2097572400 0.000064
5/K suited 74926 2097572400 0.000036
5/A suited 3564 2097572400 0.000002
6/7 suited 298833 2097572400 0.000143
6/8 suited 278693 2097572400 0.000133
6/9 suited 254833 2097572400 0.000122
6/T suited 221578 2097572400 0.000106
6/J suited 181858 2097572400 0.000087
6/Q suited 134664 2097572400 0.000064
6/K suited 74876 2097572400 0.000036
6/A suited 3514 2097572400 0.000002
7/8 suited 281613 2097572400 0.000134
7/9 suited 255001 2097572400 0.000122
7/T suited 221616 2097572400 0.000106
7/J suited 181896 2097572400 0.000087
7/Q suited 132632 2097572400 0.000063
7/K suited 74870 2097572400 0.000036
7/A suited 5444 2097572400 0.000003
8/9 suited 257921 2097572400 0.000123
8/T suited 221654 2097572400 0.000106
8/J suited 181934 2097572400 0.000087
8/Q suited 132670 2097572400 0.000063
8/K suited 72838 2097572400 0.000035
8/A suited 5438 2097572400 0.000003
9/T suited 221692 2097572400 0.000106
9/J suited 181972 2097572400 0.000087
9/Q suited 132708 2097572400 0.000063
9/K suited 72876 2097572400 0.000035
9/A suited 3406 2097572400 0.000002
T/J suited 182010 2097572400 0.000087
T/Q suited 132746 2097572400 0.000063
T/K suited 72914 2097572400 0.000035
T/A suited 3444 2097572400 0.000002
J/Q suited 132766 2097572400 0.000063
J/K suited 72934 2097572400 0.000035
J/A suited 3464 2097572400 0.000002
Q/K suited 72954 2097572400 0.000035
Q/A suited 3484 2097572400 0.000002
K/A suited 3504 2097572400 0.000002
2/3 unsuited 322500 2097572400 0.000154
2/4 unsuited 320908 2097572400 0.000153
2/5 unsuited 316940 2097572400 0.000151
2/6 unsuited 309566 2097572400 0.000148
2/7 unsuited 297812 2097572400 0.000142
2/8 unsuited 280598 2097572400 0.000134
2/9 unsuited 256912 2097572400 0.000123
2/T unsuited 223704 2097572400 0.000107
2/J unsuited 184028 2097572400 0.000088
2/Q unsuited 134808 2097572400 0.000064
2/K unsuited 75020 2097572400 0.000036
2/A unsuited 5582 2097572400 0.000003
3/4 unsuited 320866 2097572400 0.000153
3/5 unsuited 316898 2097572400 0.000151
3/6 unsuited 309524 2097572400 0.000148
3/7 unsuited 297770 2097572400 0.000142
3/8 unsuited 280568 2097572400 0.000134
3/9 unsuited 256882 2097572400 0.000123
3/T unsuited 223674 2097572400 0.000107
3/J unsuited 183998 2097572400 0.000088
3/Q unsuited 134778 2097572400 0.000064
3/K unsuited 74990 2097572400 0.000036
3/A unsuited 5552 2097572400 0.000003
4/5 unsuited 316854 2097572400 0.000151
4/6 unsuited 309480 2097572400 0.000148
4/7 unsuited 297726 2097572400 0.000142
4/8 unsuited 280524 2097572400 0.000134
4/9 unsuited 256850 2097572400 0.000123
4/T unsuited 223642 2097572400 0.000107
4/J unsuited 183966 2097572400 0.000088
4/Q unsuited 134746 2097572400 0.000064
4/K unsuited 74958 2097572400 0.000036
4/A unsuited 5520 2097572400 0.000003
5/6 unsuited 309436 2097572400 0.000148
5/7 unsuited 297682 2097572400 0.000142
5/8 unsuited 280480 2097572400 0.000134
5/9 unsuited 256806 2097572400 0.000122
5/T unsuited 223610 2097572400 0.000107
5/J unsuited 183934 2097572400 0.000088
5/Q unsuited 134714 2097572400 0.000064
5/K unsuited 74926 2097572400 0.000036
5/A unsuited 5488 2097572400 0.000003
6/7 unsuited 297620 2097572400 0.000142
6/8 unsuited 280418 2097572400 0.000134
6/9 unsuited 256744 2097572400 0.000122
6/T unsuited 223548 2097572400 0.000107
6/J unsuited 183884 2097572400 0.000088
6/Q unsuited 134664 2097572400 0.000064
6/K unsuited 74876 2097572400 0.000036
6/A unsuited 5450 2097572400 0.000003
7/8 unsuited 280400 2097572400 0.000134
7/9 unsuited 256726 2097572400 0.000122
7/T unsuited 223530 2097572400 0.000107
7/J unsuited 183866 2097572400 0.000088
7/Q unsuited 134658 2097572400 0.000064
7/K unsuited 74870 2097572400 0.000036
7/A unsuited 5444 2097572400 0.000003
8/9 unsuited 256708 2097572400 0.000122
8/T unsuited 223512 2097572400 0.000107
8/J unsuited 183848 2097572400 0.000088
8/Q unsuited 134640 2097572400 0.000064
8/K unsuited 74864 2097572400 0.000036
8/A unsuited 5438 2097572400 0.000003
9/T unsuited 223494 2097572400 0.000107
9/J unsuited 183830 2097572400 0.000088
9/Q unsuited 134622 2097572400 0.000064
9/K unsuited 74846 2097572400 0.000036
9/A unsuited 5432 2097572400 0.000003
T/J unsuited 181786 2097572400 0.000087
T/Q unsuited 132578 2097572400 0.000063
T/K unsuited 72802 2097572400 0.000035
T/A unsuited 3388 2097572400 0.000002
J/Q unsuited 132598 2097572400 0.000063
J/K unsuited 72822 2097572400 0.000035
J/A unsuited 3408 2097572400 0.000002
Q/K unsuited 72842 2097572400 0.000035
Q/A unsuited 3428 2097572400 0.000002
K/A unsuited 3448 2097572400 0.000002
Pair of 2's 358704 2097572400 0.000171
Pair of 3's 358780 2097572400 0.000171
Pair of 4's 357492 2097572400 0.00017
Pair of 5's 353692 2097572400 0.000169
Pair of 6's 345388 2097572400 0.000165
Pair of 7's 332376 2097572400 0.000159
Pair of 8's 313396 2097572400 0.000149
Pair of 9's 287296 2097572400 0.000137
Pair of T's 248892 2097572400 0.000119
Pair of J's 204364 2097572400 0.000097
Pair of Q's 149260 2097572400 0.000071
Pair of K's 82428 2097572400 0.000039
Pair of A's 7408 2097572400 0.000004

Acknowledgements

I would like to thank Scott at Online Poker Room Reviews for the bad beat probability table above. I would also like to thank WMS gaming for their cooperation answering questions about the rules and guidance in the mathematical analysis.

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Written by: Michael Shackleford

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