The Royal Flush in Video Poker
The Royal Flush will be about 2% of your return. If you do not hit it, you will probably have a negative return unless you are hitting bonus hands or other big hands.
A Royal Flush cycle is the number of hands until hitting the Royal which will average about every 40,000 hands or so. It varies by a few thousand hands game to game because your playing strategy will be less Royalcentric in games with bonus hands and more Royalcentric where you need to go after the Royal.
Below are the odds for getting a Royal. Each card needed to make a Royal is calculated separately and then multiplied together to get the odds. This is available as a Google spreadsheet.
Any 10,J,Q,K or A on your first card, gives you a chance at a Royal with odds of 20 out of 52 total cards in the deck. The next card has to be the same suit so you only have 4 out of 51 chances, etc. and then finally 1 out of 48 cards for the last card.
If all your cards are lower than a 10 and you discard them all, there will only be 47 cards left in the deck. The odds of drawing a Royal after discarding all 5 dealt cards is 383,484.8 to 1 while it is 47 to 1 if you start with 4 cards to the Royal.
Odds for a Joker game are also shown. For example, if you have 2 cards to a Natural Royal (No Jokers or wild cards) the odds are 17,296 to 1 against you making a Natural Royal while the odds are 16,215 to 1 in a 52 card deck.
The Palms has a double Joker game which can be easily calculated from the Google spreadsheet by simply increasing the cards in the dealt Royal area from 53 to 54. All the other odds will automatically change.
53 to 54. All the other odds will automatically change.
No Jokers/Wilds

1st Card

2nd Card

3rd Card

4th Card

5th Card

All Cards

Odds

Any Dealt Royal

20

4

3

2

1



Cards Left in Deck

52

51

50

49

48



Chance of Draw

0.3846

0.0784

0.0600

0.0408

0.0208

0.000154%

649,740.0









4 Cards to Royal

1







Cards Left in Deck

47







Chance of Draw

0.0213





2.127660%

47.0









3 Cards to Royal

2

1






Cards Left in Deck

47

46






Chance of Draw

0.0426

0.0217




0.092507%

1,081.0









2 Cards to Royal

3

2

1





Cards Left in Deck

47

46

45





Chance of Draw

0.0638

0.0435

0.0222



0.006167%

16,215.0









1 Card to Royal

4

3

2

1




Cards Left in Deck

47

46

45

44




Chance of Draw

0.0851

0.0652

0.0444

0.0227


0.000561%

178,365.0









0 Cards to Royal

20

4

3

2

1



Cards Left in Deck

47

46

45

44

43



Chance of Draw

0.4255

0.0870

0.0667

0.0455

0.0233

0.000261%

383,484.8

Joker Games

1st Card

2nd Card

3rd Card

4th Card

5th Card

All Cards

Odds

Dealt Natural

20

4

3

2

1



Cards Left in Deck

53

52

51

50

49



Chance of Draw

0.3774

0.0769

0.0588

0.0400

0.0204

0.000139%

717,421.3









4 Cards to Natural

1







Cards Left in Deck

48







Chance of Draw

0.0208





2.083333%

48.0









3 Cards to Natural

2

1






Cards Left in Deck

48

47






Chance of Draw

0.0417

0.0213




0.088652%

1,128.0









2 Cards to Natural

3

2

1





Cards Left in Deck

48

47

46





Chance of Draw

0.0625

0.0426

0.0217



0.005782%

17,296.0









1 Card to Natural

4

3

2

1




Cards Left in Deck

48

47

46

45




Chance of Draw

0.0833

0.0638

0.0435

0.0222


0.000514%

194,580.0









O Cards to Natural

20

4

3

2

1



Cards Left in Deck

48

47

46

45

44



Chance of Draw

0.4167

0.0851

0.0652

0.0444

0.0227

0.000234%

428,076.0









If you have 3 cards to the Royal, drawing for 2 cards, it would seem that 1,081 chances to make that draw (“at bats”) would guarantee hitting a Royal. The odds are 1,081 to 1 of making this 2 card catch. Simple arithmetic is misleading.
For any odds of more than about 500 to 1, it will always be about 63.2% to make the hand given the number of “at bats” is the same as the odds. If you look up the odds of getting a Royal when holding 3 cards, it works out to 1,081 to 1. At 1,081 attempts while holding 3 to the Royal, the odds of hitting are about 63.2%not 100%.
For smaller odds such as a 4 card Royal with a 47 to 1 draw, the odds of getting at least one Royal in 47 attempts are slightly higher at 63.6%.
You will be dealt 2 to a Royal about every 33 hands. Once you have 2 to the Royal, your odds of getting the other 3 cards is one in 16,215. For 16,215 at bats, holding 2 Royal cards, you should expect 1 or more Royals 63.2% of the time.
The table also shows how many at bats you need to be 50/50 to get a Royal(s). For example if you have 4 to the Royal, 33 at bats will put you just over 50% likely to hit at least one.
If you are playing multiple lines such as 100 hands simultaneously with 4 to the Royal as your starting hand, you have an 88.36% chance. With 200 tries when you have 4 to the Royal, you are 98.64% likely to be filling out a WG2 with a smile on your face.
As a rough rule of thumb, you can triple the odds to estimate the 95% likelihood of hitting. For the 1 out of 47 draw when you have 4 to the Royal, multiply 47 by 3 to get 141 and at 141 attempts you are over 95% likely to hit at least one. For 2 to the Royal, where the odds are 16,215 against you, multiply by 3 to get 48,645—also over a 95% probability.

Pat Royal

Draw All 5

Draw 4

Draw 3

Draw 2

Draw 1

Chance

0.00000154

0.00000261

0.00000561

0.00006167

0.00092507

0.02127660

1Chance

0.99999846

0.99999739

0.99999439

0.99993833

0.99907493

0.97872340

At Bats







1

0.00000154

0.00000261

0.00000561

0.00006167

0.00092507

0.02127660

10

0.00001539

0.00002608

0.00005606

0.00061654

0.00921228

0.19350861

33

0.00005079

0.00008605

0.00018500

0.00203315

0.03007974

0.50821063

47

0.00007233

0.00012255

0.00026347

0.00289444

0.04256590

0.63606924

50

0.00007695

0.00013037

0.00028029

0.00307891

0.04522052

0.65880812

100

0.00015390

0.00026073

0.00056049

0.00614834

0.08839614

0.88358810

141

0.00021699

0.00036761

0.00079020

0.00865822

0.12233925

0.95179897

200

0.00030777

0.00052140

0.00112067

0.01225888

0.16897841

0.98644827

250

0.00038470

0.00065170

0.00140064

0.01530005

0.20655764

0.99537626

500

0.00076924

0.00130298

0.00279932

0.03036600

0.37044922

0.99997862

749

0.00115211

0.00195124

0.00419046

0.04514256

0.50002523

0.99999990

1,081

0.00166236

0.00281492

0.00604229

0.06449494

0.63229078

1.00000000

5,000

0.00766586

0.01295371

0.02764322

0.26535359

0.99022070

1.00000000

10,000

0.01527295

0.02573963

0.05452229

0.46029465

0.99990437

1.00000000

11,240

0.01715047

0.02888482

0.06107251

0.50002976

0.99996965

1.00000000

16,215

0.02464733

0.04140188

0.08689952

0.63213190

0.99999970

1.00000000

48,645

0.07213448

0.11913426

0.23870020

0.95021754

1.00000000

1.00000000

100,000

0.14264897

0.22953951

0.42916192

0.99790315

1.00000000

1.00000000

123,633

0.17327310

0.27558724

0.50000042

0.99951183

1.00000000

1.00000000

178,365

0.24006145

0.37193831

0.63212159

0.99998330

1.00000000

1.00000000

265,812

0.33575585

0.50000127

0.77468912

0.99999992

1.00000000

1.00000000

383,485

0.44579103

0.63212128

0.88351671

1.00000000

1.00000000

1.00000000

450,366

0.50000069

0.69099736

0.91993973

1.00000000

1.00000000

1.00000000

500,000

0.53677352

0.72851123

0.93938715

1.00000000

1.00000000

1.00000000

649,740

0.63212084

0.81627347

0.97382015

1.00000000

1.00000000

1.00000000

1,000,000

0.78542122

0.92629385

0.99632608

1.00000000

1.00000000

1.00000000

2,598,960

0.98168442

0.99886057

0.99999953

1.00000000

1.00000000

1.00000000

Maximum Coin
By betting the maximum 5 coin per hand, you will gain about 1 full percentage point on most games. This means you are better off playing a nickel machine for 5 coins ($0.25) than a Quarter Video Poker game for 1 coin even though the bet amount is the same.
The single coin payout for Natural Royals (no wild cards) is 250 coins. The 5 coin payout is not 1,250 but 4,000 or an extra 2,750 coins.
A Royal on a quarter Video Poker game will pay $62.50 for a single coin bet. If you hit a Royal on a nickel machine playing max coins of $0.25 total, you will get $200.00—$137.50 more for the same amount of money bet.
Joker games have higher payouts for Natural Royals because there is an extra card (or cards if more than 1 Joker). A Natural for Joker Poker will pay 400 coins for a 1 coin bet but either 4,000 or rarely 4,700 for all 5 coins bet.
A single quarter player will only get $100 while a max nickel player betting the same $0.25 total bet will get either $200 or rarely $235 for their Natural Royal on single Joker games.
Unlike many slot machines, you are better off with a max coin bet in Las Vegas Video Poker even if you have to go to a smaller denomination.
Variance
There are only a few Video Poker games that have lower Variance than Deuces Wild. In Pick Em, you are dealt 2 cards and choose 1 of 2 additional cards. Your next 2 unseen cards complete your 5 card hand.
Jacks or better (JOB) has a Variance lower than FPDW and Double Bonus (DB) is not too much higher. Both games are commonly found in Las Vegas. One of the factors that affects Variance is the Royal Flush cycle which is the number of hands until the Royal that contribute to the calculated return of the game.
Name

Return

Variance

Cycle

Pick Em

99.95%

15.0%

351,851

Jacks or Better 9/6 (JOB 9/6)

99.54%

19.5%

40,390

Deuces Wild (FPDW)

100.76%

25.8%

45,281

Deuces Wild (NSUD)

99.73%

25.8%

43,456

Deuces Wild Deluxe (DWDLX)

100.32%

26.0%

43,465

JokerKings or Better (JKOB)

100.65%

26.2%

41,214

All American

100.72%

26.8%

43,450

Double Bonus (DB)

100.17%

28.3%

48,048

Joker2 Pair (J2)

99.92%

31.3%

43,617

Bonus Poker Deluxe (BDLX)

99.64%

32.1%

42,077

Bonus Deuces Wild (BDW)

99.45%

32.7%

42,070

Super Double Bonus (SDB)

99.69%

38.0%

40,619

Double Bonus Deuces Wild (DBDW)

99.81%

40.4%

44,211

Double Double Bonus 10/6 (DDB 10/6)

100.07%

42.2%

40,782

White Hot Aces (WHA)

99.57%

43.7%

39,030

Sam's Town Deuces

100.95%

50.4%

44,362

Double Deuces Wild (DDW)

99.62%

50.9%

44,913

Super Aces

99.94%

63.0%

39,140

Loose Deuces Wild (LDW)

100.15%

70.7%

44,890

Double Bonus Double Jackpot (DBDJ)

100.09%

92.7%

32,928

Triple Bonus (TB)

99.58%

98.3%

43,358

Average of Selected Games


41.9%

57,102.5

Multiline Games
Some games allow you to play more than one line at a time. You have a base hand which is usually at the bottom of the screen—sometimes middle. All other hands use the same cards you keep from this base hand. If you have 4 cards to the Royal and draw for 1, then you will have 4 card Royal draws on all your hands.
The Multistrike (MS) games have 4 levels with bonus multipliers of 0,2,4 and 8 times your bet. You must win to make the next level (or get a random free pass that takes you to the next level, win or lose). If you do not make a winning hand, you stop at whatever level you are on despite paying for all 4 levels.
Strategy is different from regular optimal play for each level until you get to the 8X level. Returns are slightly higher in Multistrike so a 9/6 Jacks or Better single line is 99.54% while the Multistrike version is 99.79%.
Spin Poker (9 lines) and Spin Poker Deluxe (20 lines) have a similar look to some slot machines. Hands are formed similar to slot machines but the strategy is the same as Video Poker. You are simply playing multiple lines squished into a video reel slot machine format.
A Super Times Pay (STP) game has a multiplier that increases your winnings (if any) by a random number. STP games are also slightly higher returns than the single line games so an STP Jacks or Better will be 99.82% not 99.54%.
The 3, 5, 10, 50,100, etc. games are similar with a base hand that partially determines results on the other hands. For 50 and 100 plays, the cards are so small that outline colors are used to identify winning hands by types.
Variance on multiline games is higher than single line games because one of your hands partially determines outcomes on the other hands. If each hand were completely independent then it would be as if you were playing a single line game extremely quickly but with no increase in Variance. But this is NOT what multiline games are.
Here are some estimates for increase in Variance for Deuces Wild (Full Pay or FPDW), Jacks or Better (JOB) and Double Bonus (DB) given number of lines played.
The 3 columns on the right are the multiples of a single line game. This means Variance for Full Pay Deuces Wild is almost 1.5X than a single line game when playing 5 lines at once. At 100 lines, the Variance for Jacks or Better will be almost 11X that of a single line Jacks or Better.
Lines

FPDW

JOB

DB

FPDW

JOB

DB

Comments

1

25.84

19.51

28.26

1.00

1.00

1.00


2

28.98

21.48

31.65

1.12

1.10

1.12


3

32.12

23.44

35.04

1.24

1.20

1.24


4

35.26

25.41

38.43

1.36

1.30

1.36


5

38.40

27.37

41.82

1.49

1.40

1.48

Almost 1.5X

6

41.54

29.34

45.21

1.61

1.50

1.60


7

44.68

31.31

48.60

1.73

1.60

1.72


8

47.82

33.27

51.99

1.85

1.71

1.84


9

50.96

35.24

55.39

1.97

1.81

1.96


10

54.10

37.20

58.78

2.09

1.91

2.08

About 2X

15

69.80

47.03

75.73

2.70

2.41

2.68


20

85.50

56.86

92.69

3.31

2.91

3.28


25

101.20

66.69

109.64

3.92

3.42

3.88

Almost 4X

30

116.90

76.52

126.60

4.52

3.92

4.48


35

132.60

86.35

143.55

5.13

4.43

5.08


40

148.30

96.18

160.51

5.74

4.93

5.68


45

164.00

106.01

177.46

6.35

5.43

6.28


50

179.70

115.84

194.42

6.95

5.94

6.88

About 67X

55

195.40

125.67

211.37

7.56

6.44

7.48


60

211.10

135.50

228.33

8.17

6.95

8.08


65

226.80

145.33

245.28

8.78

7.45

8.68


70

242.50

155.16

262.24

9.38

7.95

9.28


75

258.20

164.99

279.19

9.99

8.46

9.88

Almost 10X

80

273.90

174.82

296.15

10.60

8.96

10.48


85

289.60

184.65

313.10

11.21

9.46

11.08


90

305.30

194.48

330.06

11.81

9.97

11.68


95

321.00

204.31

347.01

12.42

10.47

12.28


100

336.70

214.14

363.97

13.03

10.98

12.88

About 1113X

Bankroll and Risk of Ruin
Video Poker requires a larger than expected bankroll. Deuces Wild with Full Payout (FPDW) has expected return of 100.76% and Variance is about 15 percentage points lower than many other Video Poker games. Its lower Variance and higher expected return mean it has lower than average required bankroll but still higher than what one would expect.
For example, a 5 dollar player (max coin of $25) who wanted a risk of ruin on FPDW of a tenth of one percent, would need $266,718.
A nickel player ($0.25 max coin) desiring a 90% likelihood of not busting out on FPDW, should have $889. Dollar players (playing $5 max per hand) are a 50/50 coin flip for wiping out if they only bring $5,353.
High roller Video Poker players risking $500 max coin a pull on the $100 machines would need over $3.5M to have a 1% risk of ruin.
Comps lower the bankroll necessary although a disturbing trend at casinos such as Sam’s Town, Palms, and Palace Station, etc. is diminished comps for 100% plus machines. For some promotions, they are specifically excluded. See FPDW table below for required bankroll without adding in comps.
Risk of Ruin

Not Busting

Nickel $0.25

Quarter $1.25

Dollar $5.00

$5 $25.00

$25 $125.00

$100 $500.00

0.1%

99.9%

$2,667

$13,336

$53,344

$266,718

$1,333,592

$5,334,367

0.5%

99.5%

$2,046

$10,229

$40,915

$204,576

$1,022,878

$4,091,513

1.0%

99.0%

$1,778

$8,891

$35,562

$177,812

$889,061

$3,556,245

2.0%

98.0%

$1,510

$7,552

$30,210

$151,049

$755,244

$3,020,977

3.0%

97.0%

$1,354

$6,770

$27,079

$135,393

$676,966

$2,707,865

4.0%

96.0%

$1,243

$6,214

$24,857

$124,285

$621,427

$2,485,708

5.0%

95.0%

$1,157

$5,783

$23,134

$115,670

$578,348

$2,313,390

6.0%

94.0%

$1,086

$5,431

$21,726

$108,630

$543,149

$2,172,597

7.0%

93.0%

$1,027

$5,134

$20,536

$102,678

$513,389

$2,053,557

8.0%

92.0%

$975

$4,876

$19,504

$97,522

$487,610

$1,950,440

9.0%

91.0%

$930

$4,649

$18,595

$92,974

$464,871

$1,859,485

10.0%

90.0%

$889

$4,445

$17,781

$88,906

$444,531

$1,778,122

20.0%

80.0%

$621

$3,107

$12,429

$62,143

$310,714

$1,242,854

25.0%

75.0%

$535

$2,676

$10,705

$53,527

$267,634

$1,070,536

33.3%

66.7%

$424

$2,121

$8,484

$42,419

$212,095

$848,380

50.0%

50.0%

$268

$1,338

$5,353

$26,763

$133,817

$535,268

66.7%

33.3%

$157

$783

$3,131

$15,656

$78,278

$313,112

75.0%

25.0%

$111

$555

$2,222

$11,108

$55,539

$222,156

90.0%

10.0%

$41

$203

$814

$4,068

$20,341

$81,362

95.0%

5.0%

$20

$99

$396

$1,981

$9,903

$39,610

99.0%

1.0%

$4

$19

$78

$388

$1,940

$7,761

