# Guaranteed Play Video Poker Appendix 1

The following table shows the expected return for any given state in Guaranteed Play Video Poker. By recursively moving backwards the player can enter the expected values into Video Poker strategy software, such as "Video Poker for Winners", "Frugal Video Poker", or "Video Poker Strategy Master."

This particular table is for 9/6 Double Double Bonus, in which the player buys 100 hands. The first hand the player plays is numbered 1, and the last (assuming he doesn't quit) is 100. The bankroll column is the number of units in the player's bankroll at the start of the hand, before paying for it. The expected value column is just that, what the state of the game is worth at that moment.

If the player's bankroll is ever more than the number of hands remaining, then he should quit. These rows are omitted from the table. Some rows in the table are impossible to achieve, so please don't write in about that, I know.

You can see in the last row the hand number is 1, the bankroll is 0, and the expected value is 17.24752. The player must pay 20 units for these 100 hands, so the expected return of the game is 17.24752/20 = 86.2376%.

To generate a strategy for the first hand, note the expected value for all possible outcomes of the first hand. For example, if the player loses, then he will be at hand 2 with a bankroll of -1. The value of this state is 16.868927. If the player gets a royal flush the value of his state will be 799 (deducting one unit for the cost of the bet). The player should subtract the expected value of a loss from the expected value of each win, then multiply by a large number, such as 1000, round to the nearest integer, and put these values into the desired video poker strategy engine. This is what the last column of the following table shows. The reason for the subtracting is that the video poker software does not allow for a win on what is normally a losing hand. The reason for the multiplying by a large number is because the software does not allow decimal values for wins.

### Hand 1 Expected Value Table — Guaranteed Play Video Poker

Hand Gross Win Net Win EV Hand 99 Adj. EV
Royal Flush 800 799 799 782131
Straight Flush 50 49 49 32131
4 Aces w/ any 2,3,4 400 399 399 382131
4 2s,3s,4s w/A,2,3,4 160 159 159 142131
4 Aces 160 159 159 142131
4 2s,3s,4s 80 79 79 62131
4 5s thru Ks 50 49 49 32131
Full House 9 8 19.460159 2591
Flush 6 5 18.522996 1654
Straight 4 3 17.943913 1075
3 of a KIND 3 2 17.665722 797
2 Pair 1 0 17.128776 260
Jacks or Better 1 0 17.128776 260
Loss 0 -1 16.868927 0

The next table shows the strategy table generated by Video Poker for Winners.

### Hand 1 Strategy Table — Guaranteed Play Video Poker

Rank Hand Description Exp. Val. after Deal
1 ROYAL FLUSH 782131
2 FOUR of a KIND A with 2-4; 2-4 with 2-4,A 202131
3 FOUR of a KIND A; 2-4 112769.29787234
4 FOUR of a KIND 5-K 32131
5 STRAIGHT FLUSH 32131
6 RF4 17176.55646481
7 THREE of a KIND 2-4,A 5644.25486646
8 FULL HOUSE 2591
9 THREE of a KIND 5-K 2239.89361702
10 SF4 2h0i \'QJT9\'; 1h0i \'JT98\'; 0h0i \'2345\'-\'789T\' 1748.59991884
11 FLUSH 1654
12 STRAIGHT 1075
13 SF4 2h1i \'KQT9\'-\'QJ98\'; 1h1i \'QT98\'-\'J987\'; A-low \'A234\'-\'A345\'; 3h1i \'KQJ9\'; 0h1i \'2346\'-\'689T\' 1044.7358156
14 RF3 \'KQJ\'; \'QJT\' 944.28770522
15 HIGH PAIR A 905.44969828
16 RF3 \'AHH\'; \'AHT\'; \'KHT\' 889.51014683
17 TWO PAIR 458.38297872
18 HIGH PAIR J-K 433.56817761
19 Low Pair 2-4 386.98808184
20 FL4 2h; 1h; 0h 334.57285751
21 Low Pair 5-T 248.22497687
22 SF3 1h0i \'JT9\' 238.48152064
23 ST4 3h0i KQJT 232.76595745
24 SF3 2h1i \'QJ9\' 222.8664458
25 ST4 2h0i QJT9 216.17021277
26 SF3 0h0i \'345\'-\'89T\' 212.31373067
27 ST4 1h0i JT98 199.57446809
28 SF3 1h1i \'QT9\'-\'J98\' 197.78561733
29 RF2 \'AH\' 185.01987576
30 ST4 0h0i 2345-789T 182.9787234
31 SF3 2h2i \'QJ8\' 181.37372803
32 RF2 \'QJ\' 189.02332474
33 SF3 2h2i \'KH9\' 181.14621097
34 RF2 \'KH\' 183.79349283
35 SF3 0h1i \'234\',\'235\'-\'79T\' 171.59259502
36 RF2 \'JT\' 161.54990192
37 ST4 4h1i AKQJ 157.87234043
38 RF2 \'QT\' 156.18968283
39 SF3 \'A43\'-\'A32\' 155.39777983
40 RF2 \'AT\' 155.35794018
41 HC1 A 161.49303919
42 SF3 1h2i \'KT9\'-\'J87\' 155.08215539
43 RF2 \'KT\' 150.63259629
44 ST4 3h1i KQJ9 141.27659574
45 SF3 0h2i \'236\'-\'69T\' 128.84538855
46 HC3 KQJ 128.65217391
47 ST4 2h1i KQT9-QJ98 124.68085106
48 HC2 KJ; QJ 123.80511246
49 HC1 J 123.9308868
50 HC2 KQ 120.80937136
51 HC1 Q-K 122.79886549
52 Draw 5 new cards 96.07344152
53 LC1 4 95.39165195

Finally, here is the exhaustive Expected Value table for hand #1 of 100-hand, 9/6 Double Double Bonus. If the expected value equals the hand number, then the player should collect his balance and quit.

Exhaustive Expected Value Table — Guaranteed Play Video Poker
Hand Bankroll Exp. Val.
100 -99 0.073103
100 -98 0.073608
100 -97 0.074114
100 -96 0.074619
100 -95 0.075125
100 -94 0.075631
100 -93 0.076136
100 -92 0.076642
100 -91 0.077148
100 -90 0.077654
100 -89 0.07816
100 -88 0.078665
100 -87 0.079173
100 -86 0.079681
100 -85 0.080189
100 -84 0.080697
100 -83 0.081205
100 -82 0.081713
100 -81 0.082221
100 -80 0.082729
100 -79 0.083237
100 -78 0.084049
100 -77 0.08486
100 -76 0.085672
100 -75 0.086483
100 -74 0.087295
100 -73 0.088106
100 -72 0.088918
100 -71 0.089729
100 -70 0.090541
100 -69 0.091353
100 -68 0.092186
100 -67 0.093062
100 -66 0.093938
100 -65 0.094831
100 -64 0.095732
100 -63 0.096635
100 -62 0.097539
100 -61 0.098444
100 -60 0.099349
100 -59 0.100253
100 -58 0.101174
100 -57 0.102094
100 -56 0.103014
100 -55 0.103935
100 -54 0.104856
100 -53 0.105779
100 -52 0.106701
100 -51 0.107624
100 -50 0.108548
100 -49 0.109472
100 -48 0.110964
100 -47 0.112792
100 -46 0.114658
100 -45 0.116535
100 -44 0.118538
100 -43 0.120572
100 -42 0.122804
100 -41 0.125158
100 -40 0.127513
100 -39 0.129871
100 -38 0.132236
100 -37 0.134614
100 -36 0.137026
100 -35 0.139439
100 -34 0.141851
100 -33 0.144281
100 -32 0.146719
100 -31 0.149174
100 -30 0.151721
100 -29 0.154349
100 -28 0.157098
100 -27 0.15986
100 -26 0.162622
100 -25 0.165384
100 -24 0.168149
100 -23 0.170916
100 -22 0.173686
100 -21 0.176457
100 -20 0.17923
100 -19 0.182005
100 -18 0.184782
100 -17 0.18756
100 -16 0.190339
100 -15 0.193119
100 -14 0.195902
100 -13 0.198687
100 -12 0.201472
100 -11 0.204258
100 -10 0.207043
100 -9 0.209829
100 -8 0.212614
100 -7 0.222186
100 -6 0.232455
100 -5 0.24448
100 -4 0.265781
100 -3 0.294444
100 -2 0.33468
100 -1 0.451303
100 0 0.569496
99 -98 0.14692
99 -97 0.147932
99 -96 0.148943
99 -95 0.149955
99 -94 0.150967
99 -93 0.15198
99 -92 0.152992
99 -91 0.154004
99 -90 0.155017
99 -89 0.15603
99 -88 0.157043
99 -87 0.158058
99 -86 0.159078
99 -85 0.160098
99 -84 0.161118
99 -83 0.162143
99 -82 0.16317
99 -81 0.164201
99 -80 0.165268
99 -79 0.166335
99 -78 0.167566
99 -77 0.169189
99 -76 0.170811
99 -75 0.172435
99 -74 0.174058
99 -73 0.175681
99 -72 0.177304
99 -71 0.178928
99 -70 0.180553
99 -69 0.182179
99 -68 0.183829
99 -67 0.185551
99 -66 0.187305
99 -65 0.189077
99 -64 0.190874
99 -63 0.192677
99 -62 0.194485
99 -61 0.196294
99 -60 0.198104
99 -59 0.199918
99 -58 0.201746
99 -57 0.203587
99 -56 0.205431
99 -55 0.207276
99 -54 0.209123
99 -53 0.210977
99 -52 0.212838
99 -51 0.21471
99 -50 0.216662
99 -49 0.218649
99 -48 0.220997
99 -47 0.224422
99 -46 0.228136
99 -45 0.23192
99 -44 0.235869
99 -43 0.239979
99 -42 0.244389
99 -41 0.249013
99 -40 0.253718
99 -39 0.258429
99 -38 0.263155
99 -37 0.267895
99 -36 0.272694
99 -35 0.277517
99 -34 0.282341
99 -33 0.287186
99 -32 0.292063
99 -31 0.297018
99 -30 0.30209
99 -29 0.307343
99 -28 0.312763
99 -27 0.318271
99 -26 0.323788
99 -25 0.329307
99 -24 0.334828
99 -23 0.340354
99 -22 0.345885
99 -21 0.351419
99 -20 0.356957
99 -19 0.362498
99 -18 0.368043
99 -17 0.37359
99 -16 0.379141
99 -15 0.384739
99 -14 0.390346
99 -13 0.39597
99 -12 0.401685
99 -11 0.407453
99 -10 0.413328
99 -9 0.420332
99 -8 0.427461
99 -7 0.438911
99 -6 0.460093
99 -5 0.484881
99 -4 0.518499
99 -3 0.576187
99 -2 0.647596
99 -1 0.77949
99 0 1.000179
99 1 1.313819
98 -97 0.221457
98 -96 0.222976
98 -95 0.224495
98 -94 0.226014
98 -93 0.227534
98 -92 0.229054
98 -91 0.230574
98 -90 0.232095
98 -89 0.233616
98 -88 0.23514
98 -87 0.236665
98 -86 0.238195
98 -85 0.239733
98 -84 0.241272
98 -83 0.242817
98 -82 0.244375
98 -81 0.245941
98 -80 0.247546
98 -79 0.249221
98 -78 0.250962
98 -77 0.253021
98 -76 0.255455
98 -75 0.257889
98 -74 0.260324
98 -73 0.262759
98 -72 0.265194
98 -71 0.26763
98 -70 0.270068
98 -69 0.27251
98 -68 0.274978
98 -67 0.277528
98 -66 0.280137
98 -65 0.282788
98 -64 0.285468
98 -63 0.288168
98 -62 0.290876
98 -61 0.293589
98 -60 0.296303
98 -59 0.299028
98 -58 0.301767
98 -57 0.304521
98 -56 0.307288
98 -55 0.31007
98 -54 0.312858
98 -53 0.315658
98 -52 0.318491
98 -51 0.321347
98 -50 0.324296
98 -49 0.327435
98 -48 0.330804
98 -47 0.335061
98 -46 0.340466
98 -45 0.346148
98 -44 0.352053
98 -43 0.358228
98 -42 0.364792
98 -41 0.371629
98 -40 0.378628
98 -39 0.385687
98 -38 0.392766
98 -37 0.399861
98 -36 0.407027
98 -35 0.414242
98 -34 0.421476
98 -33 0.428735
98 -32 0.436072
98 -31 0.443528
98 -30 0.451144
98 -29 0.458987
98 -28 0.46705
98 -27 0.475252
98 -26 0.483511
98 -25 0.491778
98 -24 0.500049
98 -23 0.508325
98 -22 0.516609
98 -21 0.524898
98 -20 0.533193
98 -19 0.541493
98 -18 0.5498
98 -17 0.558122
98 -16 0.566451
98 -15 0.574827
98 -14 0.583317
98 -13 0.591848
98 -12 0.600507
98 -11 0.609535
98 -10 0.618773
98 -9 0.629267
98 -8 0.642048
98 -7 0.657248
98 -6 0.681738
98 -5 0.720073
98 -4 0.766457
98 -3 0.837629
98 -2 0.94084
98 -1 1.083378
98 0 1.319618
98 1 1.659181
98 2 2.165967
97 -96 0.296743
97 -95 0.298771
97 -94 0.300799
97 -93 0.302828
97 -92 0.304858
97 -91 0.306888
97 -90 0.308918
97 -89 0.310951
97 -88 0.312986
97 -87 0.315026
97 -86 0.317068
97 -85 0.31912
97 -84 0.321185
97 -83 0.323256
97 -82 0.325344
97 -81 0.327459
97 -80 0.329604
97 -79 0.331839
97 -78 0.334188
97 -77 0.336706
97 -76 0.339634
97 -75 0.34288
97 -74 0.346126
97 -73 0.349373
97 -72 0.352622
97 -71 0.355871
97 -70 0.359123
97 -69 0.362381
97 -68 0.365666
97 -67 0.36904
97 -66 0.372488
97 -65 0.376002
97 -64 0.379564
97 -63 0.383152
97 -62 0.386759
97 -61 0.390374
97 -60 0.393994
97 -59 0.39763
97 -58 0.401282
97 -57 0.404951
97 -56 0.408637
97 -55 0.412348
97 -54 0.416087
97 -53 0.419844
97 -52 0.423644
97 -51 0.427514
97 -50 0.431469
97 -49 0.435681
97 -48 0.440272
97 -47 0.445402
97 -46 0.451785
97 -45 0.459247
97 -44 0.467148
97 -43 0.475351
97 -42 0.484037
97 -41 0.493056
97 -40 0.502296
97 -39 0.511664
97 -38 0.521089
97 -37 0.530537
97 -36 0.540056
97 -35 0.549644
97 -34 0.559277
97 -33 0.568965
97 -32 0.578779
97 -31 0.588731
97 -30 0.598898
97 -29 0.609312
97 -28 0.619988
97 -27 0.630851
97 -26 0.641815
97 -25 0.652819
97 -24 0.663832
97 -23 0.674851
97 -22 0.685879
97 -21 0.696914
97 -20 0.707959
97 -19 0.719015
97 -18 0.730079
97 -17 0.741166
97 -16 0.752294
97 -15 0.76346
97 -14 0.774772
97 -13 0.786303
97 -12 0.797985
97 -11 0.810183
97 -10 0.823157
97 -9 0.837178
97 -8 0.854282
97 -7 0.875599
97 -6 0.903444
97 -5 0.947605
97 -4 1.008765
97 -3 1.090152
97 -2 1.209582
97 -1 1.373093
97 0 1.604775
97 1 1.948881
97 2 2.4159
97 3 3.082263
96 -95 0.372789
96 -94 0.375327
96 -93 0.377866
96 -92 0.380407
96 -91 0.382948
96 -90 0.38549
96 -89 0.388037
96 -88 0.390586
96 -87 0.393139
96 -86 0.395699
96 -85 0.398267
96 -84 0.400853
96 -83 0.403457
96 -82 0.406078
96 -81 0.408736
96 -80 0.411441
96 -79 0.414219
96 -78 0.417141
96 -77 0.420236
96 -76 0.423604
96 -75 0.427411
96 -74 0.43147
96 -73 0.43553
96 -72 0.439592
96 -71 0.443655
96 -70 0.447722
96 -69 0.451797
96 -68 0.455899
96 -67 0.460096
96 -66 0.464375
96 -65 0.468736
96 -64 0.473168
96 -63 0.477642
96 -62 0.482141
96 -61 0.486655
96 -60 0.491185
96 -59 0.495731
96 -58 0.500296
96 -57 0.504882
96 -56 0.50949
96 -55 0.514125
96 -54 0.518804
96 -53 0.523531
96 -52 0.528304
96 -51 0.533175
96 -50 0.538199
96 -49 0.543456
96 -48 0.549164
96 -47 0.555453
96 -46 0.562661
96 -45 0.57134
96 -44 0.581126
96 -43 0.591387
96 -42 0.602142
96 -41 0.613311
96 -40 0.624759
96 -39 0.636393
96 -38 0.648137
96 -37 0.65993
96 -36 0.671795
96 -35 0.683745
96 -34 0.69577
96 -33 0.707913
96 -32 0.720194
96 -31 0.732666
96 -30 0.745355
96 -29 0.758335
96 -28 0.771601
96 -27 0.785095
96 -26 0.798734
96 -25 0.81245
96 -24 0.826195
96 -23 0.839949
96 -22 0.853712
96 -21 0.867488
96 -20 0.881276
96 -19 0.895079
96 -18 0.908902
96 -17 0.922751
96 -16 0.936663
96 -15 0.950663
96 -14 0.964796
96 -13 0.979255
96 -12 0.994099
96 -11 1.009455
96 -10 1.02597
96 -9 1.044058
96 -8 1.064912
96 -7 1.091358
96 -6 1.125224
96 -5 1.172561
96 -4 1.24242
96 -3 1.336578
96 -2 1.464104
96 -1 1.641379
96 0 1.878853
96 1 2.208106
96 2 2.659747
96 3 3.250049
96 4 4.035453
95 -94 0.449599
95 -93 0.45265
95 -92 0.455702
95 -91 0.458756
95 -90 0.461813
95 -89 0.464874
95 -88 0.467939
95 -87 0.471009
95 -86 0.474087
95 -85 0.477176
95 -84 0.480281
95 -83 0.483413
95 -82 0.486576
95 -81 0.489774
95 -80 0.493034
95 -79 0.496373
95 -78 0.49984
95 -77 0.503509
95 -76 0.507416
95 -75 0.511675
95 -74 0.516358
95 -73 0.521231
95 -72 0.526107
95 -71 0.530984
95 -70 0.535867
95 -69 0.540759
95 -68 0.545678
95 -67 0.550696
95 -66 0.555804
95 -65 0.561004
95 -64 0.566292
95 -63 0.571642
95 -62 0.57703
95 -61 0.582441
95 -60 0.587878
95 -59 0.593336
95 -58 0.598813
95 -57 0.604315
95 -56 0.609847
95 -55 0.615412
95 -54 0.621023
95 -53 0.626707
95 -52 0.632479
95 -51 0.638365
95 -50 0.644439
95 -49 0.650774
95 -48 0.657535
95 -47 0.664974
95 -46 0.673245
95 -45 0.682865
95 -44 0.694066
95 -43 0.706317
95 -42 0.719145
95 -41 0.732418
95 -40 0.746044
95 -39 0.75991
95 -38 0.773937
95 -37 0.788056
95 -36 0.802262
95 -35 0.81657
95 -34 0.831009
95 -33 0.845592
95 -32 0.860358
95 -31 0.875329
95 -30 0.890543
95 -29 0.906067
95 -28 0.92191
95 -27 0.938012
95 -26 0.954298
95 -25 0.970697
95 -24 0.987154
95 -23 1.003634
95 -22 1.020126
95 -21 1.036633
95 -20 1.053158
95 -19 1.069703
95 -18 1.086279
95 -17 1.102897
95 -16 1.119584
95 -15 1.136408
95 -14 1.15342
95 -13 1.170763
95 -12 1.188702
95 -11 1.207375
95 -10 1.227256
95 -9 1.249292
95 -8 1.274352
95 -7 1.304898
95 -6 1.344513
95 -5 1.396923
95 -4 1.4708
95 -3 1.57438
95 -2 1.710918
95 -1 1.89368
95 0 2.137809
95 1 2.458608
95 2 2.886667
95 3 3.442014
95 4 4.141065
95 5 5.009432
94 -94 0.523617
94 -93 0.527179
94 -92 0.530745
94 -91 0.534313
94 -90 0.537885
94 -89 0.541462
94 -88 0.545045
94 -87 0.548634
94 -86 0.552231
94 -85 0.555843
94 -84 0.559472
94 -83 0.563129
94 -82 0.566828
94 -81 0.570573
94 -80 0.57438
94 -79 0.578281
94 -78 0.582305
94 -77 0.586518
94 -76 0.590987
94 -75 0.595757
94 -74 0.600925
94 -73 0.606475
94 -72 0.612165
94 -71 0.617859
94 -70 0.623557
94 -69 0.629267
94 -68 0.635002
94 -67 0.640841
94 -66 0.646776
94 -65 0.65281
94 -64 0.658945
94 -63 0.665158
94 -62 0.671428
94 -61 0.677734
94 -60 0.684075
94 -59 0.690442
94 -58 0.696835
94 -57 0.703254
94 -56 0.709708
94 -55 0.716208
94 -54 0.722764
94 -53 0.729406
94 -52 0.73617
94 -51 0.743078
94 -50 0.750191
94 -49 0.75761
94 -48 0.765455
94 -47 0.773959
94 -46 0.783379
94 -45 0.794052
94 -44 0.806292
94 -43 0.820186
94 -42 0.835041
94 -41 0.850406
94 -40 0.866169
94 -39 0.882237
94 -38 0.898516
94 -37 0.914934
94 -36 0.931468
94 -35 0.94815
94 -34 0.965009
94 -33 0.982032
94 -32 0.999275
94 -31 1.016739
94 -30 1.034467
94 -29 1.052528
94 -28 1.070928
94 -27 1.08962
94 -26 1.10853
94 -25 1.127588
94 -24 1.146734
94 -23 1.165925
94 -22 1.185138
94 -21 1.204368
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