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Value of First Card in Video Poker

Introduction

Value of First Card in Video Poker

What is the value of an individual card in video poker? In particular, what is the expected value knowing only the first card dealt on the deal? This may sound like useless information, but I had to calculate this for my page on Lucky Suit Poker. As long as I took the trouble, I may as well write about it.

Jacks or Better

The following table shows the expected value in 9-6 Jacks or Better according to the first card dealt on the deal. The table is shown in order of value, from highest to lowest.

9-6 Jacks or Better

First Card Expected Value
J 1.095186
Q 1.088332
K 1.080144
A 1.075569
10 0.979610
5 0.957507
7 0.957184
6 0.957082
8 0.957028
9 0.956661
4 0.951485
3 0.945470
2 0.939450
Average 0.995439

Bonus Poker

The following table shows the expected value in 8-5 Bonus Poker according to the first card dealt on the deal. The table is shown in order of value, from highest to lowest.

8-5 Bonus Poker

First Card Expected Value
A 1.126362
J 1.083033
Q 1.076279
K 1.068192
10 0.967372
4 0.955292
3 0.949298
5 0.944894
7 0.944605
6 0.944603
8 0.944408
9 0.943940
2 0.943300
Average 0.991660

Double Bonus Poker

The following table shows the expected value in 9-6 Jacks or Better according to the first card dealt on the deal. The table is shown in order of value, from highest to lowest.

9-7-5 Double Bonus Poker

First Card Expected Value
A 1.174523
J 1.073177
Q 1.063481
K 1.051950
10 0.963845
4 0.962894
3 0.954401
2 0.945886
9 0.939264
5 0.938820
8 0.938791
7 0.938445
6 0.938364
Average 0.991065

Double Double Bonus

The following table shows the expected value in 9-6 Double Double Bonus according to the first card dealt on the deal. The table is shown in order of value, from highest to lowest.

9-6 Double Double Bonus

First Card Expected Value
A 1.253221
J 1.058212
Q 1.051136
K 1.042708
4 0.974258
3 0.968002
2 0.961723
10 0.945851
5 0.922691
7 0.922436
6 0.922435
9 0.922420
8 0.922409
Average 0.989808

Deuces Wild

The following table shows the expected value in 25-15-10-4-4-3 Deuces Wild according to the first card dealt on the deal. The table is shown in order of value, from highest to lowest.

25-15-10-4-4-3 Deuces Wild

First Card Expected Value
2 2.178409
10 0.937501
J 0.928673
Q 0.919760
K 0.910284
A 0.901941
7 0.889937
8 0.888959
9 0.887757
6 0.881421
5 0.874804
4 0.866349
3 0.858529
Average 0.994179

Bonus Deuces Wild

The following table shows the expected value in 9-4-3-3 Bonus Deuces, according to the first card dealt on the deal. The table is shown in order of value, from highest to lowest.

9-4-3-3 Bonus Deuces

First Card Expected Value
2 2.254830
A 0.968407
10 0.910203
J 0.907065
Q 0.903448
K 0.899170
5 0.881394
4 0.878340
3 0.875306
7 0.863699
8 0.863307
9 0.862591
6 0.860761
Average 0.994502

Summary

The following table summarizes the expected value of each fist card by the games covered above.

Summary

First
Card		 Jacks or
Better		 Bonus
Poker		 Double
Bonus		 Double
Double
Bonus		 Deuces
Wild		 Bonus
Deuces
2 0.939450 0.943300 0.945886 0.961723 2.178409 2.254830
3 0.945470 0.949298 0.954401 0.968002 0.858529 0.875306
4 0.951485 0.955292 0.962894 0.974258 0.866349 0.878340
5 0.957507 0.944894 0.938820 0.922691 0.874804 0.881394
6 0.957082 0.944603 0.938364 0.922435 0.881421 0.860761
7 0.957184 0.944605 0.938445 0.922436 0.889937 0.863699
8 0.957028 0.944408 0.938791 0.922409 0.888959 0.863307
9 0.956661 0.943940 0.939264 0.922420 0.887757 0.862591
10 0.979610 0.967372 0.963845 0.945851 0.937501 0.910203
J 1.095186 1.083033 1.073177 1.058212 0.928673 0.907065
Q 1.088332 1.076279 1.063481 1.051136 0.919760 0.903448
K 1.080144 1.068192 1.051950 1.042708 0.910284 0.899170
A 1.075569 1.126362 1.174523 1.253221 0.901941 0.968407
Average 0.995439 0.991660 0.991065 0.989808 0.994179 0.994502

Written by: Michael Shackleford