# Ultimate X Keno

## Introduction

Ultimate X Keno plays like ordinary four-card spot keno, except in addition to instant wins the player also wins multipliers for the next game on the same card. For this feature, the player must double his bet. Wins for the present game are based on half the total amount bet.

This is what is called in the industry a "variable state" game, where the expected value in any given game state, before the bet, varies, according to the multipliers earned the previous game. Players of Ultimate X video poker will be immediately familiar with the concept. Unlike in the video poker version, in Ultimate X Keno the player must pay for the feature.

Advantage players love games like this because often recreational player will abandon large multipliers. If the last player play left big enough multipliers on the next game to be played, then that game state can offer a player advantage. See my section below on vulturing multipliers for more on that.

## Rules

1. The player picks 3 to 8 spots on each of four cards. The cards are labeled A, B, C, and D.
2. A quick pick feature is available to randomize the spots chosen.
3. The player will make a bet of 8, 16, 24, or 32 credits. The bet will be evenly divided between the four cards.
4. Half of the amount bet per card will pay for the multiplier feature. Thus all wins will be based on half of the amount bet on that card. The player may not decline the multiplier feature (unlike Ultimate X Video Poker).
5. Base wins for the current game will be based on one of the pay tables below.
6. In addition, the player will win multipliers based on the current game, as shown in the multiplier tables below, to be applied to the subsequent game on the same card.
7. The final win per card on the current game will be the product of the base win and the multiplier earned the previous game.
8. There is a separate multiplier for each card according to the denomination, credits bet, and number of picks.

## Pay and Multiplier Tables

The following pay and multiplier tables are from VideoPoker.com. It would be an easy assumption to make that these are the most liberal ones available.

### VideoPoker.com Pay Table

Catch Pick 3 Pick 4 Pick 5 Pick 6 Pick 7 Pick 8
0 0 0 0 0 0 0
1 1 0 0 0 0 0
2 2 2 1 1 0 0
3 15 5 3 2 1 1
4 0 99 11 4 2 2
5 0 0 458 48 38 10
6 0 0 0 800 375 110
7 0 0 0 0 2000 700
8 0 0 0 0 0 2000

### VideoPoker.com Multiplier Table

Catch Pick 3 Pick 4 Pick 5 Pick 6 Pick 7 Pick 8
0 1 1 1 1 1 1
1 2 1 1 1 1 1
2 5 4 3 2 2 1
3 7 9 5 5 3 2
4   10 11 7 6 8
5     12 12 12 12
6       12 12 12
7         12 12
8           12

The following pay and multiplier tables are from the Suncoast in Las Vegas. Note that the multiplier is the same as at VideoPoker.com, except catching 3 out of 3 earns an 8x multiplier, instead of 7x.

### Suncoast Pay Table

Catch Pick 3 Pick 4 Pick 5 Pick 6 Pick 7 Pick 8
0 0 0 0 0 0 0
1 1 0 0 0 0 0
2 2 2 1 1 0 0
3 12 5 3 2 1 1
4   86 10 4 2 2
5     420 37 35 10
6       800 365 97
7         2000 700
8           2000

### Suncoast Multiplier Table

Catch Pick 3 Pick 4 Pick 5 Pick 6 Pick 7 Pick 8
0 1 1 1 1 1 1
1 2 1 1 1 1 1
2 5 4 3 2 2 1
3 8 9 5 5 3 2
4   10 11 7 6 8
5     12 12 12 12
6       12 12 12
7         12 12
8           12

## Example

On all four cards I bet two credits and picked six numbers each. Remember that half of the total amount bet is a fee to invoke the multiplier feature, so all wins are based on half the amount bet. Thus, all wins are based on one credit per card. The following table is a reminder of the pay and multipliers for picking six at VideoPoker.com.

### Pick Six Pays and Multipliers

Catch Pays Multplier
0 0 1
1 0 1
2 1 2
3 2 5
4 4 7
5 37 12
6 800 12

Following is what happened in all four cards in the game shown above.

• Card A: Current multiplier of 1x. Zero hits for a base win of 0. Total win = 1×0=0.
• Card B: Current multiplier of 1x. Two hits for a base win of 1 and a multiplier on the next card B of 2x. Total win is 1×1 = 1
• Card C: Current multiplier of 1x. One hit for a base win of 0. Total win = 1×0=0.
• Card D: Current multiplier of 2x. Four hits for a base win of 4. The total win on that card is 2×4=8. It also earned a multiplier of 7x on the next card D.

The total win on the game above is 0+1+0+8=9.

Following is what happened in all four cards in the game shown above.

• Card A: Current multiplier of 1x. Three hits for a base win of 2. Total win = 1×2=2. It also earned a multiplier on the next card A of 5x.
• Card B: Current multiplier of 2x. One hit for a win of 0. Total win = 2×0=0.
• Card C: Current multiplier of 1x. One hit for a base win of 0. Total win = 1×0=0.
• Card D: Current multiplier of 7x. Two hits for a base win of 1. The total win on that card is 7×1=7. It also earned a multiplier of 2x on the next game.

The total win on the game above is 2+0+0+7=9.

Following is what happened in all four cards in the game shown above.

• Card A: Current multiplier of 5x. Four hits for a base win of 4. Total win = 5×4=20. It also earned a multiplier on the next card A of 7x.
• Card B: Current multiplier of 1x. One hit for a base win of 0. Total win = 1×0=0.
• Card C: Current multiplier of 1x. Two hits for a base win of 1. Total win = 1×1=1.
• Card D: Current multiplier of 2x. One hit for a base win of 0. The total win on that card is 2×0=0.

The total win on the game above is 20+0+0+1=21.

## Analysis

The following table shows the number of combinations for any possible number of catches by number of picks.

### Combinations

Catch Pick 3 Pick 4 Pick 5 Pick 6 Pick 7 Pick 8
0 34220 487635 5461512 50063860 386206920 2558620845
1 35400 684400 9752700 109230240 1001277200 7724138400
2 11400 336300 6501800 92650650 1037687280 9512133400
3 1140 68400 2017800 39010800 555903900 6226123680
4   4845 290700 8575650 165795900 2362591575
5     15504 930240 27442080 530546880
6       38760 2325600 68605200
7         77520 4651200
8           125970
Total 82160 1581580 24040016 300500200 3176716400 28987537150

The following table shows the probability for any possible number of catches by number of picks.

### Probability

Catch Pick 3 Pick 4 Pick 5 Pick 6 Pick 7 Pick 8
0 0.416504 0.308321 0.227184 0.166602 0.121574 0.088266
1 0.430867 0.432732 0.405686 0.363495 0.315193 0.266464
2 0.138754 0.212635 0.270457 0.308321 0.326654 0.328146
3 0.013875 0.043248 0.083935 0.12982 0.174993 0.214786
4 0 0.003063 0.012092 0.028538 0.052191 0.081504
5 0 0 0.000645 0.003096 0.008639 0.018303
6 0 0 0 0.000129 0.000732 0.002367
7 0 0 0 0 0.000024 0.00016
8 0 0 0 0 0 0.000004
Total 1 1 1 1 1 1

The following table shows the expected return for each combination of picks and catches under the VideoPoker.com pay table.

### Base Win Return

Catch Pick 3 Pick 4 Pick 5 Pick 6 Pick 7 Pick 8
0 0 0 0 0 0 0
1 0.430867 0 0 0 0 0
2 0.277507 0.425271 0.270457 0.308321 0 0
3 0.166504 0.216239 0.251805 0.259639 0.174993 0.214786
4 0 0.263452 0.120923 0.114152 0.104382 0.163007
5 0 0 0.270868 0.114539 0.302348 0.183026
6 0 0 0 0.103188 0.267208 0.229571
7 0 0 0 0 0.048805 0.112319
8 0 0 0 0 0 0.008691
Total 0.874878 0.904962 0.914054 0.899839 0.897736 0.911401

The following table shows the expected multiplier for each combination of picks and catches under the VideoPoker.com multiplier table.

### Average Multiplier

Catch Pick 3 Pick 4 Pick 5 Pick 6 Pick 7 Pick 8
0 0.416504 0.308321 0.227184 0.166602 0.121574 0.088266
1 0.861733 0.432732 0.405686 0.363495 0.315193 0.266464
2 0.693768 0.850542 0.811372 0.616643 0.653308 0.328146
3 0.111003 0.389231 0.419675 0.649098 0.52498 0.429572
4 0 0.030634 0.133016 0.199765 0.313146 0.65203
5 0 0 0.007739 0.037148 0.103662 0.219631
6 0 0 0 0.001548 0.008785 0.028401
7 0 0 0 0 0.000293 0.001925
8 0 0 0 0 0 0.000052
Total 2.083009 2.01146 2.004673 2.034298 2.04094 2.014487

The following table shows the average base game win, average multiplier, and the overall win under the VideoPoker.com pay and multiplier tables. The overall win is the produce of the base win, average multiplier, and 0.5. The reason for multiplying by 0.5 (or dividing by 2), is the player must double his bet to invoke the Ultimate X feature. This fee is non-refundable. All wins are based on half the total bet amount.

### VideoPoker.com Summary

Pick Avg. Base Win Avg. Multiplier Overall Win
3 0.916504 2.069133 0.948185
4 0.944786 2.011460 0.950200
5 0.950654 2.004673 0.952875
6 0.933891 2.034298 0.949906
7 0.930972 2.040940 0.950029
8 0.942168 2.014487 0.948993

## Summary

The following table shows the bottom line return by number of picks for both known sets of pay and multiplier tables.

### Return Table

Pick VideoPoker.com Suncoast
3 94.82% 91.12%
4 95.02% 91.01%
5 95.29% 91.62%
6 94.99% 91.53%
7 95.00% 91.61%
8 94.90% 91.80%

## Vulturing Ultimate X Keno

The expression "vulturing Ultimate X" has been around for years and refers to poaching Ultimate X video poker games with large abandoned multipliers. However, the same thing can be done in Ultimate X Keno.

Each card and each number of picks, from 3 to 8, present a different multiplier. You should cycle through all 4 × 6 = 24, looking for multipliers. Nobody ever said vulturing wasn't time consuming. Choose the number of picks on each card with the most multipliers. Then overlap the numbers you pick as much as possible among the four cards.

Based on the Suncoast rules, which return 91.45% on average, I find that you need at least seven multipliers for the game to have an advantage. Remember to count what looks like no multiplier as a multiplier of 1x. This considers not just the immediate win of the next bet, but earning 7+ multipliers on the next spin, allowing you to vulture yourself. In choosing your numbers on the four cards, overlap as much as possible.

## Screenshots

Click on any image for a larger version.

Base pay table

Multiplier pay table