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Last Updated: March 22, 2007

Ace Invaders

Introduction

Ace Invaders is a video poker variation in which the player may play three lines and gravity will pull down any aces if they help the hand immediately below. The game can be found at various casinos in Las Vegas. I know that Treasure Island has the game, which follows pay table D.

Rules

  1. The player shall choose between 1 or 3 lines, and 1 to 5 coins per line.
  2. Only if the player makes a max bet (15 coins) will a royal pay 4000 coins. Otherwise a royal will pay 250 times the bet on the given line, except under pay table A a royal will pay 200 times coins bet with less than max coins bet.
  3. Cards for each line shall be dealt from an independent deck. In other words the game uses three decks, one for each line.
  4. If the player chooses to play one line then the player will get one deal and one chance to discard on that line. No other lines will be active. The game will play like standard video poker.
  5. If the player chooses to play three lines then the player shall first get five cards on the lower line. The player may then keep or discard any set of these cards. Then the top and middle line shall receive five cards each and lower line will receive replacement cards. Any aces from the top line can reproduce themselves and drop to the same position on the middle line, only if the drop will improve the score of the middle line. Then any aces on the middle line (including new ones that just dropped) can reproduce and drop to the same position on the bottom line, only if the drop will improve the score of the bottom line.
  6. The program will check all possible combinations of ways to drop aces and elect the one that results in the greatest win in the hand directly below.
  7. In the event aces can be dropped different ways, resulting in the same pay the hand directly below, then the way with the greater number of aces will take priority. One result of this rule is aces dropping on aces. Another effect of this rule is when both a straight flush or four aces can result from the ace drop, in which case the drop will form four aces.
  8. In the event aces can be dropped different ways, resulting in the same pay the hand directly below, and the number of aces in each drop is equal, then the drop with the left most aces will take priority.

    For example in the following hand it makes a big difference which ace drops from hand 3 to hand 2. Either ace in hand 3 can complete the straight in hand 2. However if the ace of hearts falls it will fall again to hand one, creating four aces. However the ace of spades will fall because it is further to the left, and will not improve the bottom hand because there is already an ace in the first position.

    Hand 3 As 2c Js Ah 5d
    Hand 2 4c 2h 3d 4h 5s
    Hand 1 Ah Ad 3c 2d As

  9. In the very unlikely event an ace drop can create either a staight flush or four aces (both of which pay 50 times the bet on that hand) all four aces will drop.
  10. In addition to aces a royal flush (dealt or created on middle line) will also drop if it pays more than the hand below.

In the picture below you can see the two aces in the middle row dropped to the bottom row, forming three aces with the ace already there.

I'm told that the following pay tables are made available to the casinos.

Pay Tables in Ace Invaders

Hand Pay Table A Pay Table B Pay Table C Pay Table D Pay Table E Pay Table F
Royal Flush 800 800 800 800 800 800
5 Aces 500 500 500 500 500 500
Straight Flush 50 50 50 50 50 50
4 Aces 50 50 50 50 50 50
4 of a kind, 2-K 25 25 25 25 25 25
Full House 10 9 8 8 7 6
Flush 6 6 6 5 5 5
Straight 4 4 4 4 4 4
Three of a Kind 3 3 3 3 3 3
Two pair 2 2 2 2 2 2
Jacks or Better 1 1 1 1 1 1

One Row Analysis

The next table shows the return playing only the bottom line, which would be exactly the same as conventional video poker. Remember, a royal always pays 250 times coins bet if one line is bet, except under pay table A, which pays 200 times coins bet.

Pay Tables in Ace Invaders

Pay Table Return
A 99.92%
B 98.86%
C 97.71%
D 96.55%
E 95.4%
F 94.25%

Three Row Analysis

The next table is the return table under pay table C for the top hand when playing three hands.

Return Table for Middle Row in Three-Hand Game - Pay Table C

Hand Pays Combinations Probability Return
Royal Flush 800 4 0.000002 0.001231
5 Aces 500 0 0 0
Straight Flush 50 36 0.000014 0.000693
4 Aces 50 48 0.000018 0.000923
4 of a kind, 2-K 25 576 0.000222 0.005541
Full House 8 3744 0.001441 0.011525
Flush 6 5108 0.001965 0.011792
Straight 4 10200 0.003925 0.015699
Three of a Kind 3 54912 0.021128 0.063385
Two pair 2 123552 0.047539 0.095078
Jacks or Better 1 337920 0.130021 0.130021
Nothing 0 2062860 0.793725 0
Total 2598960 1 0.335888

The next table is the return table under pay table C for the middle hand when playing three hands.

Return Table for Middle Row in Three-Hand Game - Pay Table C

Hand Pays Combinations Probability Return
Royal Flush 800 2375049600 0.000003 0.002344
5 Aces 500 14273441280 0.000018 0.008805
Straight Flush 50 12305794176 0.000015 0.000759
4 Aces 50 821359102464 0.001013 0.050667
4 of a kind, 2-K 25 179626401792 0.000222 0.00554
Full House 8 2222693498880 0.002742 0.021938
Flush 6 2257845462144 0.002786 0.016713
Straight 4 3660774165504 0.004516 0.018066
Three of a Kind 3 29267840782080 0.036109 0.108326
Two pair 2 50056043102208 0.061756 0.123511
Jacks or Better 1 157962517189632 0.194883 0.194883
Nothing 0 564093515802240 0.695938 0
Total 810551169792000 1 0.551551

The next table is my original return table under pay table C for the middle hand when playing three hands. The lower right cell shows a total return of 2.072768. Leading Edge Design claims the return for the bottom hand is 2.076026, which I do not disagree with. So please take this table with a grain of salt.

Return Table for Bottom Row in Three-Hand Game - Pay Table C

Hand Pays Probability Return
Royal Flush 800 0.000037 0.029206
5 Aces 500 0.000583 0.291666
Straight Flush 50 0.000087 0.004359
4 Aces 50 0.011357 0.567849
4K, 2-K 25 0.001852 0.046304
Full House 8 0.017574 0.140588
Flush 6 0.011322 0.067929
Straight 4 0.008275 0.0331
3K 3 0.122033 0.3661
2 Pairs 2 0.136359 0.272717
Jacks+ 1 0.25295 0.25295
junk 0 0.437572 0
Total 1 2.072768

The next table summarizes the return for all three rows, the value of the royal drop, as well as the overall return, which is the sum of the four columns, divided by 3.

Return for Three-Hand Game

Pay Table Top Row Middle Row Bottom Row Royal Drop Combined
A 0.338769 0.557036 2.111374 0.001602 1.002927
B 0.337329 0.554293 2.093612 0.001602 0.995612
C 0.335888 0.551551 2.076026 0.001602 0.988356
D 0.333923 0.548766 2.065789 0.001602 0.98336
E 0.332482 0.546023 2.048189 0.001602 0.976099
F 0.331042 0.543281 2.030664 0.001602 0.968863

Strategy

The following table shows the strategy in a three-hand game based on pay table C. To use the strategy look up all viable ways to play the bottom hand and choose the one highest on the list. The expected value is that for the bottom hand only. The player can not control the outcome of the top two hands. This strategy should only be 0.01% less than optimal.

Return for Three-Hand Game

Index Hold Hand Expected Value
1 5 Royal Flush 800
2 5 AAAA 97.608
3 5 Straight Flush 52.222
4 5 Four of a Kind plus ace singleton 25.306
5 4 Four of a Kind 25.056
6 3 Three aces 23.934
7 4 4 to a Royal Flush 23.730
8 5 Full House 9.550
9 2 Two aces 7.302
10 5 Flush 6.212
11 4 Three 2-K, plus ace kicker 4.896
12 3 Three 2-K, no ace kicker 4.526
13 5 Straight 4.144
14 4 4 to a Straight Flush 3.162
15 3 3 to a Royal Flush 2.752
16 5 Two pair plus ace singleton 2.724
17 3 Pair J-K, plus ace kicker 2.696
18 4 Two pair 2.654
19 5 4 to a Flush plus unsuited ace 2.434
20 1 Ace 2.414
21 2 Pair J-K, no ace kicker 1.894
22 4 4 to a Flush 1.584
23 4 10, J, Q, K 1.438
24 2 low pair 1.314
25 4 2, 3, 4, 5 1.298
26 3 suited 9, 10, J 1.142
27 3 suited 9, J, Q 1.138
28 2 suited JQ, JK, or QK 1.114
29 4 9, 10, J, Q 1.076
30 0 discard all 1.056

Play for Free

The game makers, Leading Edge Design, has a very well done demo on its web site. No registration required, just start playing.

Methodology

I was hired to analyze this game in 2002. The analysis was so complicated I don't care to try to explain it here. My original return was about 0.1% lower than that claimed by Leading Edge Design, disagreeing only over the bottom hand. I tend to trust the LED numbers over mine in this case, so I inflated my bottom row returns to match those by LED.

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Written by: Michael Shackleford

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