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# Ace Buster

## Introduction

Ace Buster is a blackjack side bet that wins if the dealer busts. The winning odds depend on how many aces are in the dealer's busted hand. This is a unique side bet in that it may be made after the dealer gives the players and himself the initial two-card hands.

The side bet may be found at the Brass Ass in Cripple Creek CO and Saratoga in Blackhawk CO.

## Rules

1. The side bet is based on conventional dealer drawing rules in blackjack, which I assume the reader is familiar with.
2. Play starts as normal, with the dealer giving each player and himself two cards. If the dealer has an ace or 10-point card up, he will peek at the hole card for a blackjack. If the dealer has a blackjack, it will be revealed immediately.
3. Otherwise, if the dealer does not have a blackjack, play then shall continue as in standard blackjack.
4. After the players have finished playing their hands, if at least one player is still standing, then any player may bet the Ace Buster.
5. If there is at least one player still standing, the dealer shall play out his hand.
6. The Ace Buster wager shall win if the dealer busts.
7. Winning Ace Buster bets shall pay according to the number of aces in the dealer's hand and the original up card. See the table below for details.

The following table shows what winning Ace Buster bets pay, according to how many aces are in the dealer's busted hand and the dealer's up card. Wins are on a "to one" basis.

### Ace Buster Pay Table

Event A-6 Up 7-K Up
Bust with 4+ aces 50 100
Bust with 3 aces 10 20
Bust with 2 aces 5 10
Bust with 1 ace 3 6
Bust with 0 aces 1 2

## Six-Deck Analysis

The following ten tables show my analysis of the Ace Buster bet in a six-deck game where the dealer hits a soft 17.

The following table shows my analysis of the Ace Buster bet when the dealer has an ace up. The lower right cell shows a house edge of 3.52%.

### Six Decks — Ace Up

Event Pays Probability Return
Bust with 4+ aces 50 0.000641 0.032072
Bust with 3 aces 10 0.006014 0.060142
Bust with 2 aces 5 0.043723 0.218617
Bust with 1 ace 3 0.150902 0.452705
Bust with 0 aces 1 0.000000 0.000000
No bust -1 0.798719 -0.798719
Total   1.000000 -0.035184

The following table shows my analysis of the Ace Buster bet when the dealer has a 2 up. The lower right cell shows a house edge of 15.10%.

### Six Decks — 2 Up

Event Pays Probability Return
Bust with 4+ aces 50 0.000048 0.002379
Bust with 3 aces 10 0.000518 0.005178
Bust with 2 aces 5 0.005959 0.029794
Bust with 1 ace 3 0.052422 0.157266
Bust with 0 aces 1 0.297714 0.297714
No bust -1 0.643339 -0.643339
Total   1.000000 -0.151007

The following table shows my analysis of the Ace Buster bet when the dealer has a 3 up. The lower right cell shows a house edge of 10.98%.

### Six Decks — 3 Up

Event Pays Probability Return
Bust with 4+ aces 50 0.000024 0.001183
Bust with 3 aces 10 0.000570 0.005701
Bust with 2 aces 5 0.005710 0.028552
Bust with 1 ace 3 0.053593 0.160780
Bust with 0 aces 1 0.317061 0.317061
No bust -1 0.623042 -0.623042
Total   1.000000 -0.109765

The following table shows my analysis of the Ace Buster bet when the dealer has a 4 up. The lower right cell shows a house edge of 6.68%.

### Six Decks — 4 Up

Event Pays Probability Return
Bust with 4+ aces 50 0.000016 0.000801
Bust with 3 aces 10 0.000302 0.003022
Bust with 2 aces 5 0.006324 0.031618
Bust with 1 ace 3 0.053726 0.161179
Bust with 0 aces 1 0.338102 0.338102
No bust -1 0.601530 -0.601530
Total   1.000000 -0.066808

The following table shows my analysis of the Ace Buster bet when the dealer has a 5 up. The lower right cell shows a house edge of 2.42%.

### Six Decks — 5 Up

Event Pays Probability Return
Bust with 4+ aces 50 0.000010 0.000502
Bust with 3 aces 10 0.000204 0.002043
Bust with 2 aces 5 0.003580 0.017900
Bust with 1 ace 3 0.059921 0.179763
Bust with 0 aces 1 0.355916 0.355916
No bust -1 0.580368 -0.580368
Total   1.000000 -0.024245

The following table shows my analysis of the Ace Buster bet when the dealer has a 6 up. The lower right cell shows a house edge of 3.87%.

### Six Decks — 6 Up

Event Pays Probability Return
Bust with 4+ aces 50 0.000006 0.000284
Bust with 3 aces 10 0.000125 0.001254
Bust with 2 aces 5 0.002313 0.011567
Bust with 1 ace 3 0.036058 0.108174
Bust with 0 aces 1 0.400757 0.400757
No bust -1 0.560741 -0.560741
Total   1.000000 -0.038705

The following table shows my analysis of the Ace Buster bet when the dealer has a 7 up. The lower right cell shows a house edge of 12.59%.

### Six Decks — 7 Up

Event Pays Probability Return
Bust with 4+ aces 100 0.000003 0.000294
Bust with 3 aces 20 0.000065 0.001307
Bust with 2 aces 10 0.001215 0.012151
Bust with 1 ace 6 0.019279 0.115677
Bust with 0 aces 2 0.241373 0.482746
No bust -1 0.738064 -0.738064
Total   1.000000 -0.125890

The following table shows my analysis of the Ace Buster bet when the dealer has an 8 up. The lower right cell shows a house edge of 18.60%.

### Six Decks — 8 Up

Event Pays Probability Return
Bust with 4+ aces 100 0.000003 0.000273
Bust with 3 aces 20 0.000061 0.001218
Bust with 2 aces 10 0.001139 0.011387
Bust with 1 ace 6 0.018100 0.108602
Bust with 0 aces 2 0.224390 0.448781
No bust -1 0.756307 -0.756307
Total   1.000000 -0.186047

The following table shows my analysis of the Ace Buster bet when the dealer has a 9 up. The lower right cell shows a house edge of 23.43%.

### Six Decks — 9 Up

Event Pays Probability Return
Bust with 4+ aces 100 0.000003 0.000263
Bust with 3 aces 20 0.000058 0.001156
Bust with 2 aces 10 0.001079 0.010787
Bust with 1 ace 6 0.017006 0.102034
Bust with 0 aces 2 0.211097 0.422194
No bust -1 0.770758 -0.770758
Total   1.000000 -0.234324

The following table shows my analysis of the Ace Buster bet when the dealer has a 10 up. The lower right cell shows a house edge of 24.26%.

### Six Decks — 10 Up

Event Pays Probability Return
Bust with 4+ aces 100 0.000001 0.000147
Bust with 3 aces 20 0.000040 0.000803
Bust with 2 aces 10 0.000851 0.008510
Bust with 1 ace 6 0.014760 0.088560
Bust with 0 aces 2 0.214586 0.429172
No bust -1 0.769761 -0.769761
Total   1.000000 -0.242570

## Eight-Deck Analysis

The following ten tables show my analysis of the Ace Buster bet in a eight-deck game where the dealer hits a soft 17.

The following table shows my analysis of the Ace Buster bet when the dealer has an ace up. The lower right cell shows a house edge of 3.26%.

### Eight Decks — Ace Up

Event Pays Probability Return
Bust with 4+ aces 50 0.000680 0.033999
Bust with 3 aces 10 0.006158 0.061581
Bust with 2 aces 5 0.043940 0.219702
Bust with 1 ace 3 0.150346 0.451039
Bust with 0 aces 1 0.000000 0.000000
No bust -1 0.798875 -0.798875
Total   1.000000 -0.032553

The following table shows my analysis of the Ace Buster bet when the dealer has a 2 up. The lower right cell shows a house edge of 15.09%.

### Eight Decks — 2 Up

Event Pays Probability Return
Bust with 4+ aces 50 0.000050 0.002512
Bust with 3 aces 10 0.000530 0.005299
Bust with 2 aces 5 0.005992 0.029959
Bust with 1 ace 3 0.052283 0.156850
Bust with 0 aces 1 0.297822 0.297822
No bust -1 0.643323 -0.643323
Total   1.000000 -0.150881

The following table shows my analysis of the Ace Buster bet when the dealer has a 3 up. The lower right cell shows a house edge of 11.00%.

### Eight Decks — 3 Up

Event Pays Probability Return
Bust with 4+ aces 50 0.000025 0.001249
Bust with 3 aces 10 0.000583 0.005829
Bust with 2 aces 5 0.005733 0.028664
Bust with 1 ace 3 0.053421 0.160263
Bust with 0 aces 1 0.317129 0.317129
No bust -1 0.623109 -0.623109
Total   1.000000 -0.109975

The following table shows my analysis of the Ace Buster bet when the dealer has a 4 up. The lower right cell shows a house edge of 6.77%.

### Eight Decks — 4 Up

Event Pays Probability Return
Bust with 4+ aces 50 0.000017 0.000845
Bust with 3 aces 10 0.000309 0.003088
Bust with 2 aces 5 0.006347 0.031735
Bust with 1 ace 3 0.053528 0.160584
Bust with 0 aces 1 0.337919 0.337919
No bust -1 0.601881 -0.601881
Total   1.000000 -0.067711

The following table shows my analysis of the Ace Buster bet when the dealer has a 5 up. The lower right cell shows a house edge of 2.56%.

### Eight Decks — 5 Up

Event Pays Probability Return
Bust with 4+ aces 50 0.000011 0.000530
Bust with 3 aces 10 0.000209 0.002089
Bust with 2 aces 5 0.003593 0.017967
Bust with 1 ace 3 0.059698 0.179093
Bust with 0 aces 1 0.355625 0.355625
No bust -1 0.580864 -0.580864
Total   1.000000 -0.025561

The following table shows my analysis of the Ace Buster bet when the dealer has a 6 up. The lower right cell shows a house edge of 3.87%.

### Eight Decks — 6 Up

Event Pays Probability Return
Bust with 4+ aces 50 0.000006 0.000301
Bust with 3 aces 10 0.000129 0.001285
Bust with 2 aces 5 0.002327 0.011633
Bust with 1 ace 3 0.035972 0.107916
Bust with 0 aces 1 0.400880 0.400880
No bust -1 0.560686 -0.560686
Total   1.000000 -0.038670

The following table shows my analysis of the Ace Buster bet when the dealer has a 7 up. The lower right cell shows a house edge of 12.57%.

### Eight Decks — 7 Up

Event Pays Probability Return
Bust with 4+ aces 100 0.000003 0.000310
Bust with 3 aces 20 0.000067 0.001336
Bust with 2 aces 10 0.001222 0.012219
Bust with 1 ace 6 0.019241 0.115446
Bust with 0 aces 2 0.241498 0.482996
No bust -1 0.737969 -0.737969
Total   1.000000 -0.125661

The following table shows my analysis of the Ace Buster bet when the dealer has an 8 up. The lower right cell shows a house edge of 18.55%.

### Eight Decks — 8 Up

Event Pays Probability Return
Bust with 4+ aces 100 0.000003 0.000289
Bust with 3 aces 20 0.000062 0.001245
Bust with 2 aces 10 0.001144 0.011436
Bust with 1 ace 6 0.018033 0.108200
Bust with 0 aces 2 0.224712 0.449424
No bust -1 0.756046 -0.756046
Total   1.000000 -0.185453

The following table shows my analysis of the Ace Buster bet when the dealer has a 9 up. The lower right cell shows a house edge of 23.51%.

### Eight Decks — 9 Up

Event Pays Probability Return
Bust with 4+ aces 100 0.000003 0.000278
Bust with 3 aces 20 0.000059 0.001183
Bust with 2 aces 10 0.001083 0.010832
Bust with 1 ace 6 0.016954 0.101724
Bust with 0 aces 2 0.210938 0.421876
No bust -1 0.770963 -0.770963
Total   1.000000 -0.235070

The following table shows my analysis of the Ace Buster bet when the dealer has a 10 up. The lower right cell shows a house edge of 24.31%.

### Eight Decks — 10 Up

Event Pays Probability Return
Bust with 4+ aces 100 0.000002 0.000155
Bust with 3 aces 20 0.000041 0.000821
Bust with 2 aces 10 0.000855 0.008550
Bust with 1 ace 6 0.014711 0.088265
Bust with 0 aces 2 0.214517 0.429033
No bust -1 0.769875 -0.769875
Total   1.000000 -0.243050

## Summary

The following table shows a summary of the house edge by up card and number of decks. The table shows the lowest house edge is when the dealer has a 5 up.

### Eight Decks — 10 Up

Up Card Six Decks Eight Decks
A 3.52% 3.26%
2 15.10% 15.09%
3 10.98% 11.00%
4 6.68% 6.77%
5 2.42% 2.56%
6 3.87% 3.87%
7 12.59% 12.57%
8 18.60% 18.55%
9 23.43% 23.51%
10 24.26% 24.31%

## Card Counting

The side bet is meant to be played on a game with a continuous shuffler. Nevertheless, if there is a full table, which enables more cards to be observed, and the player uses perfect analysis of the remaining cards in the deck, rarely there is a small player advantage.

The following table shows how often there is a player advantage and the maximum advantage observed by the number of cards seen at the time the Ace Buster bet is offered. The table assumes six decks and the dealer hits a soft 17.

### Six Decks — Dealer Hits Soft 17

Cards
Observed
Ratio with
Maximum
10 0.001517 2.07%
15 0.004963 3.45%
20 0.008748 5.05%

The following table shows the same information, but for eight decks and the dealer hits a soft 17.

### Eights Decks — Dealer Hits Soft 17

Cards
Observed
Ratio with
Maximum
10 0.000104 0.87%
15 0.000986 2.13%
20 0.002644 3.41%

The information about card counting was kindly provided to me by the game owner, as taken from a GLI math report on the game.