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Ace Buster
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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
- The side bet is based on conventional dealer drawing rules in blackjack, which I assume the reader is familiar with.
- 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.
- Otherwise, if the dealer does not have a blackjack, play then shall continue as in standard blackjack.
- After the players have finished playing their hands, if at least one player is still standing, then any player may bet the Ace Buster.
- If there is at least one player still standing, the dealer shall play out his hand.
- The Ace Buster wager shall win if the dealer busts.
- 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 |
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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 |
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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% |
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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 Advantage |
Maximum Advantage |
|---|---|---|
| 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 Advantage |
Maximum Advantage |
|---|---|---|
| 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.
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