Buster Blackjack

1The bet

A dealer bust pays more for every extra card, from 1:1 at three cards to 200:1 at eight or more.

You post Buster before the deal. A dealer bust wins according to the number of cards in the completed dealer hand. Every standing hand and dealer blackjack loses. When a Buster wager is alive, the dealer finishes the hand even after the player's blackjack hand has already busted or received a natural.

This page leads with the six-rung ladder Jacobson analysed in California card rooms: 1, 3, 6, 30, 100, and 200 to one for busts with three through eight or more cards. A second table seen in casinos pays 2, 2, 4, 15, 50, and 250, and it turns out to be a different bet to count, so it gets its own section further down. The name on the felt matters, because Bust It and Dealer Bust 21 pay on different events.

2Checking against the published numbers

The fresh-shoe calculation matches every published probability and removal effect. The published counting rows need six more cards of penetration than the article states.

The finite-shoe dealer recursion returns a 4.72357% house edge, 2.724 standard deviation, and 28.576% hit rate. Those reproduce Jacobson's six-deck H17 table. The dealer bust probabilities also match Wizard of Odds through the 13-card tail for both H17 and S17.

The live counting rows did not pass the same gate. The article prints a 260-card cut, and both of its systems trigger at +4: 15.93% of rounds at a 4.64% edge for the first, 13.29% at 5.28% for the second, worth 0.739 and 0.702 units per hundred. At that cut my 20,000-shoe exact audit returns 15.293% at 4.463% and 12.610% at 5.072%, worth 0.6826 ± 0.0325 and 0.6395 ± 0.0298. Exact, quarter-deck, half-deck and whole-deck divisors, every dealer-completion rule and every table size I tried left that gap where it was.

The gap is the cut card. Dealing the same shoes six cards deeper, to 266 of 312, returns 0.7367 ± 0.0325 and 0.6933 ± 0.0301. Eight cards deeper, at 268, the two rows read 15.873% at 4.669% and 13.226% at 5.326%, worth 0.7411 and 0.7044 against the published 0.739 and 0.702. Both land at once, in all three printed columns, and eight cards is about one heads-up round.

The same shift reproduces both counting rows in his King's Bounty article, which prints the same 260-card cut. On that bet his published row is also worth more than perfect knowledge of the remaining cards can earn at 260 cards, so no counting convention could have produced it. His low-vulnerability Buster ladder reproduced at the stated cut all along, at 0.091 ± 0.014 against 0.085 published, which is what a weak trigger deep in the shoe looks like when the extra depth has little left to find. This page prices the cut cards it names.

3The ceiling

Reading all ten remaining rank counts is worth 0.533 units per hundred positions at the standard cut.

At each sampled position I removed the cards already seen and ran the dealer recursion without replacement. A machine that bets every positive composition takes 12.72% of positions at an average edge of 4.19%, worth 0.5325 units per hundred.

One deck deeper, that ceiling rises to 0.7299. Depth alone never tells the player to bet, since the average composition at every position is still a random slice of the original shoe. The value lives in which ranks remain.

4Where the value hides

Three-card bust value points against the longer rungs, but the four- and five-card awards carry most of the return.

I sampled every fourth position through 1,000 six-deck shoes and priced each one exactly, fitting the trigger on half the shoes and scoring it on the other half.

The conflict in the pay table is real. The three-card contribution's removal effects correlate −0.860 with the four- and five-card contribution, and −0.928 with six cards or more. Four- and five-card busts supply 52.6% of the gross return, though, while the long tail supplies another 11.1%. Together they pull the full payoff toward one dominant count direction.

5Fitting a count

Rounding the exact removal effects to one balanced card raises capture from 93.1% to 97.0% at the standard cut.

Jacobson's practical card is −2,−3,−2,0,0,0,+1,+1,+1,+1. Its weighted correlation with the fresh removal effects is 0.9770. Direct integer rounding, with the full shoe forced to sum to zero, gives −2,−4,−2,0,+1,0,+1,+1,+1,+1 and correlation 0.9894.

The fitted card takes 97.0% of the exact ceiling at 0.75 penetration and 97.1% at the one-deck cut. The published card takes 93.1% and 93.6%. The pay table mixes short and long dealer hands, so I checked whether interaction terms would help. A machine reading the full ten-rank composition beats the fitted card by only 3%, which is not enough to pay for a harder card.

6Playing it out of sample

Twenty thousand fresh shoes keep the fitted count positive under actual round starts, player decisions, and dealer completion.

The live engine dealt a basic-strategy player, including splits and doubles, and finished the dealer whenever any Buster wager was active. Every triggered hand was priced after player play by integrating the dealer's future draws exactly, which removes the noise of waiting for a 200:1 result to appear.

At 0.75 penetration, the fitted +5 card bets 9.657% of live rounds at +5.391%, worth 0.5206 ± 0.0276 units per hundred before the main bet. At the one-deck cut it earns 0.7115 ± 0.0289. On paired all-round-completion shoes it beats Jacobson's practical card by 0.0360 ± 0.0160 units per hundred, a 5.60% lift.

7The ledger

A flat $15 blackjack hand leaves +$42.46 per hundred rounds at the standard cut. The 200:1 tail still asks for a $40,100 bankroll.

The scenario charges the main game's −0.64% expectation on a flat $15 bet, or $9.60 per hundred rounds. The $100 Buster wager returns $52.06, leaving $42.46.

The result beats the game at a $15 table, though the top rung keeps the bankroll near $40,100. A one-deck cut raises the income and lowers the bankroll because the count sees more extreme shoes before the shuffle.

8The call

Beatable: one count captures nearly all the composition value, and a $100 side maximum clears the cost of a flat $15 main bet.

The mixed pay table looked like a two-count problem. One balanced card leaves 3% of the ceiling behind and earns 5.60% more than the published practical card on paired live shoes.

The standard-cut scenario makes +$42.46 per hundred rounds on a $40,100 bankroll. It needs a six-deck H17 game with this exact ladder, quarter-deck true-count conversion, a $100 side maximum, and no fee large enough to eat the margin.

§The 2-2-4-15-50-250 table

A second table pays more on three cards and 8+, yet leaves almost no countable window between them.

This observed casino ladder pays 2 / 2 / 4 / 15 / 50 / 250 to one for dealer busts with three through eight or more cards. Six-deck H17 comes to a 5.4230% house edge off the top, a little worse than the primary table's 4.7236%, while standard deviation falls from 2.724 units to 1.991.

The important change is not the extra fifty units at 8+. That event begins at about 0.0012% of fresh shoes. Paying twice as much on the common three-card bust shifts most of the return into the rung whose removal effects oppose the longer hands, while the four-through-seven awards are cut. The opposing signals nearly cancel: at 0.75 penetration the exact positive-composition ceiling collapses from 0.5325 units per hundred positions to 0.0303.

This table needs its own card. The primary page's count captures only 35.0% here. Rounding this table's exact removal effects gives +1,−4,−2,0,+1,−1,+2,+2,+1,0 for ace through ten, balanced over a full deck. Bet at true count +11 or higher. It captures 84.1% of the held-out ceiling at the standard cut, worth 0.0255 units per hundred positions. On a $100 side maximum that is $2.55 before the flat $15 blackjack hand loses $9.60, so the seated result is −$7.05 per hundred. The break-even side limit is about $377 if there is no collection or Buster fee.

One deck deeper the fitted trigger moves to +12 and earns 0.0557 units per hundred positions, still only $5.57 on a $100 maximum before the main-game toll. It counts, and at that limit it does not pay.

§What this verdict depends on

• The primary scenario is six decks, dealer hits soft 17, and the 1/3/6/30/100/200 ladder. The 2/2/4/15/50/250 ladder is a separate analysis in the variant section and does not inherit its count or verdict.
• A $100 Buster maximum with a $15 flat blackjack minimum. The scenario assumes the side wager may exceed the main wager.
• No collection fee and no flat Buster fee. California approvals let each cardroom set both fees, so a posted schedule must be subtracted from the scenario.
• The scenario uses the solo-counter convention: the dealer completes an otherwise finished hand only when this player has Buster out. Another Buster bettor changes later round starts, and the all-round-completion result is shown in the ledger notes.
• Quarter-deck estimation and a raw true-count trigger at +5. Rounding the true count to the nearest integer changes the betting window.
• Bankroll includes flat-main and side-bet variance with their covariance set to zero. It treats rounds as independent, so long shoe sessions can run wider than the planning figure.
• All counts are kept without error. The deuce is tagged −4, which makes this a harder card than a level-one blackjack count.
• The published counting rows reproduce at a cut card six to eight cards deeper than the 260 the article states. This page prices the cut cards it names and uses the exact live audit for its ledger.

Last updated 2026-08-11.