Lucky Ladies

1The bet

Your first two cards, paid if they total twenty, paid more the more alike they are.

You post the side bet before the deal and it pays on your own first two cards. A queen and a king is a twenty. So is ace-nine, because the ace plays as eleven, and that one is checkable: Wizard's published count of 1,008 suited twenties in a six-deck shoe only works if the 144 suited ace-nines are in it. Two ten-value cards of unequal rank account for the other 864.

The rungs stack by how the twenty is made. Same rank and same suit pays more than same suit alone, which pays more than any old twenty. Two queens of hearts sits at the top, and above even that there is a rung paid when the dealer turns up a blackjack alongside it. That last rung reaches past your own two cards to the dealer's, which is why the published return tables count permutations of 312 × 311 × 310 × 309.

This page analyses the 1000/125/19/9/4 ladder, which is the standard six- and eight-deck table and the one the counting literature targets. The 1000/200/25/10/4 ladder, normally a double-deck table and occasionally spread on six, gets the variant section.

2Checking it against the published record

Every published house edge, every row of the six-deck return table, and the published win rate for the published count.

The bet is small enough to enumerate exactly, so there is no excuse for approximate agreement. I count ordered four-card deals over the 52 rank-and-suit types and compare against Wizard's tables directly. Every published house edge came out exact on the first pass, at every deck count listed.

Row-level agreement matters more than a matching total, because a total can be right for two compensating reasons. The six-deck return table reproduces permutation for permutation: 135,360 queen-of-hearts pairs alongside a dealer blackjack, 2,738,340 without, 43,105,500 matched twenties, 193,112,640 suited, 744,863,040 plain, and 8,310,740,400 losers, over 9,294,695,280 deals.

The counting record gets its own check, and that one produced a finding instead of a tick. Jacobson reports the six-deck Ten count betting 2.973% of rounds at a 13.23% edge, worth 0.393 units per 100 rounds. Running the same tags I read 2.817% of rounds at +14.45%, worth 0.4069, at a 0.85 cut. At the 0.75 cut this site uses as standard the same card earns 0.188, which is less than half. His published win rate implies a deep cut, and anyone quoting it at a table with an early cut card is quoting a number for a different game.

His eight-deck remark checks out too. He writes that there is "very little profit to the AP" at eight decks, and the entire eight-deck ceiling, with perfect knowledge of all 52 card counts, is 0.125 units per 100 rounds.

3The ceiling

Composition-exact by enumeration, and the mean does not move with depth at all.

Because the bet reads four cards off the top of the shoe, the exact expected value of any composition is a closed form over the 52 type counts. No simulation is involved in the ceiling. At every point in every shoe I know precisely what the bet is worth, so the perfect-information player comes for free and needs no approximating.

One structural fact governs everything downstream. The undealt cards of a shuffled shoe are a uniformly random subset of the shoe, so the four cards this bet reads are four uniformly random cards of the original shoe, whatever the depth. The average expected value at every depth is therefore exactly the off-the-top house edge. I proved that by enumerating every subset of a twelve-card toy shoe in exact fractions, and the simulation then measured it: a rule that bets purely on depth, with no card information at all, captures exactly 0.00% of the ceiling.

Penetration still matters, and it matters through spread. Deeper into the shoe the composition wanders further from average, so the positive tail gets fatter even though the mean is pinned. Waiting for the end of the shoe is not by itself a strategy, and the size of that effect is what makes Jacobson's cut assumption worth pulling out.

4The curve

Four thousand shoes, every deal position scored against the exact answer.

I dealt 4,000 six-deck shoes and scored every deal position in each one, banking the exact expected value of the bet alongside the value of every candidate count. Eight decks got the same treatment and double deck got 8,000 shoes. Scoring positions is an approximation to scoring round starts, and it is the one place this page samples something slightly different from what a player meets. Positions sample the shoe uniformly and round starts do not, because how many cards a round consumes depends on the cards.

The window is narrow at this pay table and it moves fast with the cut. At a 0.75 cut the Ten count's best fixed trigger is +9, which fires on 2.1% of rounds. At 0.85 the same card wants +9 or +10 and fires on 2.8% to 3.7%, and earns more than twice as much per 100 rounds.

5Fitting the count

The published tags are nearly optimal, and what they leave behind is a side count.

The effect of removing a single card is computable exactly, and on this ladder it collapses to five distinct answers across the whole 52-card deck, because the rules only ever distinguish five kinds of card. Suits are interchangeable apart from hearts, and hearts only matter because the top rungs name the queen of hearts.

Fitting integer tags to that vector gets a betting correlation of 0.9995 against the Ten count's 0.9431, and cashes out as almost nothing: 76.6% capture against 75.0% at a 0.75 cut. The two systems differ in only two places once you put them on the same scale. The Ten count tags the ace 0 where the truth wants +0.26, and tags the nine as a full low card where the truth wants +0.37. Both errors are small and they partly cancel. I went in expecting to beat the published tags by 20% to 60% and the honest answer is 2%.

Higher-order terms are where the gap actually is. The top two rungs pay on a pair of queens of hearts, so their value goes as the number left times one fewer than that, and no linear tag can express a square. A side count of the queen of hearts is the exact statistic for it, and it lifts capture from 76.6% to 87.7% at six decks.

The published reasoning for dropping that side count beyond double deck is that the effect of removing a queen of hearts shrinks as decks are added. That is true: it falls from 5.23% at two decks to 2.37% at six and 1.84% at eight. The conclusion does not follow, because the whole bet's capturable edge falls faster over the same range, from 0.7633 to 0.2520 to 0.1249 units per 100. The side count is a bigger share of a smaller pie, worth 11.8% more money at two decks, 14.6% at six and 22.6% at eight.

The last thing I checked was how much is left after all of that. Tracking exactly four numbers, the tens, aces, nines and queens of hearts, and knowing nothing whatsoever about which other tens or which suits remain, prices 99.5% of the ceiling. Everything the composition-exact oracle knows beyond those four numbers is worth half a percent.

6Playing it out of sample

87.7% of the ceiling at six decks, learned on half the shoes and scored on the other half.

Every trigger on this page is learned on half the shoes and scored on the other half, so no capture number here has seen its own data. The rule learned is always of the form "bet when the count is at or above this threshold", which is the shape of a real card. Learning an arbitrary set of favourable bins would fit the noise instead.

The best carryable system is the fitted tags plus a queen-of-hearts side count, and it holds up across deck counts without retuning. What it does not do is turn a 24.71% house edge into a living, which the ledger step deals with.

7The money

−$4.07 per 100 rounds at a $25 maximum, and it needs $43 before the seat pays for itself.

To bet the side you have to hold a seat, and the seat costs a main wager on every round while the side bet fires on one round in forty. I charge that in full. The main bet is flat table minimum on basic strategy with no count on it, which costs 0.64% of $15 every round, or $9.60 per 100 rounds.

At a $25 side maximum the card returns $5.52 per 100 rounds against that $9.60, so the play is under water. The breakeven maximum is about $43. At $100 it clears $12.50 per 100 rounds, and it needs a $150,700 bankroll to do it, with N0 above 800,000 rounds.

The reason the bankroll is so large sits in the pay table. Splitting the winnings by rung shows the 1000-to-1 top rung carrying 2.8% of the money and 64.9% of the variance, and it comes up about once in 36,000 bets. Put that next to N0 and the shape of the problem is plain: the top rung lands about once per 2.9 million rounds while N0 sits above 800,000, so you would pass the point where your edge outruns the noise three or four times before collecting it once. That money is real in a spreadsheet and is not real in a life.

A deeper cut roughly doubles the take and does not change the verdict, since it is doubling a number that starts below the toll.

8The call

A real edge, correctly described by the people who described it, on a bet that cannot pay for its own chair.

Not beatable would be false. The bet goes positive on 2.6% of rounds at six decks, a carryable card captures 87.7% of that, and someone already sitting at the table with a big enough side maximum makes money on it.

Not worth it is the accurate call. At the maximums this bet is normally posted with, the seat costs more than the side edge returns, and the configuration where it does clear needs a six-figure bankroll and the better part of a million rounds to settle. The same dollar has better places to be, several of them on this site.

What I would keep from the exercise is the queen-of-hearts side count. The published record drops it beyond double deck for a stated reason that is true and does not imply the conclusion, and it is worth 22.6% more money at eight decks than the tags alone.

§The 1000/200/25/10/4 table

A 17.64% house edge instead of 24.71%, three times the ceiling, and still not enough at a small maximum.

This is normally the double-deck ladder and it turns up on six decks too. Every rung above the base pays more, and the house edge drops by seven points, which moves the bet a long way without moving it far enough.

At six decks and a 0.75 cut the ceiling is 0.7694 units per 100 against the standard table's 0.2520, and it is worth betting on 7.1% of rounds instead of 2.6%. The best carryable card captures 85.0%. Seated at a $15 table with a $25 side maximum that is +$6.75 per 100 rounds, so it clears the seat where the standard table does not, on a $54,800 bankroll with N0 around 542,000 rounds.

Double deck is where the published record concentrates, and it is the better game. The ceiling there is 1.3981 units per 100 at a 0.75 cut and 2.2778 at 0.85, and the queen-of-hearts side count is worth carrying at any deck count. It is also the version least likely to be sitting in front of you with a large maximum on it.

§What this verdict depends on

• Six decks with the 1000/125/19/9/4 pay table, or the 1000/200/25/10/4 table in the variant section.
• A $25 side maximum in the scenario, which is a guess at a normal posting. The breakeven figure of $43 is the number that matters, and it is what to check against a real placard.
• A 0.75 cut. The published win rate for this bet implies about 0.85, which roughly doubles it.
• The main bet is flat table minimum on basic strategy with no count on it, so the seat toll is charged at its full 0.64%. Counting the main bet as well would change both the money and the attention budget, and is not priced here.
• Deal positions stand in for round starts. Positions sample the shoe uniformly and round starts do not, because round length depends on the cards.

Last updated 2026-08-10.