3 to 2 vs. 6 to 5 Blackjack Payouts: The Full Arithmetic

A six-deck shoe holds 312 cards, 24 aces and 96 cards worth 10 points. The chance the first card is an ace and the second a 10 is 24/312 times 96/311. The reverse order is equally likely, so double it: 2 x (24/312) x (96/311) = 0.047489, or 4.7489 percent.

Fewer decks means slightly more naturals, because pulling your ace out of 52 cards raises the concentration of 10s more sharply than pulling it out of 416.

Most write-ups skip this step, and it moves the answer. When you hold a natural and the dealer holds one too, the hand pushes and the payout rule is never exercised, so the correct multiplier is the chance of a natural the dealer does not match. Holding an ace and a 10 from a six-deck shoe leaves 310 cards, 23 aces and 95 tens, so the dealer’s chance is 2 x (23/310) x (95/309) = 0.045620. That gives 0.047489 x (1 – 0.045620) = 0.045323, or 4.5323 percent.

Three to two returns 1.5 units per unit wagered; 6 to 5 returns 1.2. The gap is 0.3 units regardless of stake or deck count. So the cost in percentage points is 0.3 times the paid-natural frequency. For six decks: 0.3 x 0.045323 = 0.013597, or 1.36 percentage points. Run that across every payout you might meet on a felt and you get the full ladder.

All figures are percentage points added to the house edge. Basic strategy does not change when only the payout changes, so these add cleanly to whatever the rest of the rules produce.

Look at the first column. The familiar 1.39 is the single-deck answer, which is no accident: 6 to 5 spread on single-deck tables first, so that number entered circulation and has been repeated ever since for shoe games where the true cost is 1.36. A rougher check gets close too. Ignore the push correction, use 4.8 percent, and 0.048 x 0.3 = 1.44 points, which overstates the cost by about a tenth of a point because it counts naturals that push.

In New Jersey you can read the stacking directly in Chapter 69F, which treats 6 to 5 as a separate variation with its own restrictions.

The citations behind that comparison, in the order they appear in the code:

• N.J.A.C. 13:69F-2.3(e) sets the payout. Wagers pay 1 to 1 “with the exception of standard blackjack which shall be paid at odds of 3 to 2, or at odds of 6 to 5 for the 6 to 5 blackjack variation.”
• 13:69F-2.12(d) makes hitting soft 17 mandatory: the dealer draws “until he or she has a hard total of 17 or a hard or soft total of 18, 19, 20, or 21.” Subsection (b) lets a standard table choose either way. On a 6 to 5 table the choice is gone, in the direction that costs you.
• 13:69F-2.8(c) removes surrender: the option may be offered at the casino’s discretion “except that … on any blackjack table which offers the 6 to 5 blackjack variation … the surrender option shall not be available.”
• 13:69F-2.10(d) permits killing double-after-split: “In the 6 to 5 blackjack variation, a casino licensee may prohibit doubling down after splitting pairs.”
• 13:69F-2.3(e) also strips the optional bonus payouts. Suited 6-7-8 at 2 to 1, three sevens at 3 to 2 and five cards totaling 21 at 2 to 1 are all permitted at a standard table and all expressly unavailable in the 6 to 5 variation.

Stack them, starting from a liberal six-deck game.

That is about six times where you started. So 6 to 5 does not merely cost 1.4 points; it arrives bundled with the rules a casino wants but cannot sell separately. Compare whole rule sets, and read the sign: N.J.A.C. 13:69F-8.3 requires a licensee to post the rules in effect at the table, and to give a half hour of notice, an announcement to seated players and notice to the Division before changing them mid-shift.

The rule appeared in Las Vegas in the early 2000s on single-deck tables, inverting a familiar pitch. Players had spent decades being told fewer decks is better, and single-deck 6 to 5 let a casino advertise exactly that while removing something worth three times as much.

The direction it spread is not in dispute. It moved down the bet-size range, not up: onto low-minimum tables, where the marginal player is least likely to know what a natural should pay and least likely to have an affordable alternative. It stays off high-limit tables, where customers would walk. Recent coverage describes 6 to 5 as standard on the Strip’s low-minimum shoe games and true 3 to 2 single deck as gone from the city. No regulator publishes payout-by-table data, so every prevalence figure in circulation comes from a private hand count.

The clearest evidence that the low-limit pattern is deliberate is that a regulator once codified it. On Aug. 21, 2024 the New Jersey Division of Gaming Enforcement approved a test, requested on behalf of the Casino Association of New Jersey, allowing 6 to 5 on shoe-dealt blackjack. The conditions are the interesting part.

The letter confirms that hand-dealt 6 to 5 was already permitted year-round under N.J.A.C. 13:69E-1.19(b)(2). We could not verify whether the shoe test was extended past Jan. 2, 2025 or what the hold comparison showed, so check the table rather than assuming. That any of this is on the record follows from how the state regulator handles game approvals.

Cutting the payout does not create a new game, so Nevada triggers no approval. What it requires is disclosure. Nevada Gaming Commission Regulation 5.012, “Publication of payoffs,” provides that payoff schedules “applicable to every licensed game or slot machine shall be displayed at all times either on the table or machine or in a conspicuous place immediately adjacent thereto,” must “accurately state actual payoffs,” must not mislead the public, and that failing to pay in strict accordance with a posted schedule “may be deemed an unsuitable method of operation.”

More on the board is on our Nevada Gaming Control Board page, and the state’s wider picture, including that its licensed online product is poker rather than casino games, is on the Nevada page.

This is the variation players consistently underprice, because the intuition that the dealer still busted is exactly backwards. Here is the dealer’s final-total distribution, computed under an infinite-deck approximation with the dealer hitting soft 17 and playing every hand out.

About one dealer bust in four is a bust with exactly 22. A push-22 rule turns every one of those from a win into a tie for each player still holding a live hand. Since a basic-strategy player busts on roughly one hand in six, that is on the order of 6 percentage points of pure conversion, running higher once doubled and split hands carrying more than one unit are counted. Call it 6 to 7 points, four to five times what 6 to 5 costs.

Games built on it have to give a great deal back. New Jersey’s temporary rules for Free Bet Blackjack require the layout to read “Dealer Must Hit Soft 17 and Will Push with a Total of 22,” “Free Splits On All Pairs, Except 10-Value Cards” and “Free Doubles on Hard 9, 10 and 11 (First Two Cards Only),” and the natural still pays 3 to 2. The giveaways are what make the game playable; the net edge lands near 1 percent. When a variant hands you something generous, find what it took.

Those figures come from the Nevada Gaming Control Board’s monthly revenue report. Blackjack is the largest table game by unit count.

Nearly 13 percent, against a house edge that should be under 2 percent even at a bad table. There is no contradiction. That 12.88 percent is win divided by drop, and drop is not the amount wagered; it is cash and markers exchanged for chips at the table. A player who buys in for $200 and plays 70 hands at $10 wagers $700 against a $200 drop, so the same dollar is bet and rebet several times over. Casinos measure against buy-in because that is what they can count; the house edge is measured against handle.

Three things push hold up inside that gap: how long a buy-in is recycled, how much action goes into side bets carrying edges of 2 to 15 percent or worse, and whether the base game pays 3 to 2 or 6 to 5. Side bets and the payout rule work in the same direction and compound. A player making a $10 main bet with a $5 side bet at a 6 to 5 table is paying more per hand on the small wager than on the large one, which is the design. None of it is cheating and none of it is hidden, which is the point the fair play section keeps returning to.