Put 10 units on the main blackjack bet and suppose your first two cards are an ace and a king. If the dealer has no natural, a 3:2 table pays 15 units of profit and returns the original 10. At 6:5 the same cards earn 12 units of profit and return the same 10. The difference is 3 units on that hand. The lower ratio cuts the profit from a paid natural by 20%.
| Result on a 10-unit bet | Net profit at 3:2 | Total returned at 3:2 | Net profit at 6:5 | Total returned at 6:5 |
|---|---|---|---|---|
| Paid natural blackjack | +15 | 25 | +12 | 22 |
| Both player and dealer have a natural | 0 | 10 | 0 | 10 |
| Ordinary win paid 1:1 | +10 | 20 | +10 | 20 |
These examples count the main wager only. A natural is an ace plus a ten-value card on the original deal, so a ten drawn onto a split ace is generally treated as a regular 21 under the rules used here. A dealer who reaches 21 with three cards also has a regular 21. Section 1 of the Massachusetts Gaming Commission blackjack rules defines the natural, and section 7 describes payment and the push when both sides have it. Check the rules for a particular game if it offers a bonus or changes the treatment of ties.
Count paid naturals
The tricky part of comparing the ratios is figuring out which rounds change. Ordinary hands that win, lose or push keep the same settlement in this comparison. So does a natural that pushes against a dealer natural. A count of all player naturals includes hands where neither ratio pays a profit, and that overstates the cost of switching to 6:5.
Take a fresh shoe made of D complete 52-card decks. There are N = 52D cards, A = 4D aces and T = 16D ten-value cards. For one specified player seat, the chance of a natural is 2 × A × T / [N × (N − 1)]. The factor of two accounts for the ace coming first or second. Even when the dealer’s cards are interleaved with the player's, a uniformly shuffled shoe gives the same probabilities for those four designated card positions.
Now set aside the player's ace and ten-value card. Conditional on a player natural, the dealer's two cards come from N − 2 cards with A − 1 aces and T − 1 ten-value cards left. The dealer natural probability on this branch is 2 × (A − 1) × (T − 1) / [(N − 2) × (N − 3)]. The player natural and the dealer natural share a shoe. Using a single unconditioned dealer probability for both would miss the two cards already removed.
Multiply the player natural probability by one minus that conditional dealer probability. That gives the chance of a paid natural. For six decks, N = 312, A = 24 and T = 96. The conditional calculation uses 23 aces and 95 tens among 310 cards. On the full deal, the probability of both naturals is 0.2167%, so paid naturals account for 4.5323% of initial bets.
Extra house edge from the payout change alone
The payout difference is 1.50 − 1.20 = 0.30 units per paid natural per unit initially wagered. The player loses that much on the affected branch, so the increase in house edge is 0.30 × P(paid natural). Use probabilities as fractions in the multiplication and convert the result to percentage points. In six decks that adds 1.3597 percentage points to the house edge when all other rules and settlement choices are held fixed.
| Decks in a fresh shoe | Player natural | Both naturals push | Paid player natural | Extra house edge, percentage points |
|---|---|---|---|---|
| 1 | 4.8265% | 0.1773% | 4.6492% | 1.3948 |
| 2 | 4.7797% | 0.2014% | 4.5783% | 1.3735 |
| 4 | 4.7566% | 0.2129% | 4.5437% | 1.3631 |
| 6 | 4.7489% | 0.2167% | 4.5323% | 1.3597 |
| 8 | 4.7451% | 0.2185% | 4.5266% | 1.3580 |
The columns describe a full randomly shuffled shoe and an initial deal to a specified seat. They are calculated probabilities. If you know that certain cards have already been removed, the counts of aces, tens and remaining cards can differ from these values. A reshuffled teaching model also leaves out practical factors such as rounding a payout to the chip denomination. Read the payout and settlement terms if rounding matters to the bet size.
For the six-deck example, moving 1,000 units through original bets under the fresh-shoe assumptions changes the expected result by about 13.6 units. One way to picture the amount is a set of 100 example deals at 10 units each with the full shoe restored before each deal. Actual results over 100 hands can easily move in either direction. The estimate prices the change in the rule over repeated deals and does not predict a player's next session.
A larger payout and a smaller house edge answer different questions
The 20% reduction is relative to the 15 units of profit a winning natural would have earned on a 10-unit bet. The 1.3597 percentage point figure is an average over all initial bets in the six-deck model. Neither number gives the total house edge on its own. To get that, start with the edge under 3:2 for the full ruleset and add the payout penalty only if the 6:5 game really holds everything else fixed.
Two real tables may differ in deck count, whether the dealer draws on soft 17, what can be doubled, how split hands work and whether surrender is offered. They may also have different minimum bets. A percentage point comparison measures cost per initial unit. To compare expected cost per hand at different stakes, multiply each game's own house edge by its own starting bet. A higher minimum cannot be treated as a change in the payout ratio alone.
A few details can change even when the felt looks familiar. The linked Massachusetts rule example treats the two naturals as a push and makes a separate provision for an even-money option on eligible 3:2 games. The table above assumes ordinary settlement of the main wager with no insurance or even-money choice. Other rule variations can change which hands pay or how side wagers settle. Keep those outside the comparison until you have the actual terms.
At a table, read the natural payout and then the rest of the rule card before comparing games. If all other conditions match, 3:2 pays more on every winning natural and the remaining outcomes are worth the same. For the parts of the house edge that come from other rules, see the house edge guide and the analysis of deck count.
