21+3 Blackjack Side Bet: Every Pay Table, the Odds and House Edge

The wager sits in its own betting spot next to the main bet and is placed before the cards are dealt. Once the player's two cards and the dealer's upcard are face up, they are read as one three-card poker hand. Nothing else counts. The dealer's hole card, the cards drawn later and the result of the main hand play no part in it.

Four hands pay on the base table. A flush is three cards of one suit. A straight is three consecutive ranks in any suits. Three of a kind is three cards of one rank. A straight flush is three consecutive ranks of one suit. Only the highest hand pays, so a straight flush is paid as a straight flush and not also as a flush.

Ace placement is the rule that trips up most readers. The ace is low in A-2-3 and high in Q-K-A, but it does not wrap around, so K-A-2 is not a straight. Because the bet reads the dealer's upcard, the dealer's card is shared with every player at the table, and two players at one table can win or lose together on the same dealer card.

Two extra hands appear on some tables. A suited three of a kind, three identical cards of one suit, needs at least two decks to exist and appears on the Nevada live-dealer table. A mini-royal is a suited A-K-Q and appears on the three Pennsylvania mini-royal tables. Where a table does not list one of these, the hand pays as the next qualifying hand down.

Seven pay tables are documented, and the pay table posted at your table is the one that applies. They fall into three families.

The graded tables pay a different multiple for each hand. The base table, printed in Pennsylvania 58 Pa. Code 633a.13(k), Massachusetts Table B and a Washington State submission, pays 30 to 1 for a straight flush, 20 to 1 for three of a kind, 10 to 1 for a straight and 5 to 1 for a flush. A richer Washington table pays 40 to 1 and 30 to 1 on the two top hands and keeps the straight and flush pays of the base table.

The flat table, printed as Massachusetts Table A and in a Washington submission, pays 9 to 1 on every qualifying hand. It has no graded list, and it is documented from two decks upward.

The mini-royal tables come from Pennsylvania 58 Pa. Code 633b.29. The first pays 100 to 1 for a mini-royal, 35 to 1 for a straight flush and 33 to 1 for three of a kind. The second keeps the base table's 30 to 1 and 20 to 1 and adds 100 to 1 for the mini-royal. The third pays only 50 to 1 for it. The Nevada live-dealer table adds 100 to 1 for a suited three of a kind at eight decks.

Every pay list is shown in the explorer below, and none of the tables has been left out for lack of a figure.

The house edge of a side bet is the average loss as a share of the side bet itself, not of the main bet. It is one minus the average return, where each paying hand returns the stake plus its pay. On 21+3 the result depends on the pay list far more than on anything else.

At six decks the base table costs 13.39% (House edge, 21+3, pay table 30 / 20 / 10 / 5, 6 decks. Exact count over a fresh, randomly shuffled shoe.). The flat table pays 9 to 1 on everything and costs 3.24% (House edge, 21+3, pay table 9 / 9 / 9 / 9, 6 decks. Exact count over a fresh, randomly shuffled shoe.), less than a quarter of that, even though its top pay is far smaller than the base table's. The reason is arithmetic. A straight flush is a very rare hand and a flush is a common one, so a flat pay that lifts the flush from 5 to 1 to 9 to 1 gives back far more than the drop on the rare hands takes away. The richer Washington table, with 40 and 30 on its two top hands, costs 6.07% (House edge, 21+3, pay table 40 / 30 / 10 / 5, 6 decks. Exact count over a fresh, randomly shuffled shoe.) at the same six decks.

The mini-royal tables show how much a small change matters. Pennsylvania's first mini-royal table costs 4.41% (House edge, 21+3, pay table 100 / 35 / 33 / 10 / 5, 6 decks. Exact count over a fresh, randomly shuffled shoe.) at six decks and 3.71% (House edge, 21+3, pay table 100 / 35 / 33 / 10 / 5, 8 decks. Exact count over a fresh, randomly shuffled shoe.) at eight, while the second costs 12.18% (House edge, 21+3, pay table 100 / 30 / 20 / 10 / 5, 6 decks. Exact count over a fresh, randomly shuffled shoe.) and 11.69% (House edge, 21+3, pay table 100 / 30 / 20 / 10 / 5, 8 decks. Exact count over a fresh, randomly shuffled shoe.). The two differ only in the pays for straight flush and three of a kind. The third costs 13.04% (House edge, 21+3, pay table 50 / 30 / 20 / 10 / 5, 6 decks. Exact count over a fresh, randomly shuffled shoe.) at six decks. The Nevada live-dealer table costs 3.70% (House edge, 21+3, pay table 100 / 40 / 30 / 10 / 5, 8 decks. Exact count over a fresh, randomly shuffled shoe.) at its single documented deck count.

For comparison, the main game under the comparison rules used on this site costs 0.62% (Comparison rules: 6 decks, dealer hits soft 17, double after split, blackjack pays 3:2. House edge per starting bet: the average loss per round as a share of the bet placed before the cards are dealt, doubles and splits included in the result. Rules: 6 decks, dealer hits soft 17, dealer checks for blackjack with a hole card, blackjack pays 3:2, double on any first two cards, double after split, split up to 4 hands, aces are not resplit, one card to each split ace, no surrender. The player follows the printed strategy chart for these rules from a full shoe, and never takes insurance or even money.). Even the cheapest 21+3 table, 2.74% (House edge, lowest of the published versions of 21+3, every documented pay table: 9 / 9 / 9 / 9, 8 decks. Exact count over a fresh shoe.), costs several times that. The table below sets every pay table next to the others.

Every figure is an exact count. Each possible set of three cards from a fresh, randomly shuffled shoe is counted without replacement, so nothing is estimated. On the base table at six decks the four paying hands are distributed like this:

• Flush: 5.84% (Chance of 21+3, pay table 30 / 20 / 10 / 5, 6 decks: Flush. Exact count over a fresh, randomly shuffled shoe.), or 1 in 17.
• Straight: 3.10% (Chance of 21+3, pay table 30 / 20 / 10 / 5, 6 decks: Straight. Exact count over a fresh, randomly shuffled shoe.), or 1 in 32.
• Three of a kind: 0.52% (Chance of 21+3, pay table 30 / 20 / 10 / 5, 6 decks: Three of a kind. Exact count over a fresh, randomly shuffled shoe.), or 1 in 191.
• Straight flush: 0.21% (Chance of 21+3, pay table 30 / 20 / 10 / 5, 6 decks: Straight flush. Exact count over a fresh, randomly shuffled shoe.), or 1 in 484.

Taken together the bet pays on 9.68% (Chance of a win, 21+3, pay table 30 / 20 / 10 / 5, 6 decks. Exact count over a fresh, randomly shuffled shoe.) of rounds. The other rounds lose the stake, and the explorer lists that share as the no-win row for every table and deck count. Counted exactly, the straight flush is 62,208 of 30,079,920 three-card combinations at six decks, which is why it sits at the top of the pay list.

A rule of thumb follows from the bars. Well under one round in ten pays anything, and most of the paying rounds are flushes at the smallest multiple. The hands that give the bet its look are far rarer. The mini-royal, the rarest hand on the Pennsylvania tables, comes up in 0.017% (Chance of 21+3, pay table 100 / 35 / 33 / 10 / 5, 6 decks: Mini royal, suited A-K-Q. Exact count over a fresh, randomly shuffled shoe.) of rounds, or 1 in 5,802, at six decks.

More decks lower the house edge of every table that is documented at several deck counts, and the change is large. The base table costs 22.73% (House edge, 21+3, pay table 30 / 20 / 10 / 5, 1 deck. Exact count over a fresh, randomly shuffled shoe.) at one deck, 17.27% (House edge, 21+3, pay table 30 / 20 / 10 / 5, 2 decks. Exact count over a fresh, randomly shuffled shoe.) at two, 13.39% (House edge, 21+3, pay table 30 / 20 / 10 / 5, 6 decks. Exact count over a fresh, randomly shuffled shoe.) at six and 12.89% (House edge, 21+3, pay table 30 / 20 / 10 / 5, 8 decks. Exact count over a fresh, randomly shuffled shoe.) at eight. The flat table falls from 7.26% (House edge, 21+3, pay table 9 / 9 / 9 / 9, 2 decks. Exact count over a fresh, randomly shuffled shoe.) at two decks to 2.74% (House edge, 21+3, pay table 9 / 9 / 9 / 9, 8 decks. Exact count over a fresh, randomly shuffled shoe.) at eight.

The cause is the shape of the hands. Three of a kind needs three cards of one rank. With one deck there are only four of each rank, and the first two cards use up two of them, so the chance of a match on the dealer's card is low: 0.24% (Chance of 21+3, pay table 30 / 20 / 10 / 5, 1 deck: Three of a kind. Exact count over a fresh, randomly shuffled shoe.) on the base table, against 0.54% (Chance of 21+3, pay table 30 / 20 / 10 / 5, 8 decks: Three of a kind. Exact count over a fresh, randomly shuffled shoe.) at eight decks. A flush behaves the same way, at 4.96% (Chance of 21+3, pay table 30 / 20 / 10 / 5, 1 deck: Flush. Exact count over a fresh, randomly shuffled shoe.) at one deck and 5.88% (Chance of 21+3, pay table 30 / 20 / 10 / 5, 8 decks: Flush. Exact count over a fresh, randomly shuffled shoe.) at eight. A straight moves the other way, from 3.26% (Chance of 21+3, pay table 30 / 20 / 10 / 5, 1 deck: Straight. Exact count over a fresh, randomly shuffled shoe.) to 3.09% (Chance of 21+3, pay table 30 / 20 / 10 / 5, 8 decks: Straight. Exact count over a fresh, randomly shuffled shoe.), because in a bigger shoe repeated ranks make an ordered run less likely. Three of a kind pays 20 to 1 and the flush pays 5 to 1, and both grow, so the return climbs and the edge shrinks.

Deck count is therefore worth reading off the table before the pay list is compared. A generous list on a single deck can cost more than a modest list on eight decks. The deck-by-deck matrix above is the quickest way to see it. Every figure is for a fresh shoe. This page has no figure for a shoe that has been partly dealt.

No. The bet is decided by the first two cards and the dealer upcard, all of which are on the table before you make a decision. Hitting, standing, doubling, splitting or surrendering cannot change a hand that is already settled. The strategy that fits the rules of the game is the same whether or not you staked on the side, and the side bet has no documented effect on it.

Three points about how the two wagers relate are worth knowing. The side bet pays or loses on its own, so a winning main hand does not rescue a losing side bet, and the reverse. It is settled on the three visible cards, so the dealer's hole card plays no part. And it is placed with its own stake, so its house edge is a cost on that stake and not a change to the main game's edge, which stays at 0.62% (Comparison rules: 6 decks, dealer hits soft 17, double after split, blackjack pays 3:2. House edge per starting bet: the average loss per round as a share of the bet placed before the cards are dealt, doubles and splits included in the result. Rules: 6 decks, dealer hits soft 17, dealer checks for blackjack with a hole card, blackjack pays 3:2, double on any first two cards, double after split, split up to 4 hands, aces are not resplit, one card to each split ace, no surrender. The player follows the printed strategy chart for these rules from a full shoe, and never takes insurance or even money.) under the comparison rules.

Nothing here is advice to place the bet. Each table costs more than the main game, and the figures show the price, not a way to win. Everything on the site is for information and play money only.