Baccarat side bets
The pair bets are the only part of a baccarat layout where the price is hidden. Here is what each one is actually worth, computed from the shoe composition rather than from a rule of thumb.
Short answer
Skip them. In an eight-deck shoe, Player Pair and Banker Pair each hit 7.47% of the time and pay 11 to 1, a house edge of 10.36%. Either Pair hits 14.38% and pays 5 to 1, a house edge of 13.71%. Perfect Pair on either hand hits 3.35% and pays 25 to 1, a house edge of 13.03%. The cheapest of them costs about ten times what the Banker bet costs.
The pair bets, priced
| Side bet (8 decks) | Frequency | Payout | House edge |
|---|---|---|---|
| Player Pair | 7.47% | 11 to 1 | 10.36% |
| Banker Pair | 7.47% | 11 to 1 | 10.36% |
| Perfect Pair, either hand, same rank and suit | 3.35% | 25 to 1 | 13.03% |
| Either Pair | 14.38% | 5 to 1 | 13.71% |
A pair means the first two cards of that hand share a rank. The third card never counts, so these bets are settled before the drawing rules even come into play.
Where the numbers come from
An eight-deck shoe holds 416 cards and 32 of each rank. Once the first card of a hand is dealt, 31 of the remaining 415 cards match its rank, so a named hand pairs 31/415 = 7.4699% of the time. At 11 to 1 the expected value is 12 × 0.074699 - 1 = -0.103614, a house edge of 10.36%. Either Pair is the same idea with the small overlap removed: both hands pair together on 0.56% of deals, so the chance that at least one pairs is 14.38%, and at 5 to 1 that is a 13.71% edge.
Six decks are worse, not better
| Side bet | 8 decks | 6 decks |
|---|---|---|
| Player or Banker Pair at 11 to 1 | 10.36% | 11.25% |
| Either Pair at 5 to 1 | 13.71% | 14.54% |
| Perfect Pair, either hand, at 25 to 1 | 13.03% | 17.07% |
Fewer decks mean fewer matching cards left after the first one is dealt, so pairs get rarer while the payout stays fixed. If you are going to ignore these bets anyway, ignore them harder on a six-deck table.
Other side bets
Layouts also carry Dragon Bonus, Big and Small, Lucky 6, Panda 8 and various house-specific bets, and their pay tables vary between casinos. TODO: these bets are not yet solved by the engine and no figures are published here. Do not fill them in from memory.
Common questions
Is a pair bet ever a good hedge?
No. A hedge that costs 10% of its stake is not protection, it is a second losing bet. Adding a pair bet to a Banker bet raises the average cost of your action rather than lowering your risk.
Does a Perfect Pair pay on top of a normal pair?
That depends on the layout, and this page prices the common version where the Perfect Pair bet is separate and pays 25 to 1 when either hand shows two identical cards, same rank and same suit. Check the felt before assuming.
Why do pair bets look so tempting?
Because 11 to 1 sounds large next to a 7.47% hit rate. Fair odds on 7.47% would be about 12.4 to 1. The gap between fair and posted is the whole product.