In Jacks or Better, two pair pays 2 for 1. In Double Bonus Poker it pays 1 for 1, the same as a single pair of jacks, queens, kings or aces. A hand with two pairs in it looks stronger than a hand with one, and on the paytable it is no longer worth more. This post uses the standard 10/7 Double Bonus table to show what that does to the hold.
The paytable, per coin bet at the five-coin maximum: royal flush 800, straight flush 50, four aces 160, four 2s to 4s 80, four 5s to kings 50, full house 10, flush 7, straight 5, three of a kind 3, two pair 1, jacks or better 1. Played correctly, the full table returns about 100.17%. Expected value (EV) means coins returned per coin bet, from counting every possible draw.
Where the missing coin went
Compare the two tables row by row. Double Bonus raises the full house from 9 to 10, the flush from 6 to 7 and the straight from 4 to 5. It at least doubles the quads: 25 becomes 50, 80 or 160 depending on the rank. Four aces pays 160 against 25, more than six times as much. The royal and the three of a kind are unchanged. Exactly one row goes down, and it is two pair.
That is not an accident. On Jacks or Better with perfect play, two pair finishes about 12.9% of hands, second among paying hands only to a high pair (the frequency table has the full list). A row that busy is the cheapest place to take a coin from, because the cut is felt on roughly one hand in eight, while the quads that pay for it are rare. That is why Double Bonus reads as a high-variance game even though its return is slightly above 100%.
What a dealt two pair is now worth
Take A♠ A♥ 7♦ 7♣ K♠. Two pair is dealt to you in 123,552 of 2,598,960 hands, about 4.75% or one in 21. The obvious play is to hold both pairs and replace the king. That leaves 47 unseen cards, and 4 of them (two aces, two sevens) complete a full house.
- Jacks or Better: (4 × 9 + 43 × 2) / 47 = 122 / 47 = 2.596
- Double Bonus: (4 × 10 + 43 × 1) / 47 = 83 / 47 = 1.766
Same cards, same draw, and the hand has lost about a third of its value. In 43 of the 47 draws you finish with the two pair you already held, which now pays 1; only the 4 full houses add anything. On Double Bonus a made two pair behaves like a pair that has already collected its payout, plus a one-in-twelve shot at 10.
The alternative: keep only the aces
On Jacks or Better there is no contest. Holding just the aces and drawing three is worth 24,980 / 16,215 = 1.541, far behind 2.596, so you keep both pairs. On Double Bonus the sums come out differently. Holding A♠ A♥ alone, you draw three cards from 47, which is 47 × 46 × 45 / 6 = 16,215 possible draws. I counted every one:
| Final hand | Pays | Draws | Coins returned |
|---|---|---|---|
| Four aces | 160 | 45 | 7,200 |
| Full house | 10 | 169 | 1,690 |
| Three of a kind | 3 | 1,852 | 5,556 |
| Pair of aces or two pair | 1 | 14,149 | 14,149 |
The coins add to 28,595. Divided by 16,215 draws, that is 1.7635, against 1.7660 for holding both pairs. The holds are 0.0025 coins apart per coin bet, a quarter of a coin over a hundred such hands. Two pair still wins, but the margin is a rounding error compared with the 1.055 it was worth on Jacks or Better.
The aces hold gets there through the top rows. It finishes as four aces 45 times in 16,215 draws (0.28%), and that single row supplies 7,200 of the 28,595 coins, about a quarter. Otherwise, in 87.3% of draws, it finishes with a pair of aces (11,520 draws) or picks up a second pair (2,629), and both pay 1, exactly what the two pair pays.
Why the gap closes
The two-pair hold keeps a guaranteed 1 and chases a 10. The aces hold keeps a guaranteed 1 and chases a 160, a 10 and a 3. When two pair paid 2, its guarantee was worth twice the other hold's, and the aces could not catch up. Cut the pay to 1 and both start from the same floor, so only the chase matters.
It also depends on the aces. Change the hand to A♠ A♥ K♦ K♣ 5♠ and holding the kings alone returns 23,645 / 16,215 = 1.458, well behind. The 160 row belongs to aces. With low two pair such as 3-3-4-4-K, holding both pairs still returns 1.766, since the full-house count does not depend on rank, while holding the 4s alone returns only 0.831.
What to take from it
- Count a made two pair on Double Bonus as one coin plus a 4-in-47 chance of a full house paying 10. It is no longer a hand to be proud of.
- With two pair that includes a pair of aces, the choice between both pairs and the aces alone is close to level (1.766 against 1.763). Hold both pairs, but do not expect a visible difference between the two.
- With two pair that does not include aces, keep both pairs. The lone pair loses ground quickly.
- Do not carry the Jacks or Better habit across. The post on holding two pair is right for that table and wrong in size for this one.
Before you play any variant, read the paytable on the screen. A single changed row, here a 2 turned into a 1, can reshape which holds are correct, as the guide to reading a video poker paytable explains.
Video Poker: Jacks or Better includes Double Bonus Poker alongside Jacks or Better, Deuces Wild and Bonus Poker, shows a full paytable on screen for every variant, and has strategy hints that show which cards to hold. It plays offline, is a free practice game with no real money, and the chips have no cash value.