3 Card Poker Odds: Ante, Pair Plus & 6 Card Bonus
Every probability and house edge on this page is computed by full enumeration of all 22,100 three-card player hands against all 18,424 unseen dealer hands. Test these numbers in our Free 3 Card Poker Game.
Ante & Play Summary (Q-6-4 Optimal Strategy)
| Metric | Exact Value | Notes |
|---|---|---|
| Ante House Edge | 3.3730% (3.37%) | Expected loss per initial Ante wager under Q-6-4 strategy |
| Element of Risk (Total Action) | 2.0147% (2.01%) | Expected loss divided by average units wagered (1.6742 units/hand) |
| Play (Raise) Frequency | 67.42% (14,900 / 22,100) | All hands Q-6-4 or better raise; 7,200 hands (32.58%) fold |
| Dealer Qualification Rate | 69.59% | Dealer holds Queen-high (Q-3-2) or better |
| Ante Bonus Frequency | 3.71% (820 / 22,100) | Straight (720), Three of a Kind (52), or Straight Flush (48) |
| Exceptions to Q-6-4 Rule | 0 of 22,100 hands | Zero suit-removal exceptions across the entire deck |
Pair Plus House Edge by Pay Table
Cutting the Flush payout by a single unit—from 4 to 1 down to 3 to 1—costs 4.96% of your wager on every hand, raising the Pair Plus house edge from 2.32% to 7.28%.
| Pay Table | Mini Royal | Str. Flush | Trips | Straight | Flush | Pair | House Edge |
|---|---|---|---|---|---|---|---|
| 1-4-6-30-40 | 40 to 1 | 40 to 1 | 30 to 1 | 6 to 1 | 4 to 1 | 1 to 1 | 2.32% (2.3167%) |
| 1-4-6-33-35 | 35 to 1 | 35 to 1 | 33 to 1 | 6 to 1 | 4 to 1 | 1 to 1 | 2.70% (2.6968%) |
| 1-3-6-30-40-100 | 100 to 1 | 40 to 1 | 30 to 1 | 6 to 1 | 3 to 1 | 1 to 1 | 6.19% (6.1900%) |
| 1-3-6-30-40 | 40 to 1 | 40 to 1 | 30 to 1 | 6 to 1 | 3 to 1 | 1 to 1 | 7.28% (7.2760%) |
| 1-3-5-30-40 | 40 to 1 | 40 to 1 | 30 to 1 | 5 to 1 | 3 to 1 | 1 to 1 | 10.53% (10.5339%) |
Borderline Hands Around the Q-6-4 Cutoff
When you fold, your return is exactly −1.0000 unit. Below is the exact expected value of raising across all 18,424 unseen dealer hands on the hands immediately above and below the Q-6-4 boundary (full derivation):
| Player Hand | Suit Pattern | Dealer No-Qual (+1) | Player Wins (+2) | Dealer Wins (−2) | Ties (0) | Play EV | Best Action |
|---|---|---|---|---|---|---|---|
| Q-6-5 | Rainbow (3 suits) | 5,754 | 339 | 12,305 | 26 | -0.9866 | Play |
| Q-6-4 | Rainbow (3 suits) | 5,758 | 305 | 12,335 | 26 | -0.9934 | Play |
| Q-6-4 | Two-suited | 5,758 | 303 | 12,338 | 25 | -0.9939 | Play |
| Q-6-3 | Rainbow (3 suits) | 5,747 | 271 | 12,380 | 26 | -1.0026 | Fold |
| Q-6-3 | Two-suited | 5,747 | 270 | 12,382 | 25 | -1.0029 | Fold |
| Q-6-2 | Rainbow (3 suits) | 5,732 | 237 | 12,429 | 26 | -1.0124 | Fold |
| J-10-8 | Rainbow (highest Jack-high) | 5,277 | 0 | 13,147 | 0 | -1.1407 | Fold |
6 Card Bonus Combinatorics (20,358,520 Hands)
The optional 6 Card Bonus combines your three cards and the dealer's three cards to form the best five-card poker hand out of C(52, 6) = 20,358,520 combinations:
| Best 5-Card Hand (of 6 Cards) | Combinations | Probability | 1000-200-100-20-15-10-7 | 1000-200-50-25-15-10-5 |
|---|---|---|---|---|
| Royal Flush | 188 | 0.0009% | 1,000 to 1 | 1,000 to 1 |
| Straight Flush | 1,656 | 0.0081% | 200 to 1 | 200 to 1 |
| Four of a Kind | 14,664 | 0.0720% | 100 to 1 | 50 to 1 |
| Full House | 165,984 | 0.815% | 20 to 1 | 25 to 1 |
| Flush | 205,792 | 1.011% | 15 to 1 | 15 to 1 |
| Straight | 361,620 | 1.776% | 10 to 1 | 10 to 1 |
| Three of a Kind | 732,160 | 3.596% | 7 to 1 | 5 to 1 |
| House Edge | 20,358,520 six-card deals | 8.56% | 15.28% | |
Frequently asked questions
- What is the house edge on the Ante bet in 3 Card Poker?
- Under optimal Q-6-4 strategy, the house edge on the Ante bet is 3.3730% (3.37%). Because you raise with an equal Play wager on 67.42% of hands, your average bet per round is 1.6742 units and your element of risk per unit wagered is 2.01%.
- What is the house edge on Pair Plus in Three Card Poker?
- On the full-pay 1-4-6-30-40 pay table, Pair Plus has a 2.3167% (2.32%) house edge. On the common 1-3-6-30-40 table where a Flush pays 3:1 instead of 4:1, the house edge more than triples to 7.28%.
- How often do you get a Pair or better in 3 Card Poker?
- Out of C(52, 3) = 22,100 three-card hands, 5,660 hands form a Pair or better (25.61%), while 16,440 hands are High Card (74.39%).
- Are there any hands where suits change the Q-6-4 play or fold rule?
- No. Exhaustive enumeration of all 22,100 player hands against all 18,424 unseen dealer hands confirms 0 exceptions: Q-6-4 rainbow (−0.9934 EV) and Q-6-4 two-suited (−0.9939 EV) both beat folding (−1.0000), while Q-6-3 rainbow (−1.0026 EV) and Q-6-3 two-suited (−1.0029 EV) are both folds.