Perfect strategy I: the whole picture
Everything on one page, and what 'perfect' can and can't do.
Here's the lowest-edge strategy for the standard Blind paytable. Its rules are the ones the Wizard of Odds publishes as basic strategy, with flop and river rules after James Grosjean:
Preflop. Bet 4x with: 33+, any ace, any suited king, K5o+, Q6s+, Q8o+, J8s+, JTo. Otherwise check. Never bet 3x.
Flop. Bet 2x with two pair or better (using your cards), a hidden pair (not pocket deuces) or four to a flush with a ten or better of that suit in hand. Otherwise check. Perfect play differs in a few rare spots (lesson 10), and the EV sheet always shows the exact answer.
River. Play 1x with a hidden pair or better, or when the dealer has fewer than 21 outs. Otherwise fold. Again, the EV sheet shows the rare exceptions.
What happens over the long run when you play this way:
| Decision | Share of hands |
|---|---|
| Bet 4x preflop | 37.7% |
| Bet 2x on the flop | 21.3% |
| Bet 1x on the river | 21.8% |
| Fold on the river | 19.2% |
On average you'll have 4.15 antes in action per hand, and lose 2.185% of one Ante per hand (the app computes this exactly; it agrees with the Wizard of Odds figure). At a $10 Ante and 30 hands an hour, that's an expected cost of $6.55 an hour.
What perfect means, and what it doesn't. No decision you make can give you an edge over the house. "Perfect" means you lose the least possible: 2.19% of the Ante. It doesn't mean you'll win tonight, and it doesn't make Trips or any other side bet cheaper.
| A | K | Q | J | T | 9 | 8 | 7 | 6 | 5 | 4 | 3 | 2 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| A | AA 4x | AKs 4x | AQs 4x | AJs 4x | ATs 4x | A9s 4x | A8s 4x | A7s 4x | A6s 4x | A5s 4x | A4s 4x | A3s 4x | A2s 4x |
| K | AKo 4x | KK 4x | KQs 4x | KJs 4x | KTs 4x | K9s 4x | K8s 4x | K7s 4x | K6s 4x | K5s 4x | K4s 4x | K3s 4x | K2s 4x |
| Q | AQo 4x | KQo 4x | QQ 4x | QJs 4x | QTs 4x | Q9s 4x | Q8s 4x | Q7s 4x | Q6s 4x | Q5s check | Q4s check | Q3s check | Q2s check |
| J | AJo 4x | KJo 4x | QJo 4x | JJ 4x | JTs 4x | J9s 4x | J8s 4x | J7s check | J6s check | J5s check | J4s check | J3s check | J2s check |
| T | ATo 4x | KTo 4x | QTo 4x | JTo 4x | TT 4x | T9s check | T8s check | T7s check | T6s check | T5s check | T4s check | T3s check | T2s check |
| 9 | A9o 4x | K9o 4x | Q9o 4x | J9o check | T9o check | 99 4x | 98s check | 97s check | 96s check | 95s check | 94s check | 93s check | 92s check |
| 8 | A8o 4x | K8o 4x | Q8o 4x | J8o check | T8o check | 98o check | 88 4x | 87s check | 86s check | 85s check | 84s check | 83s check | 82s check |
| 7 | A7o 4x | K7o 4x | Q7o check | J7o check | T7o check | 97o check | 87o check | 77 4x | 76s check | 75s check | 74s check | 73s check | 72s check |
| 6 | A6o 4x | K6o 4x | Q6o check | J6o check | T6o check | 96o check | 86o check | 76o check | 66 4x | 65s check | 64s check | 63s check | 62s check |
| 5 | A5o 4x | K5o 4x | Q5o check | J5o check | T5o check | 95o check | 85o check | 75o check | 65o check | 55 4x | 54s check | 53s check | 52s check |
| 4 | A4o 4x | K4o check | Q4o check | J4o check | T4o check | 94o check | 84o check | 74o check | 64o check | 54o check | 44 4x | 43s check | 42s check |
| 3 | A3o 4x | K3o check | Q3o check | J3o check | T3o check | 93o check | 83o check | 73o check | 63o check | 53o check | 43o check | 33 4x | 32s check |
| 2 | A2o 4x | K2o check | Q2o check | J2o check | T2o check | 92o check | 82o check | 72o check | 62o check | 52o check | 42o check | 32o check | 22 check |
4xBet 4x –Check. Pairs on the diagonal, suited hands above it, offsuit below. 69 of 169 hand kinds bet 4x; the rest check.
Show the math: The exact numbers
EV per hand = −50643648973/2317817502000 ≈ −0.0218497 antes. P(4x) = 250/663 (500 of 1,326 hands). P(2x) = 1382947/6497400 ≈ 21.28%. P(1x) ≈ 21.82%. P(fold) ≈ 19.19%. Average total wagered = 29163830173/7023689400 ≈ 4.1522 antes. Standard deviation ≈ 4.94 antes per hand.
These come from an exhaustive solve: every one of the 169 starting-hand kinds, all 19,600 flops, all 1,081 turn/river pairs and all 990 dealer hands, with the best decision at every step.
Quiz
What's the house edge of UTH with perfect strategy (standard Blind)?
- 0.53% of the Ante
- 1.09% of the Ante
- 2.19% of the Ante
- 3.5% of the Ante
Show the answer
C: 2.19% of the Ante. 2.185% of the Ante. 0.53% is the element of risk (lesson 15).
Quiz
What share of hands are 4x bets under perfect play?
- About 20%
- About 38%
- About 50%
- About 60%
Show the answer
B: About 38%. 37.7% (500 of 1,326 hands).
Quiz
Which statement is true?
- Perfect play wins in the long run
- Perfect play loses about 22¢ a hand at a $10 Ante
- Perfect play has no variance
- Perfect play makes Trips free
Show the answer
B: Perfect play loses about 22¢ a hand at a $10 Ante. 2.185% × $10 ≈ $0.22 per hand on average.