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Perfect strategy II: the card you can remember

Lesson 16 of 23 · Perfect strategy II: practical · 8 min read

A strategy card that costs 59¢ an hour more than perfect.

The EV sheet plays perfectly, but at a real table you only have your memory. Here's the card that most strong players use: the Wizard of Odds basic strategy, with flop and river rules after James Grosjean. The prices below are computed by the app.

The basic card

You know this already. It's what Perfect strategy I taught, minus the EV sheet's rare exceptions.

The simple card (for when even that's too much)

Strategy House edge per Ante Extra cost vs perfect Extra per hour at $10
Perfect (EV sheet) 2.185% — —
Basic card 2.381% 0.196% $0.59
Basic card without the flush rule 2.449% 0.264% $0.79
Simple card 2.708% 0.523% $1.57

Why the river matters most. Every shortcut that drops the outs count costs about 5% of the Ante, far more than all the other simplifications put together. "Bet 1x only with a pair" sounds safe, but it folds hands that win often enough. Even with the chart's preflop and the basic flop rule, a river rule of "bet 1x only with a hidden pair or better" raises the edge from 2.19% to 7.13%. Simplifying preflop to "any pair or ace" costs 3.5% on its own. Keep the chart's preflop rules and the outs count, and you're within pennies of perfect.

Preflop strategy chart
AKQJT98765432
AAA 4xAKs 4xAQs 4xAJs 4xATs 4xA9s 4xA8s 4xA7s 4xA6s 4xA5s 4xA4s 4xA3s 4xA2s 4x
KAKo 4xKK 4xKQs 4xKJs 4xKTs 4xK9s 4xK8s 4xK7s 4xK6s 4xK5s 4xK4s 4xK3s 4xK2s 4x
QAQo 4xKQo 4xQQ 4xQJs 4xQTs 4xQ9s 4xQ8s 4xQ7s 4xQ6s 4xQ5s checkQ4s checkQ3s checkQ2s check
JAJo 4xKJo 4xQJo 4xJJ 4xJTs 4xJ9s 4xJ8s 4xJ7s checkJ6s checkJ5s checkJ4s checkJ3s checkJ2s check
TATo 4xKTo 4xQTo 4xJTo 4xTT 4xT9s checkT8s checkT7s checkT6s checkT5s checkT4s checkT3s checkT2s check
9A9o 4xK9o 4xQ9o 4xJ9o checkT9o check99 4x98s check97s check96s check95s check94s check93s check92s check
8A8o 4xK8o 4xQ8o 4xJ8o checkT8o check98o check88 4x87s check86s check85s check84s check83s check82s check
7A7o 4xK7o 4xQ7o checkJ7o checkT7o check97o check87o check77 4x76s check75s check74s check73s check72s check
6A6o 4xK6o 4xQ6o checkJ6o checkT6o check96o check86o check76o check66 4x65s check64s check63s check62s check
5A5o 4xK5o 4xQ5o checkJ5o checkT5o check95o check85o check75o check65o check55 4x54s check53s check52s check
4A4o 4xK4o checkQ4o checkJ4o checkT4o check94o check84o check74o check64o check54o check44 4x43s check42s check
3A3o 4xK3o checkQ3o checkJ3o checkT3o check93o check83o check73o check63o check53o check43o check33 4x32s check
2A2o 4xK2o checkQ2o checkJ2o checkT2o check92o check82o check72o check62o check52o check42o check32o check22 check

4xBet 4x –Check. Pairs on the diagonal, suited hands above it, offsuit below. 69 of 169 hand kinds bet 4x; the rest check.

A practical session, at $10 and 30 hands an hour

Show the math: Where the basic card loses its 0.196%

Exact decomposition, each step changing one street:

  • Perfect preflop + basic flop + perfect river (expert): 2.2714%, so the flop rule costs 0.086%.
  • Then the outs-count river instead of a perfect river: 2.3814%, so the river rule costs 0.110%.
  • The basic preflop rules are exactly the perfect ones, so preflop costs 0.

Basic card EV = −54758439/2299422125 antes per hand. Simple card EV = −47068162901/1738363126500.

Quiz

How much more per hour does the basic card cost than perfect play, at $10 and 30 hands an hour?

  1. About 6¢
  2. About 59¢
  3. About $5
  4. About $15
Show the answer

B: About 59¢. 0.196% × $10 × 30 ≈ $0.59.

Quiz

Which shortcut costs the most?

  1. Dropping the flush-draw rule on the flop
  2. Using 'any king' preflop
  3. Playing the river 1x only with a pair
  4. Checking pocket deuces
Show the answer

C: Playing the river 1x only with a pair. Dropping the outs count on the river costs about 5% of the Ante. The others cost tenths of a percent or less.

Quiz

With the simple card, what do you do with K3o preflop?

  1. Bet 4x
  2. Check
Show the answer

A: Bet 4x. The simple card bets 4x with any king. (Perfect play checks K3o, a small mistake that's part of the simple card's price.)

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