Part 2 · Lesson 7 of 25 · Free

Playing accurately with the cards face up

Course by Hernan Alejandro Gajardo Morales

J♥ T♥ against A♠ K♦, all in before the flop: you are behind, 41% to 59%, and calling still earns money. Start with the simplest case, both hands known. Then equity is a plain number, the price is a plain number, and the right play is whichever has the higher EV.

The hand

Imagine both hands face up. The Tight-aggressive player moves all in for 40 bb more into a 20 bb pot, so the pot with his all-in is 60 bb and you must call 40 bb.

Predict first

Your J♥ T♥ against his A♠ K♦: call or fold?

1. Fold: you win less than half the time
2. Call
3. Either: it is a coin flip

Working it out

Price: 40 ÷ (60 + 40) = 40%. Equity: counting every one of the 1,712,304 possible boards, J♥ T♥ wins 41.2% against A♠ K♦, with ties counted as half. EV of calling: 0.412 × 100 − 40 = +1.2 bb. A thin call, but a call; with 38% it would be a fold, at −2 bb.

Practice these until the arithmetic is fast; mistakes here are pure leaks because nothing is hidden. The face-up case is also the building block of every hidden one: equity against a range is the average of these face-up equities across the range, as the next lesson shows.

Formula

EV(call) = equity × (pot + call) − call, with his all-in in the pot; call when equity > call ÷ (pot + call)

Check your understanding

1. His all-in makes the pot 90 bb; you must call 50 bb with 40% equity. EV of calling, in bb?

   Show the answer

   Answer: 6 bb

   0.40 × (90 + 50) − 50 = 56 − 50 = +6 bb.

2. Cards face up, no more betting to come. What can turn a call into a fold?

   1. A bigger all-in into the same pot
   2. Having more chips behind than he does
   3. Knowing that he is a tight player
   Show the answer

   Answer: A bigger all-in into the same pot

   Only equity and price decide, and face up the equity is fixed. A bigger all-in raises the price: 80 bb into the same 20 bb pot would need 80 ÷ (100 + 80) = 44.4%, more than your 41.2%.