Reading the EV sheet (and why 3x is never right)
Best play, close calls and big mistakes, plus the 3x trap.
Whenever you have a decision, the EV sheet lists every option:
Bet 4x: +$36.01 · Best play
Bet 3x: +$28.97 · −$7.04 vs best · Big mistake
Check: +$21.93 · −$14.08 vs best · Big mistake
That's pocket aces at a $10 Ante. Every line is the average result for the whole hand, assuming you play the rest of the hand perfectly. The "vs best" figure is what the choice costs you on average. The badge sorts that cost into five tiers:
| Tier | Cost vs best | Badge | Example |
|---|---|---|---|
| Best | 0 | Best play | Bet 4x with |
| Close | up to 0.02 antes | Close | Checking (costs 0.011) |
| Small | up to 0.10 antes | Small mistake | Betting 4x with (costs 0.023) |
| Costly | up to 0.50 antes | Mistake | Betting 4x with (costs 0.108) |
| Blunder | over 0.50 antes | Big mistake | Betting 4x with (costs 1.23) |
A Big mistake asks for a second tap before it goes through, and the sheet suggests the better option. You're always allowed to make it. It's your sandbox.
Why 3x is never the best play. The Play bet's result is just Play × (+1 if you win, −1 if you lose, 0 on a tie). So the EV of betting P antes is
EV(P) = (what Ante and Blind earn) + P × (how often you win − how often you lose)
That's a straight line in P. If you win more often than you lose, a bigger bet is better and 4x beats 3x. If you don't, even 3x is worse than checking and playing just 1x later. Either 4x or check always beats 3x, for every hand. 3x exists so that players who are short on chips can still make a Play bet.
Show the math: The 3x proof, with numbers
Write the preflop EV of betting P as EV(P) = a + P·b, where b = P(win) − P(lose) for the hand at showdown.
- If b ≥ 0: EV(4) − EV(3) = b ≥ 0, so 4x is at least as good.
- If b < 0: EV(3) = a + 3b < a + b = EV(check, then always bet 1x) ≤ EV(check, then play the river perfectly).
For aces: EV(4x) = 472094411/131098275 ≈ 3.6011, EV(3x) ≈ 2.8970, EV(check) = 38331809/17479770 ≈ 2.1929. Playing perfect strategy except always betting 3x instead of 4x raises the house edge from 2.19% to 9.86%.
Quiz
The EV sheet says "Check: −$0.23 vs best · Small mistake" at a $10 Ante. What does that mean?
- You will lose $0.23
- On average, checking earns $0.23 less than the best option
- The house edge is 0.23%
- Checking is free
Show the answer
B: On average, checking earns $0.23 less than the best option. 'vs best' is the average cost of the choice compared with the best option.
Quiz
Is betting 3× preflop ever the best play?
- Yes, with medium hands
- Yes, with small pairs
- No: 4x or check is always at least as good
- Only when the dealer shows an ace
Show the answer
C: No: 4x or check is always at least as good. EV is a straight line in the bet size, so the best choice is always one of the ends: 4x, or check.
Quiz
Which tier asks you to confirm with a second tap?
- Close
- Small mistake
- Mistake
- Big mistake
Show the answer
D: Big mistake. Only Big mistakes (over 0.5 antes) need a second tap.