Trainers & Games
EV Decision Trainer
Bet or fold? See a quick wager and decide if it's a good deal, on the clock. Trains the expected-value reflex traders live by.
EV Decision Trainer
Expected value is the probability-weighted average of every outcome, what a bet pays on average if you could play it over and over. Good traders judge it in seconds: a bet is worth taking when its EV is positive (repeat it enough and you come out ahead). Real position sizing also weighs risk, not just EV, that's the job of the Kelly tool.
Snap-judge each gamble: is it a good bet (positive EV) or bad? Keys, F or ← to Pass, J or → to Take it.
Learn how it works
Five worked examples. Read a couple before you dive in, try to answer first, then reveal the solution.
Coin flip
Flip a fair coin: win $10 on heads, lose $8 on tails. Take it or Pass?
Show solution
Expected value = probability × payoff, summed over outcomes:
- EV = ½ × (+10) + ½ × (−8)
- = 5 − 4
- = +$1
Positive EV → Take it. On average each flip nets you a dollar, even though any single flip is a win or a loss.
Single die, one winning face
Roll one die: win $30 if it lands on a 6, otherwise lose $5. Take it or Pass?
Show solution
A 6 has probability 1/6; the other five faces (probability 5/6) lose:
- EV = (1/6) × 30 + (5/6) × (−5)
- = 5 − 4.17
- = +$0.83
Positive → Take it. The rare $30 win is just big enough to outweigh the frequent small losses.
Pay to play
Pay $5 to enter. You then win $9 with probability 60%, and get nothing (60% of the time you keep the $9, otherwise you lose your stake). Take it or Pass?
Show solution
Count the $5 cost against the expected winnings:
- EV = 0.60 × 9 − 5
- = 5.40 − 5
- = +$0.40
Positive → Take it. Same answer the long way: 60% of the time you're up 9 − 5 = 4, 40% of the time you're down 5 → 0.6×4 − 0.4×5 = 2.4 − 2 = +0.40.
A tempting but negative bet
70% chance to win $5, 30% chance to lose $15. Take it or Pass?
Show solution
The high win chance is bait, weigh it against the size of the loss:
- EV = 0.70 × 5 + 0.30 × (−15)
- = 3.5 − 4.5
- = −$1.00
Negative → Pass. Winning often isn't enough when the occasional loss is three times the size of the win. Always size the payoffs, not just the odds.
Draw a card
Draw one card. Win $12 if it's a heart (25%), otherwise lose $3. Take it or Pass?
Show solution
Hearts are one suit of four, so probability 1/4 = 25%:
- EV = 0.25 × 12 + 0.75 × (−3)
- = 3 − 2.25
- = +$0.75
Positive → Take it. A one-in-four shot at $12 comfortably beats the frequent small $3 losses.
What you'll learn
Judging expected value in seconds, the reflex behind every good trading and market-making decision, drilled until it's automatic.