Expected Value: The Only Number That Matters Long-Term
Every bet you will ever place can be summarized by one number: its expected value. EV tells you what a bet is worth on average, stripped of luck, streaks and feelings. Learn to compute it in ten seconds and you will never be confused about what a casino game costs again — including every game on Llamabet, where the odds are published and provably enforced on Sui.
See the games and their edges →The formula, defined once
Expected value is the probability-weighted average of every possible outcome: EV = (probability of winning x amount won) minus (probability of losing x amount lost). That is the whole thing. Flip a fair coin for 1 SUI and EV = (0.5 x 1) - (0.5 x 1) = 0. That is a fair bet — nobody has an edge. Casino bets are never fair bets: the payout is always set slightly below the true odds, so the weighted average lands a little under zero. The gap between a fair payout and the actual payout is the house edge, and EV is just the house edge expressed per unit staked. A bet with -1% EV costs you, on average, 0.01 SUI for every 1 SUI wagered. Not per session, not per win or loss — per unit through the machine, forever.
Worked example: dice at 49.5%
Llamabet dice pays 99 divided by your chosen win chance. Pick 49.5% and the payout is 99 / 49.5 = 2.00x your stake. EV on a 1 SUI bet: you win 1 SUI of profit 49.5% of the time and lose 1 SUI 50.5% of the time, so EV = (0.495 x 1) - (0.505 x 1) = -0.01 SUI. Exactly -1% of stake. Now slide the win chance to 10%: payout becomes 99 / 10 = 9.9x, and EV = (0.10 x 8.9) - (0.90 x 1) = 0.89 - 0.90 = -0.01. Same -1%. Every slider position on the dice game has identical EV; what changes is the shape of the ride, not its price. That flat 1% edge — 99% RTP — is the whole pricing model, and because the roll comes from a seed hash committed on Sui before you bet, you can verify the stated probability is the real one.
Worked example: roulette and blackjack
Single-zero roulette, red or black: 18 winning pockets out of 37, paying even money. EV = (18/37 x 1) - (19/37 x 1) = -1/37, about -2.70% of stake. The zero is the entire edge — nothing else about the layout matters mathematically, which is also why double-zero wheels (5.26%) are simply a worse price for the same game. Blackjack is the interesting one because your decisions move the number: played with basic strategy, the edge lands around -0.5%, roughly 99.5% RTP, helped by the 3:2 bonus on naturals. Played by feel — standing on 16 versus a dealer ten because you are scared, skipping doubles — the same table can quietly cost several times that. Same game, same cards, different EV, purely from decision quality.
Every casino bet is negative EV — say it plainly
There is no betting pattern, progression, streak-reading system or lucky table that turns a -EV game positive. Bet sizing and timing redistribute variance; they cannot touch the average. What negative EV honestly means is this: casino gambling is paid entertainment. You are buying variance — the genuine possibility of walking away up — and the ticket price is the edge times your total volume. A hundred 1 SUI dice bets at 49.5% costs about 1 SUI in expectation, and for that price you get a real chance of finishing +15 or -18. Framed that way, a low-edge game is simply cheaper entertainment per hour than a high-edge one. Players who understand they are paying for the ride budget for it. Players who believe they are earning are the ones who get hurt.
EV versus results in the short run
EV is invisible over a session. Over 100 even-money-style bets, the random noise (a standard deviation of about 10 units) completely swamps a 1-unit expected loss, so short-run results carry almost no information about whether you played well. This cuts both ways: winning does not mean your system works, and losing does not mean the game is rigged — on Llamabet you can check the second claim directly, since every outcome recomputes from the revealed seed. The professional habit is to grade decisions by the EV they had when made, not by how the card fell. A bad double that wins is still a bad double. That mental separation of decision quality from outcome is what EV thinking actually buys you.
Using EV to compare bets — and to stay off tilt
EV gives you a single axis to rank everything: blackjack with basic strategy (~-0.5%) beats dice (-1%), which beats single-zero roulette (-2.70%), which beats double-zero (-5.26%). Within a game it ranks bets too — every bet on a single-zero wheel has the same -2.70%, so no roulette bet is smarter than another; in blackjack, each decision has a computable best line. EV is also the best tilt protection ever invented. Tilt is the belief that the game owes you something after a losing stretch. EV says the game owes you nothing and never did: the next bet costs the same 1% whether you are down five buy-ins or up ten. When you feel the urge to raise stakes to get back to even, you are proposing to pay the house edge on a much larger volume. The formula does not care how you feel.
Where positive EV actually exists
Against the house, essentially nowhere — that is the business model, and any site telling you otherwise is selling something. But poker is different in kind: in a cash game or tournament you are not betting against the house, you are betting against other players, and the house takes a rake off the top. If your decisions are sufficiently better than your opponents' to overcome the rake, your EV is genuinely positive — poker is the one room in the casino where skill sets the sign of the number. That is also the honest hierarchy of gambling: -EV games are entertainment with a known price, and poker is a competitive skill game with an uncertain one. Know which one you are playing before you sit down, and size your bankroll for it.
Frequently asked questions
How do you calculate expected value on a casino bet?
Multiply each outcome by its probability and add them up: EV = (win probability x profit if you win) - (loss probability x stake). Example: dice at 49.5% win chance pays 2.00x, so EV = (0.495 x 1) - (0.505 x 1) = -0.01, or -1% of stake per bet.
Are any casino games positive EV for the player?
House-banked games are not — the payout is always set below true odds, which is the house edge. The practical exceptions are player-versus-player games like poker, where a skilled player can beat opponents by more than the rake. Against the house, the best you can do is pick low-edge games like blackjack with basic strategy (~99.5% RTP) or 1%-edge dice.
If every bet is negative EV, why does anyone win?
Variance. EV is an average; over a short session the random spread of results is many times larger than the expected loss, so plenty of sessions finish in profit. The edge only becomes visible over thousands of bets — which is exactly why the house, running millions of bets, wins reliably while individual sessions swing both ways.