Expected Value — The Moment One Bad Bet Becomes a Guaranteed Loss
See how a tiny 1.06% house edge compounds into a guaranteed loss over time. We calculate exactly how many hands it takes to turn $1,000 into $0.
Last reviewed 2026-07-29
In Chapter 1, we saw that the house edge on baccarat’s banker bet is about 1.06%. One dollar out of a hundred. That sounds like nothing.
This chapter calculates how that one dollar becomes your entire bankroll.
What is expected value?
Expected value (EV) is the average amount you win or lose on a single bet. The math is simple.
Let’s check it with a coin flip. Heads wins you $10; tails loses you $10. The expected value is:
(0.5 × $10) − (0.5 × $10) = $0
A game with an expected value of zero is called a fair game. Play it forever, and on average, you break even.
Real-world gambling has no fair games.
The real expected value of baccarat’s banker bet
Bet $100 on the banker:
- ~45.86% chance to win → you’re paid $95 after a 5% commission
- ~44.62% chance to lose → you lose $100
- ~9.52% chance of a tie → your bet is returned
Work out the expected value and you get roughly −$1.06. In other words, every $100 you wager, on average, $1.06 disappears.
The critical thing about that $1.06 is that it’s not “money you lose if you’re unlucky.” It’s money you are, on average, guaranteed to lose. You’ll win some hands and lose others, but as the hands add up, the actual outcome gets pulled toward this average.
How many hands does it take to lose $1,000?
Bet $10 per hand, and on average $1.06 evaporates per hand. For a starting bankroll of $1,000 to hit zero:
About 943 hands. Sound like a lot? Online gambling rounds take less than 30 seconds each. Play without stopping, and arithmetically that’s under eight hours.
Here’s the expected balance at each stage:
| Hands played | Expected balance |
|---|---|
| 0 | $1,000 |
| 10 | $989.40 |
| 50 | $947.00 |
| 100 | $894.00 |
| 200 | $788.00 |
| 500 | $470.00 |
| 943 | $0 |
The gray dashed line is the hope that “at least I’ll break even.” The red line is reality. The two never meet, and the gap only widens.
Why people don’t feel it
Given how clear the expected value is, why does gambling keep going? Because over a short stretch, that line is invisible.
After 100 hands, the expected loss is only about $10 — an amount that gets completely buried in the swings of luck. Some 100-hand sessions end up ahead; some end up behind. So it looks like “a game you could win.”
But as more hands are played, luck’s influence shrinks relative to the total, and only the house edge remains. That’s the Law of Large Numbers, which we cover next chapter.
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Think about it
A friend says, “I won $500 at baccarat yesterday.”
Does that disprove the house edge?
Answer: No. The house edge doesn’t predict the outcome of a single hand, or even a single day. It only says where the numbers converge once enough hands are played. Winning $500 yesterday works as the exact mechanism that keeps your friend playing — and as long as they keep playing, the results will track the chart above.
Summary
- Expected value isn’t “the loss you take on a bad day” — it’s a loss that is, on average, guaranteed.
- On baccarat’s banker bet, that’s $1.06 per $100. A $1,000 bankroll is mathematically drained in about 943 hands.
- Play briefly and you won’t see it. Play long enough and you always will. Getting you to play a lot of hands is the operator’s entire business model.
Next chapter, we test how brutal “on average” really is — running a simulation to directly count how often players go broke.
Sources
- House edge figures are the publicly known calculations under standard rules (5% banker commission).
- This chapter’s math assumes a flat bet size on every hand for simplicity.
- Verified: 2026-07-29
If gambling is a problem for you — in Korea, call the Gambling Problem Helpline at 1336, toll-free, 24/7, free of charge. If you’re outside Korea, search for your country’s national problem-gambling helpline.