The short version
The 3-Card Bonus carries a house edge of 2.1357%, which reads better than the base game’s 4.915% but is measured against a much smaller bet. Per dollar you actually put at risk it is the more expensive of the two wagers, and it is not a hedge: it pays far more often when your main hand is already winning.
What the bet actually is
The 3-Card Bonus is an optional wager placed alongside your ante, before any cards come out. It is settled on three cards (your two hole cards plus the first community card, the one turned on 3rd Street) and it is paid or taken as soon as that card is exposed. It does not care what you do afterwards. You can fold the hand on the same street and still collect a 50-to-1 mini royal.
Because it is settled on exactly three cards off a fresh deck, there is no strategy attached to it. There are 22,100 possible three-card combinations and the bet has been decided the moment they are dealt. The only decision is whether to make it at all.
The exact numbers
Every one of those 22,100 combinations was categorised and counted, and the categoriser was checked against the one in this site’s game engine with no disagreements.
| Hand | Pays | Combinations | Probability | 1 in | Return | Share of winnings |
|---|---|---|---|---|---|---|
| Mini royal (A-K-Q suited) | 50 to 1 | 4 | 0.00018100 | 5,525 | +0.00904977 | 1.25% |
| Straight flush | 40 to 1 | 44 | 0.00199095 | 502 | +0.07963801 | 11.02% |
| Three of a kind | 30 to 1 | 52 | 0.00235294 | 425 | +0.07058824 | 9.77% |
| Straight | 6 to 1 | 720 | 0.03257919 | 30.7 | +0.19547511 | 27.05% |
| Flush | 4 to 1 | 1,096 | 0.04959276 | 20.2 | +0.19837104 | 27.45% |
| Pair | 1 to 1 | 3,744 | 0.16941176 | 5.9 | +0.16941176 | 23.45% |
| Nothing | loses | 16,440 | 0.74389140 | 1.3 | −0.74389140 | n/a |
| Total | 22,100 | 1.00000000 | −0.02135747 | 100.00% |
Return is per unit staked. The winning lines return +0.72253393 in total and the losing line takes back 0.74389140, which leaves a house edge of 2.1357%.
Two things in that table are worth pausing on. The first is that the flush and straight lines, not the pair, do most of the work: between them they are 54.5% of everything the bet returns. The second is that the mini royal (the line the bet is named and marketed for) contributes 1.25%. You will see it once in 5,525 hands.
Why a smaller edge is not a better bet
2.1357% against 4.915% looks like an easy comparison, and it is the wrong one. The base game charges its edge against your ante, but by the end of a hand you have an average of 3.590 antes on the table. Per dollar actually wagered the base game costs 1.3728%. The bonus charges 2.1357% against a bet that is settled once and never grows.
Ante and raises, $5 table
- Average money at risk
- $17.95
- Edge per dollar risked
- 1.3728%
- Expected loss per hand
- 24.6¢
- Per 100 hands
- $24.64
3-Card Bonus, $5 bet
- Money at risk
- $5.00
- Edge per dollar risked
- 2.1357%
- Expected loss per hand
- 10.7¢
- Per 100 hands
- $10.68
Adding a $5 bonus to a $5 ante increases the money you put through the table by about 28% and increases what the hand is expected to cost you by about 43%. That is the honest way to state it. The bonus is not a terrible bet by casino side-bet standards (plenty of them run at 5% or worse), but it is the worse half of the two bets in front of you.
It loses three times in four
The bonus pays something on 25.61% of hands and takes your chips on 74.39%. Two thirds of those wins, 3,744 of the 5,660 paying combinations, are a 1-to-1 pair, which returns your stake and the same again and is over before you have registered it. A run of twenty hands with nothing is entirely ordinary.
It is not a hedge
The most common defence of the side bet is that it covers you on the hands you fold. It does not, and the reason is structural: three of the five cards that decide your hand are the three that decide the bonus. The two bets move together.
On the hands where you needed rescuing, the bonus pays less than one time in six. On the hands where you were already being paid, it pays more than half the time. It does not smooth your session out; it makes the good hands better and leaves the bad ones exactly as they were, which is the opposite of what a hedge does.
So should you make it?
If you are playing to lose as little as possible per hour, no. Put the same money into a larger ante instead and it buys you a cheaper rate on every dollar, because the ante is the bet the pay table multiplies.
If you are playing for the shape of the session rather than the rate (and most people are), then it is a defensible five dollars. It is cheaper per hand than the base game in absolute terms, it adds a line of the game you would otherwise never see paid, and 2.14% is a fair price by side-bet standards. Just make it because you want the 40-to-1 line live, not because you have been told it protects your ante. It does not.
Whatever you decide, decide it once and keep it for the session. The worst version of this bet is the one that appears only after a bad run, when the reasoning has quietly become “I am due”. The three cards do not know what the last twenty did. If the bonus is worth five dollars on the first hand, it is worth five on the fiftieth, and if it is not, it never was.
You can leave the bonus on or off at the free table and watch what a few hundred hands of each looks like without paying for the lesson. The payouts page has both pay tables side by side.