Why this is computable when the game beside it is not
Ultimate Texas Hold'em itself is not computed on this site, and the page says so. The player acts three separate times against every dealer holding consistent with what is visible, which is tens of trillions of deals and a dedicated computation measured in machine-days.
Trips escapes all of that. It pays on your best five-card hand out of the seven you can see, whatever the dealer holds, whether or not the dealer qualifies, and whether or not you beat them. There is no decision in it and no opponent. So the only thing it depends on is how often seven cards make each kind of hand, and that is a finite question with an exact answer.
The exact seven-card distribution
| Hand | Trips pays | Hands in 133,784,560 | Frequency |
|---|---|---|---|
| Royal flush | 50 to 1 | 4,324 | 0.003232% |
| Straight flush | 40 to 1 | 37,260 | 0.027851% |
| Four of a kind | 30 to 1 | 224,848 | 0.168067% |
| Full house | 8 to 1 | 3,473,184 | 2.596102% |
| Flush | 7 to 1 | 4,047,644 | 3.025494% |
| Straight | 4 to 1 | 6,180,020 | 4.619382% |
| Three of a kind | 3 to 1 | 6,461,620 | 4.829870% |
| Two pair or less | loses | 113,355,660 | 84.730002% |
These counts are enumerated, not quoted. They also happen to be the strongest available check on the program that produced them: an evaluator with a bug in it cannot arrive at 58,627,800 one-pair hands by accident, and the build refuses to write anything if any of the nine categories disagrees with the published frequency.
What the numbers say about the bet
It pays on 15.27% of hands. Three of a kind or better, and nothing else. The single most common outcome by a wide margin is one pair, at 43.82% of hands, and one pair pays nothing here.
The royal flush line is almost decorative. There are 4,324 seven-card hands containing a royal, which is one in 30,940. At 50 to 1 it contributes 0.2% of the bet's total return. The headline payout on the felt is doing advertising rather than arithmetic.
It is a worse bet than the game it sits on. Published analyses put the main Ultimate Texas Hold'em bet near 2.2% of the ante. Trips costs 3.4979%, which is more than half again as much, and about seven times blackjack at 0.5153%. Ranked against every bet on this site it sits with the expensive ones.
If your table pays differently
Every figure above describes the 50-40-30-8-7-4-3 schedule shown. Trips pay tables vary between casinos and the full house and flush lines are the ones that usually move. A schedule paying less on those is a more expensive bet, and the difference is not small: those two categories together are 5.62% of all hands, far more than the headline payouts you are being shown. Read the felt before deciding, which is the same advice this site gives about keno and sic bo for the same reason.
Frequently Asked Questions
- What is the house edge on the Trips bet?
- 3.4979% on the common 50-40-30-8-7-4-3 pay table, computed here from all 133,784,560 seven-card hands. Published analyses give 3.50%.
- Does the Trips bet depend on the dealer?
- No. It pays on your best five-card hand out of seven, whether or not you beat the dealer and whether or not the dealer qualifies. That independence is why it can be computed exactly while the main game cannot.
- Is Trips worth playing?
- It costs about seven times what the main Ultimate Texas Hold'em bet costs and more than six times a blackjack hand at 0.5153%. It is a worse bet than the game it sits beside.
- How often does Trips actually pay?
- On 15.27% of hands: three of a kind or better. The other 84.73% of the time it loses, and roughly 44% of all hands are a single pair, which pays nothing.
Every figure on this page is produced by
seven_card_math.py, which enumerates all 133,784,560 seven-card
hands and checks its category counts against the frequencies published in
every reference before writing anything. All nine agree. The result,
3.4979%, matches the 3.50% published analyses give for this pay table. Last
computed September 2026.