The short answer
A “Buy” bet carries a house edge of 4.76% if the 5% commission is charged up front, but it drops to 1.67% on the 4 and 10 if the commission is only charged on a win.
The full calculation
In a Buy bet, you pay a 5% commission (“vig”) to get paid “True Odds” (2:1 on the 4/10) instead of the standard “Place” payout (9:5).
If the $1 vig is charged on a $20 bet upfront: $HE = rac{Vig}{Wager + Vig} = rac{1}{20 + 1} pprox 4.76%$
If the vig is only charged on a win (standard at “good” tables): The probability of winning a 4 or 10 is $ rac{3}{9}$ (since we ignore all numbers except the 4 and 7). $EV = ( rac{1}{3} imes (2 - 0.05)) + ( rac{2}{3} imes -1) pprox -0.0167$ This result is a 1.67% house edge.
What this means at the table
Buying the 4 and 10 is mathematically superior to Placing them (which has a 6.67% edge), provided you are at a table that only collects the vig on a win. If you bet $20 to Buy the 10, your expected loss per resolution is only 33 cents. If you “Place” it, you lose $1.33. Over a long session, this choice saves you significant bankroll.
Common mistakes around this number
Never “Buy” the 6 or 8. The Place bet on the 6 and 8 has a tiny 1.52% house edge. Paying a 5% commission to “Buy” them increases the house edge against you. Only use Buy bets for the outside numbers (4 and 10) and occasionally the 5 and 9 if the vig-on-win rules are exceptionally favorable.
See also
Compare this to the Craps House Edge Place Bets or look at the payout differences in the Craps Odds Chart.
In Detail
The house edge on buy bets is a tiny commission story with a big punchline. Same dice, same number, different vig timing — different value.
This page is about how commission changes buy-bet value. On the surface, that may sound like one small corner of craps, but in a real casino it touches the three things that decide whether a player survives the table: the written rule, the payout, and the way the bet feels when chips are already in action. Craps is dangerous for beginners because a bet can feel smart, social, or lucky while still being badly priced.
The math that matters: Two dice create 36 equally likely ordered combinations. The shape of the game comes from that grid: 7 has 6 combinations, 6 and 8 have 5 each, 5 and 9 have 4 each, 4 and 10 have 3 each, 3 and 11 have 2 each, and 2 and 12 have only 1 each. When vig is paid only on wins, a buy 4 or 10 can be attractive. Upfront vig increases cost because you pay even when the number never hits. Expected value is the grown-up way to price a bet: $EV=\sum(P_i\times W_i)-\sum(P_j\times L_j)$. If the payout is smaller than the true probability deserves, the difference is the house edge.
What it means on the felt: The best buy-bet spots are usually 4 and 10 at bet sizes where commission rounding behaves. A player who understands this subject does not need to act like a robot. You can still enjoy the noise, the shooter, the stick calls, and the little rush when the dice leave the hand. The point is to know when you are paying for entertainment and when you are making a lower-cost decision.
Casino-floor truth: Craps is built to move. The table crew wants clear bets, fast decisions, and clean payouts. The layout also nudges attention toward action. The safest-looking move is not always the cheapest move, and the loudest bet is almost never the best one. Good craps play is not about predicting the next roll. It is about refusing to overpay for it.
The mistake to avoid: Do not accept the word “buy” without asking when and how the vig is taken. Also, never judge this topic by one lucky hit or one ugly loss. Short sessions are noisy. The math only shows its face over repeated decisions, which is exactly why casinos are patient and players are usually not.