Betting on a number without a line bet
Craps is a game of chance with a built-in house edge, and no strategy, system or timing changes that in the player’s favor over time. Most players lose money over time, and nobody should gamble money they cannot afford to lose. Place bets and buy bets are two ways to wager on a specific number, and both carry a cost larger than the line bets.
Each bet says that a chosen number (4, 5, 6, 8, 9 or 10) will be rolled before a 7. Unlike a Pass Line bet, it does not need a come-out roll or a point, and it can usually be added or taken down at any time. The bet can be “working” or “off” depending on the table and the player’s call.
The true odds and the place payout
The fair payout for each number comes from counting dice combinations against the six ways to make a 7:
| Number | Ways | True odds against | Typical place payout |
|---|---|---|---|
| 4 or 10 | 3 | 2 to 1 | 9 to 5 |
| 5 or 9 | 4 | 3 to 2 | 7 to 5 |
| 6 or 8 | 5 | 6 to 5 | 7 to 6 |
In each case the casino pays slightly less than the true odds. That shortfall is the house edge. Payouts at a particular table may differ, so the layout and the dealer are the reliable sources.
Working out the edge on a place bet
All three of these examples are hypothetical but follow standard counting.
Place 6 with $6. The 6 wins 5 times in 11 and loses 6 times in 11. A win pays $7. Expected result: (5 × $7 − 6 × $6) ÷ 11 = ($35 − $36) ÷ 11, which is about −$0.09. As a share of the $6 bet, that is about 1.5%.
Place 5 with $5. The 5 wins 4 times in 10 and loses 6 times in 10. A win pays $7. Expected result: 0.4 × $7 − 0.6 × $5 = $2.80 − $3.00 = −$0.20. That is 4% of the bet.
Place 4 with $5. The 4 wins 1 time in 3 and loses 2 times in 3. A win pays $9. Expected result: ($9 − 2 × $5) ÷ 3 = −$1 ÷ 3, about −$0.33. That is about 6.7% of the bet.
So the cost of a place bet depends on the number. The 6 and 8 are the cheapest, the 5 and 9 are in the middle, and the 4 and 10 are the most costly, even though they feel similar at the table.
What a buy bet changes
A buy bet pays the true odds, but the player pays a commission to the house for that privilege. The commission is commonly 5% of the bet and is often collected up front, whether the bet wins or loses. Some casinos instead take it only on winning bets, which makes the effective edge lower. Practices differ, and so does the rounding of commission, so it is worth asking the dealer.
Buy 4 with $20. The 4 wins 1 time in 3 and pays 2 to 1, so a win returns $40. A loss costs $20. The $1 commission is paid either way. Expected result: ($40 ÷ 3) − (2 × $20 ÷ 3) − $1 = $13.33 − $13.33 − $1 = −$1. That is 5% of the $20 bet, or about 4.76% of the $21 total put up.
Buy 5 with $20. A win pays 3 to 2, or $30. Expected result: 0.4 × $30 − 0.6 × $20 − $1 = $12 − $12 − $1 = −$1. Again 5% of the bet.
The commission is the same 5% whichever number is bought, since the underlying bet is fair. That explains the two-way comparison with place bets:
- On the 4 and 10, buying (5%) is cheaper than placing (about 6.7%).
- On the 5 and 9, placing (4%) is cheaper than buying (5%).
- On the 6 and 8, placing (about 1.5%) is far cheaper than buying (5%).
A buy bet is therefore a reasonable comparison only on the 4 and 10, and then only when the commission is charged at 5% on a bet that is large enough to make the commission worth the trouble. On small bets, a minimum commission of a whole dollar can raise the cost.
Why the extra cost matters
A line bet costs about 1.4% of the amount wagered. Even the cheapest place bet, on the 6 or 8, costs a little more than that, and the other numbers cost several times as much. Players choose these bets because they are simple and quick, not because they are cheap.
Because place bets pay on any roll where the number appears, they can resolve quickly, and the money placed at risk per hour can be substantial. The speed of play therefore matters, since the same percentage edge applied to more bets per hour means a larger expected cost per hour. Hypothetical example: 40 resolved $12 place bets on the 6 in an hour is $480 wagered, and an edge of about 1.5% gives an expected cost of about $7. The same $480 wagered on the 4 at about 6.7% would cost about $32, more than four times as much.
Takeaway
The only bets in craps that pay the true odds are the odds bets, and they must be backed by a bet that has an edge. Place and buy bets approach fair payouts, but they charge for it in the payout shortfall or the commission. Results in any session are uncertain and can run far from the average. Set a limit of truly spare money in advance, and stop when it is reached.