Play Under and Over 7 Online

What Is Under and Over 7?

Under and Over 7 is the simplest bet you can make with two dice. The layout has three boxes: Under 7, Exactly 7 and Over 7. You put chips on one or more of them, two dice are rolled, and the total decides everything at once. A total of 2 to 6 pays the Under box, 8 to 12 pays the Over box, and a 7 pays the middle box at longer odds. There is no shooter’s hand, no point, no come-out and no strategy in the roll; every bet is a one-roll bet and the table is swept clean after each throw.

It is also, once you look at it, one of the most instructive gambling games in existence. The three boxes look balanced and the payouts look generous, and yet the operator keeps one chip in every six wagered no matter which box you choose. If you want to understand what a house edge is before you tackle the layout of Craps or the choice of main in Hazard, a hundred rolls of Under and Over 7 will teach you.

A Short History of Under and Over 7

Under and Over 7 belongs to the world of the carnival midway and the traveling fair rather than the casino floor. The game needs nothing more than a painted cloth or board with three boxes, a pair of dice and a cup or a small chute to roll them down, and it can be run by one operator with one hand on the money. That made it a fixture of American fairgrounds, church bazaars and “casino nights” through the twentieth century, alongside the wheel of fortune, the crown-and-anchor cloth and the three-dice cage of Chuck-a-Luck. Two-dice over-under betting is old and appears in many places; the specific three-box layout with 7 in the middle is the form that took hold in the United States.

Its appeal to operators was never a secret. Mid-century writers on gambling and carnival games grouped it with the layouts whose advantage came not from crooked equipment but from the payout table: the boxes are honest, the dice are honest, and the operator still keeps 16.67 percent of everything bet. That is nearly twelve times the edge on a craps Pass Line, which is why the game never became a serious casino table. Where it does appear in casinos and online, it is usually as a novelty or a side bet, sometimes under names such as Over Under or Easy Over Under, with slightly different payouts on the 7.

The game survives because it is fast, obvious and social. A crowd can see the dice, the boxes and the money, everyone understands the result instantly, and the operator can run a roll every fifteen seconds. Those are exactly the qualities that make it a good first dice game to learn the mathematics on.

Under and Over 7 Rules

Equipment

• Two six-sided dice.
• A layout with three boxes: Under 7, Exactly 7 (often just “7”) and Over 7.
• Chips to bet with. Our game uses 5-, 25- and 100-chip pieces.

Object

To predict whether the total of the two dice will be under seven, exactly seven or over seven.

How a Round Works

1. Place bets. Put chips on any box or boxes. You may bet several boxes at once, although as the strategy section explains, you should not.
2. Roll. The two dice are thrown and their pips added.
3. Settle. Every box is decided by that one total: - 2, 3, 4, 5 or 6: Under 7 wins, the other two boxes lose. - 7: Exactly 7 wins, Under and Over lose. - 8, 9, 10, 11 or 12: Over 7 wins, the other two boxes lose.
4. Clear. Winning bets are paid and returned, losing bets are collected, and the layout is empty for the next roll.

Payout Table

This is exactly what the game on this page pays.

“4 to 1” means a winning 10-chip bet on the 7 receives 40 in winnings and keeps its 10. Some layouts phrase the same payout as “5 for 1,” meaning the 10 comes back as part of 50; check which convention a live game uses, because “5 for 1” is not the same as “5 to 1.”

Worked Examples

• 25 on Under 7, roll 3-2 = 5. Under wins. You receive 25 in winnings and your 25 stake back: 50 to the bankroll.
• 25 on Under 7, roll 4-3 = 7. Under loses. The 25 is gone. A 7 is nobody’s friend on the Under and Over boxes.
• 10 on Exactly 7, roll 6-1 = 7. The 7 box pays 4 to 1: you get 40 plus your 10 back, 50 in total.
• 100 on Over 7, roll 6-6 = 12. Over wins even money. 200 comes back. The size of the total does not matter; a 12 pays the same as an 8.
• 25 on Under 7 and 25 on Over 7, roll 5-4 = 9. Over wins 25, Under loses 25. Net zero. Roll 3-4 = 7: both lose. Net minus 50. You have constructed a bet that cannot win.
• 25 on Under, 5 on 7, 25 on Over, roll 1-6 = 7. The 7 pays 20 and returns 5; Under and Over lose 50. Net minus 25 on the roll where your “coverage” hit.

The Odds: 36 Rolls and a 16.67 Percent Edge

Two dice produce 36 equally likely combinations. There is one way to roll a 2 (1-1) and one way to roll a 12 (6-6), but six ways to roll a 7 (1-6, 2-5, 3-4, 4-3, 5-2, 6-1). Laid out in full:

Add the columns and the three boxes come out as 15, 6 and 15 ways out of 36. The distribution is symmetric around 7, which is why Under and Over are priced identically, and the 7 in the middle takes a full sixth of all rolls away from both of them.

Now price each bet. Bet one chip on Under 36 times, once for each combination:

• You win 15 times and collect 15 chips.
• You lose 21 times (the six 7s and the fifteen Over totals) and pay 21 chips.
• Net: minus 6 chips over 36 bets, or 16.67 percent of everything wagered.

Over is the mirror image with the same result. Bet one chip on Exactly 7 thirty-six times:

• You win 6 times at 4 to 1 and collect 24 chips.
• You lose 30 times and pay 30 chips.
• Net: minus 6 chips over 36 bets, again 16.67 percent.

All three boxes cost the same one chip in six. To see how heavy that is, compare it with other two-dice bets: the Pass Line in Craps costs 1.41 percent, a craps Field bet 5.56 percent and the notoriously bad Any 7 proposition, which is the same bet as Exactly 7 here, 16.67 percent. Under and Over 7 is a whole table made of Any 7.

Change the payout on the 7 and the edge on that box moves fast. At 5 to 1 the seven bet collects 30 and loses 30 over 36 rolls: zero edge, a genuinely fair bet. At 3 to 1 it collects 18 against 30 lost, a 33.3 percent edge, the worst common payout on any dice layout. Under and Over cannot be fixed by changing their payouts short of paying more than even money, which no operator does; some layouts instead push Under and Over bets on a 7, which cuts their edge to zero as well.

What 16.67 percent does to a bankroll

An edge of one chip in six means that for every 100 chips you bet, you expect to lose about 16.7. Betting 25 a roll, that is a little over 4 chips per roll, so a 1,000-chip bankroll lasts on average about 240 rolls. The number of rolls survived is exactly what our game records as your score, and the swings around that average are large: a lucky player can double up in fifty rolls, an unlucky one can be gone in a hundred. Over thousands of rolls the average always wins.

Under and Over 7 Strategy

Honest strategy for a game where every bet has the same negative expectation is short. These tips are about losing slowly and understanding what you are doing, not about beating the game, because there is no way to beat it at 4 to 1.

1. Bet one box, never two

Under and Over together is a guaranteed loss: any non-7 roll is a wash and a 7 loses both stakes. Adding the 7 box does not rescue it. Every extra box you cover adds another 16.67 percent bite to your total action without changing a single probability. Pick one box per roll.

2. Under and Over are interchangeable; so is the 7

All three boxes have exactly the same expectation. The only real difference is variance: Under and Over win 41.7 percent of rolls at even money, the 7 wins 16.7 percent at 4 to 1. If you want a smooth, slow decline bet Under or Over; if you want big swings bet the 7. Neither is smarter.

3. Bet small

Because the edge is fixed per chip wagered, the only lever you control is how many chips you wager. At 5 a roll a 1,000-chip bankroll lasts about 1,200 rolls on average; at 100 a roll it lasts about 60. Our score is rolls survived, and the way to maximize it is to bet the minimum on one box every time.

4. Ignore the history strip for prediction

The last fifteen totals are shown because they are interesting, not because they help. Dice have no memory. After five Under rolls in a row, the next roll is still 15 in 36 Under, 6 in 36 seven, 15 in 36 Over. Betting Over because Under is “due,” or Under because it is “hot,” changes nothing but your mood.

5. If the 7 ever pays 5 to 1, bet only the 7

This is the one situation in which the game has a good bet. At 5 to 1 the 7 box is exactly fair, while Under and Over remain at 16.67 percent. A carnival or casino-night layout that advertises “7 pays 5 to 1” is offering the only free roll on the table. Make sure it is 5 to 1 and not 5 for 1.

6. Progressions do not work

Doubling after a loss on Under (a Martingale) does not change the edge; it just moves the loss into a rare, catastrophic streak. Six straight losses on Under happen 4 percent of the time (0.583 to the sixth power), and with a 5-chip start the seventh bet in the sequence would be 320 chips. With a 1,000-chip bankroll, a run like that arrives well before you have made a meaningful profit from all the small wins.

7. Set a roll budget

Decide how many rolls or how many chips you want to spend and stop there. The pleasure of the game is its speed and clarity; its arithmetic is relentless. Treating your 1,000 free chips as a ticket for a certain number of rolls is the right frame.

Common Mistakes

• Reading 4 to 1 as a bonus. It is priced to give the house the same one-in-six edge as the even-money boxes, not more, not less.
• Hedging Under with Over. The most common beginner move and a guaranteed loser; see the worked examples.
• Believing a 7 is rare. It is the single most common total, one roll in six, and it is the reason the Under and Over boxes are not 50-50.
• Confusing “5 for 1” with “5 to 1.” The first returns 50 on a 10-chip bet including the stake (4 to 1 in disguise); the second returns 60.
• Chasing after a losing streak. Every roll is independent, and a bigger bet is a bigger expected loss.

Variants and House Rules

• 7 pays 5 to 1. Offered on some layouts and in some online versions; it makes the 7 box a fair bet and leaves the other two unchanged. We use the standard 4 to 1.
• 7 pays 3 to 1. Found on the stingiest carnival cloths; the edge on the 7 box rises to 33.3 percent.
• Push on 7. A player-friendly rule in which Under and Over bets are returned rather than lost when a 7 rolls. This removes the house edge on those two boxes entirely, so it is rare.
• Under or Over including 7. Some games move the 7 into one side (for example, Over means 7 to 12) and adjust the payout; the arithmetic changes completely, so read the layout.
• Bar layouts with 2 and 12 bonuses. Occasional versions pay extra on a 2 or 12, borrowing from the craps Field bet.
• Casino Over Under. Table-game and online versions dress the same three-box structure with side bets on doubles or specific totals; those side bets carry their own, usually large, edges.

If you enjoy the two-dice distribution itself, Sevens Out turns the 7 into the number that ends your turn, and Chicago has you chase every total from 2 to 12 in order. For a three-box layout with real strategy, try Sic Bo.

Glossary

• Under / Over: The two even-money boxes, covering totals 2 to 6 and 8 to 12.
• Exactly 7 / the 7 box: The middle box, paid at 4 to 1 in the standard game.
• X to 1 / X for 1: “To” means winnings on top of a returned stake; “for” means the stake is included in the amount returned.
• House edge: The percentage of all money wagered that the operator expects to keep in the long run; 16.67 percent here.
• Ways: The number of dice combinations that make a given total, out of 36.
• Hedge: Betting opposite outcomes at once; in this game, a way to lose on purpose.
• Rolls survived: Our score, the number of rolls you make before your bankroll can no longer cover a 5-chip bet.

Play Under and Over 7 Online on Dice.now

The game at the top of this page is free play with virtual chips only. You start with 1,000 chips. Pick a chip size (5, 25 or 100), click Under 7, Exactly 7 or Over 7 to add chips to that box (you may cover more than one box, though the strategy section explains why you should not), and click Roll. Under and Over pay 1 to 1 and Exactly 7 pays 4 to 1, every box is settled and cleared on each roll, and Clear bets returns anything on the table before you roll. The strip of the last fifteen totals is colored blue for under, yellow for seven and green for over, the payout log explains every settlement, and the status bar shows your bankroll, the chips on the table, the rolls you have survived and your best run on this device. When your bankroll drops below 5 chips the game ends and Play again resets you to 1,000. There is no real money, no account and nothing to download. Pick a box and roll the dice.