This guide compares two common fractional labels, 7/2 and 5/1, in plain math and in the context of craps pay tables. It explains how to convert fractions to decimal odds and implied probability, shows dollar examples on the same stake, and walks through expected value so you can decide which approach fits your goals. The article is aimed at players who want a clear, methodical comparison rather than a quick slogan. It is useful for beginners learning conversion formulas and for experienced players who want a compact checklist to use when reviewing a table's posted payouts.

5/1 yields a larger payout per win, while 7/2 corresponds to a higher implied chance to win.

Expected value depends on the posted pay schedule and true event probability, not the fractional label alone.

Any Seven and similar proposition bets can carry much higher house edges despite attractive payouts.

Quick answer and what this article covers

Short verdict, craps payouts calculator: 5/1 pays more on a winning hit while 7/2 implies a higher chance to win. Which is better depends on whether you prioritize payout size or win frequency, and ultimately on expected value after you account for the table pay schedule and house edge.

This article separates three lenses you should use when comparing odds: payout per hit, implied probability and expected value. You will get the conversion formulas for fractional odds, worked dollar examples on the same stake, a brief look at how craps pay tables change EV, a house edge illustration using Any Seven, a simple decision framework, and a step-by-step calculator example to use at the table.

Roadmap: first we cover the basic math behind fractional odds and show how to convert 7/2 and 5/1 into decimal odds and implied probabilities. Next we show dollar examples on a common stake, explain expected value and how pay tables affect it, and map the discussion to craps proposition bets. The latter half gives practical checklists, player scenarios and a compact calculator you can use to test a posted payout. The examples make it easy to copy the math and test a table's numbers yourself. For related reading see our blog.

Compute EV before you bet

Use the steps in this article to compute expected value for any posted payout; the examples make it easy to copy the math and test a table's numbers yourself.

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Short verdict

Viewed only as a multiplier, 5/1 is larger: it turns a win into a greater multiple of your stake. Viewed only as a chance to win, 7/2 corresponds to a higher implied probability. Neither label alone tells you about long-term outcome; for that you need expected value and the table's pay schedule.

Why we separate payout, probability and EV

Players often conflate a bigger payout with a better bet. That is a mistake because payout per hit and true win probability move in opposite directions for these fractions. Separating the three lenses keeps decisions objective and helps you pick a bet that matches your goals, bankroll and tolerance for variance.

How fractional odds work: the basic math

Definition first: fractional odds written as a over b, shown as a/b, indicate the profit a for a stake of b. This notation is common in many betting contexts and expresses the ratio between profit and stake rather than the chance directly.

To use these numbers in calculations you commonly convert to decimal odds and to an implied probability. The decimal conversion is decimal odds equals 1 plus a divided by b, and the implied probability is b divided by a plus b. Those are standard conventions you can apply to any fractional odds notation, and they are widely explained in betting math resources Investopedia implied probability. See also Wizard of Odds craps basics.

Convert 7/2 and 5/1 into decimal odds and implied probability

Step-by-step conversion for 7/2: treat 7 as a and 2 as b. Decimal odds are 1 plus 7 divided by 2, which is 1 plus 3.5, giving decimal 4.5. The implied probability is b divided by a plus b, so 2 divided by 9, about 0.2222 or 22.22 percent. These conversions follow the same formula described above and are mechanical to reproduce Fractional odds reference.

Which is better, 7/2 or 5/1 odds?

Neither is inherently better; 5/1 pays more per win while 7/2 implies a higher chance to win. The right choice depends on your objective, the casino's posted pay schedule and the expected value after accounting for true event probabilities and house edge.

Step-by-step conversion for 5/1: treat 5 as a and 1 as b. Decimal odds are 1 plus 5 divided by 1, which is 6.0 as a decimal. The implied probability is 1 divided by 6, about 0.1667 or 16.67 percent. Again, these are straightforward mechanical conversions you can repeat for any fractional odds using the same formulas Investopedia implied probability.

Side-by-side: 7/2 gives decimal 4.5 and implied probability about 22.22 percent, while 5/1 gives decimal 6.0 and implied probability about 16.67 percent. The mechanics do not change with context; what does change is whether the posted payout on a table matches these quoted fractions and how the house edge alters EV.

Payout examples on the same stake: illustrating the difference

Dollar-return examples on a $10 stake make the contrast concrete. For 7/2 the decimal 4.5 applied to a $10 stake returns 4.5 times 10, or $45 total. That is $35 profit plus your original $10 stake returned. The conversion math behind this example follows the fractional-to-decimal rule and the implied probability formula described earlier Investopedia implied probability.

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For 5/1 the decimal 6.0 applied to a $10 stake returns 6.0 times 10, or $60 total. That is $50 profit plus your original $10 stake returned. Comparing the two on the same stake shows clearly that 5/1 yields greater payout per hit, while 7/2 yields a higher chance the bet lands.

$Side by side comparison of odds seven to two and five to one showing fractional decimal implied probability and dollar payouts on a ten dollar stake craps payouts calculator$

Interpreting profit versus total return is important: profit is the amount you gain beyond the stake, while total return includes the stake. When you compute expected value you must use total return for a win and zero for a loss or the posted loss convention the table uses.

Expected value: why payout and probability alone are incomplete

Expected value, or EV, is the average outcome per wager over many identical bets. The basic formula is EV equals probability of win times payout on win plus probability of loss times payout on loss. In most simple single-bet cases that simplifies to EV equals implied probability times total return on a win plus one minus implied probability times zero, which is the same as implied probability times total return on a win.

Crucially, the quoted fractional odds are not the same as EV. Casinos post pay tables and the house edge describes the gap between true probability and the pay schedule. For table games like craps you must use the posted payout and the actual probability of the event to compute EV; otherwise you can be misled by a large nominal payout that does not reflect the true likelihood of winning, which is why checking pay tables is essential Wizard of Odds craps overview.

Craps payout schedules and where fractional odds appear

Which bets in craps use fractional-style payouts? Many single-roll proposition bets and some multi-roll side bets are described with ratio-style payouts that look like fractional odds. However, these posted ratios are essentially pay table entries and can vary by venue, so treat them as fixed payouts for EV calculations rather than market-style odds.

Casinos publish pay tables for single-roll propositions at the table or in the pit, and those tables specify the exact payout you will receive if the roll hits. That means you should always confirm the table's posted payout before comparing a 7/2-like label to a 5/1-like label, because a different pay schedule changes the expected value even if fractional labels look similar Wizard of Odds bets index. Additional pay table explanations can be found at VegasInsider.

Because pay tables are fixed, your task at the table is to translate the posted payout into decimal form, compute the implied probability for the underlying event, and then calculate EV using the true combinatorial probability for the event if you want a precise check of value.

House edge example: Any Seven and why attractive payouts can be costly

A common illustration is the Any Seven bet in craps. Under a standard pay schedule Any Seven pays 4 to 1 even though the true combinatorial probability of rolling a seven with two dice is 6 out of 36, or 1 in 6. The posted payout and the true probability combine to produce a large house edge on the wager, making it costly in expectation compared with lower-edge line bets Wizard of Odds Any Seven.

That example shows a general principle: a payout that looks attractive on its face can hide a poor expected value if the true probability is low relative to the payout. Line bets like pass and come have much lower house edges than many single-roll propositions, so comparing edges is crucial when you are choosing which bets to place in a session.

A simple decision framework: when 7/2 might be better and when 5/1 might be better

Player goals and priorities determine the right choice. If your objective is to maximize the frequency of wins and enjoy steady payouts, favor bets with higher implied probability, which is the side where a 7/2-style label would be preferred. If your objective is to maximize payout per hit and you can accept long losing runs, then the larger multiple like 5/1 fits that preference.

Checklist for choosing: first, confirm the posted pay schedule at the table; second, compute the implied probability from the fractional label or translate the posted payout to decimal; third, estimate EV using the true probability for the event; fourth, size your stake relative to bankroll and variance. These steps keep you from choosing purely on the superficial appeal of higher payouts, and they map back to the conversion rules discussed earlier Investopedia implied probability.

How bankroll and risk tolerance change the right choice

Bankroll sizing matters. A larger bankroll lets you tolerate the variance of low-probability, high-payout bets like a 5/1-style proposition without catastrophic drawdown. Conversely, players with limited bankrolls who prefer more consistent short-term outcomes should favor higher implied-probability bets and smaller relative stakes.

Minimal 2D vector checklist card with icons for decimal conversion slider and expected value balance scale for quick table reference in Funded Plays dark palette craps payouts calculator

Variance affects short-term outcomes dramatically. Even when two bets have similar EV, the one with lower probability and higher payout will have larger variance and longer losing streaks. Use simple bankroll fractions for single-roll speculative bets and avoid risking a large share of your session bankroll on a small number of low-probability wagers.

Common mistakes and pitfalls when comparing odds

Ignoring implied probability is a frequent error. Treating a payout label alone as a measure of value without computing the underlying implied chance will mislead you about likely outcomes and EV.

Another common mistake is confusing profit with total payout. When you calculate EV be explicit whether you are using profit or total return in the arithmetic. Also do not assume the same fractional label corresponds to the same EV across games; always check the posted pay table because casino schedules vary and that changes house edge substantially Wizard of Odds craps overview.

Practical tools and step-by-step calculator example, craps payouts calculator

How to calculate EV for a single bet in three steps: convert the posted fractional payout to decimal if needed, compute the true probability of the event, and apply EV equals probability times total return minus stake times probability of loss where appropriate. A compact formula you can copy is EV per unit stake equals implied probability times decimal payout minus one minus implied probability times 1, which simplifies depending on whether you count stake in the payout. Use the decimal conversion and probability formulas shown earlier when working from fractional labels Fractional odds reference.

Quick table checklist to compute EV for a posted payout

Convert fraction to decimal
Compute true probability
Compute EV
Compare to alternatives
Size stake

Use whole numbers for cents rounding

Worked example for a $10 stake using the same numbers earlier: for 7/2 with decimal 4.5 and implied probability 22.22 percent, EV per $10 if the posted payout truly matched the fraction would be 0.2222 times 45, or about 10.00 in gross expectation before adjusting for true probability differences or house edge. For 5/1 the equivalent is 0.1667 times 60, or about 10.00 in gross expectation under the mechanical fraction interpretation. Those identical gross EVs illustrate why payout and implied probability are complements; the real difference comes from whether the posted payout and true probability align with the fraction or if the house adjusts pay tables.

Note: the arithmetic above uses the mechanical fractional conversion and shows how a larger payout pairs with a lower implied probability. In practice you must replace the implied probability with the true combinatorial probability of the event in craps and use the posted payout to compute a true EV for that table, because many proposition payouts are set in ways that favor the house.

Sample player scenarios: examples choosing based on objective

Conservative player who wants steady wins: a player with limited session bankroll and low tolerance for variance should favor higher implied-probability bets and smaller stakes. That approach accepts smaller profits per hit but reduces the chance of long losing runs and aligns with a steady, risk-managed session plan.

Speculator chasing large payouts: a player who enjoys high variance and can afford large bankroll swings may prefer low-probability, high-payout bets like a 5/1-style proposition. This profile requires a clear plan for stake sizing and acceptance of frequent losses between occasional large wins.

EV-focused player optimizing long-term returns: this player ignores the fraction label and focuses on expected value using the actual combinatorial probabilities and the posted pay table. They will avoid bets where the house edge is large relative to alternatives and choose wagers with lower negative EV or better relative value when available Wizard of Odds craps overview.

Quick checklist and cheat sheet for table play

Items to check before placing a wager: confirm the posted payout, convert fractional labels to decimal, compute or verify the true probability for the event, calculate EV, compare to lower-edge alternatives, and size your stake relative to bankroll. Keep this checklist handy when you walk up to a table.

Short formulas to memorize: decimal conversion equals 1 plus a divided by b, and implied probability equals b divided by a plus b. A practical rounding rule is to keep probabilities to two decimal places for hand calculations and to check precise combinatorial probabilities if you need exact EV numbers for a session Investopedia implied probability.

Conclusion: evaluating "better" as a personal choice backed by math

Recap: 5/1 pays more per win while 7/2 implies a higher chance to win; neither is universally better. Your objective, the posted pay schedule, the true probability for the event and the resulting expected value determine which is preferable in practice.

Next steps: before you wager, confirm the table's posted payout, do the decimal and implied probability conversion, compute EV using the true event probability, and size your stake according to your bankroll and risk tolerance. For more on craps odds and common pay tables see authoritative game guides and pay table analyses to confirm the numbers you will use at the table Wizard of Odds bets index. Also see Funded Plays for more resources.

How do I convert fractional odds to probability?

Divide the denominator by the sum of numerator and denominator. For a/b the implied probability is b divided by a plus b.

Does a bigger payout mean a better bet?

No. Bigger payout per hit comes with a lower implied probability; evaluate expected value using the true probability and pay table before deciding.

Where should I check pay schedules for craps?

Check the table's posted pay table at the casino or use authoritative game resources that list common pay schedules and house edges.

Use the conversion formulas and the EV steps here to test any posted payout before you wager. Confirm pay tables, compute expected value, and size stakes to match your bankroll and objectives. If you want to practice this math without risking cash, consider platforms that let you test prediction and bankroll management skills in simulated challenges.