Infinity Dice Calculator

Your expert tool for calculating probabilities in Infinity the Game

Unopposed Roll Calculator

Enter the parameters for a standard, unopposed roll to determine your chances of success. Results are updated in real-time.

84.0%

Probability of At Least One Success

Key Statistical Outcomes

Formula Used: The probability of at least one success is calculated as `1 – P(All Failures)`. The probability of a single die failing is `(20 – Target Number) / 20`. For multiple dice, this is `((20 – TN) / 20) ^ Number of Dice`.

Detailed Success Probability Table

Number of Successes	Probability

This table provides the exact probability for each possible number of successful dice rolls.

What is an Infinity Dice Calculator?

An infinity dice calculator is a specialized probability tool designed for players of Corvus Belli’s tabletop wargame, Infinity the Game. Unlike generic dice calculators, an infinity dice calculator is built around the game’s unique d20 roll-under system. It allows players to input specific in-game variables—such as the number of dice in a combat roll (Burst), the modified Target Number for a skill, and other situational modifiers—to instantly see the statistical outcomes. This is crucial for competitive play, where understanding the odds can mean the difference between a successful mission and a squad wipe.

This type of calculator is primarily used by players during army list creation and strategic planning. By running scenarios through an infinity dice calculator, a commander can determine the most efficient way to spend their orders, assess the risk of a particular maneuver, and decide whether a high-burst, low-skill model is better than a low-burst, high-skill specialist for a specific job. It removes the guesswork and allows for data-driven decision-making, a hallmark of high-level Infinity play.

Infinity Dice Calculator Formula and Mathematical Explanation

The core of any infinity dice calculator is the binomial probability formula, adapted for a d20 roll-under system. The goal is to calculate the chance of achieving a certain number of successes (k) from a set number of dice rolls (n), where each roll has a specific probability of success (p).

The steps are as follows:

1. Determine Single-Die Success Probability (p): In Infinity, a success is rolling a number equal to or less than the Target Number (TN). Therefore, the probability is `p = TN / 20`.
2. Determine Single-Die Failure Probability (q): The chance of failure is simply `q = 1 – p`, or `(20 – TN) / 20`.
3. Use the Binomial Probability Formula: The probability of getting exactly ‘k’ successes in ‘n’ dice rolls is given by: `P(X=k) = C(n, k) * (p^k) * (q^(n-k))`.

The most important calculation for many players is the probability of at least one success, which is easier to calculate as `1 – P(zero successes)`. The probability of zero successes is `q^n`, making the final formula: `P(at least one success) = 1 – ((20 – TN) / 20)^n`.

Variable Explanations for the Infinity Dice Calculator

Variable	Meaning	Unit	Typical Range
n	Number of Dice (Burst)	Dice	1 – 5
TN	Target Number	Skill Value	1 – 20
p	Probability of one success	Percentage	0.05 – 1.0
q	Probability of one failure	Percentage	0.00 – 0.95
k	Desired number of successes	Successes	0 – n

Practical Examples (Real-World Use Cases)

Example 1: Veteran Fusilier Fireteam

A PanOceania player has a 3-man Fusilier link team. The lead Fusilier is taking an unopposed shot at an enemy in good range. His Ballistic Skill (BS) is 12, and he gets a +3 range bonus and a +1 link bonus, for a final Target Number of 16. His combi-rifle has a Burst (B) of 3.

• Inputs: Number of Dice = 3, Target Number = 16
• Using the infinity dice calculator: The tool shows a 99.2% chance of at least one success. The expected number of successes is 2.4.
• Interpretation: This is an extremely reliable action. The player can be very confident in spending the order to take this shot, as it’s almost guaranteed to force at least one saving roll from the opponent.

Example 2: Haqqislam Specialist Hacking Attempt

A Haqqislam player is trying to complete a mission objective by having their Hafza (WIP 13) make an unopposed WIP roll. There are no modifiers. The Hafza is on his own, so he is rolling 1 die.

• Inputs: Number of Dice = 1, Target Number = 13
• Using the infinity dice calculator: The calculator shows a 65% chance of success.
• Interpretation: This is a reasonably good chance, but far from guaranteed. The player might consider using a Command Token to re-roll a failure. An infinity probability calculator helps quantify this risk, showing that there’s a 1-in-3 chance of failure, which could be critical if it’s the last order of the game.

How to Use This Infinity Dice Calculator

Our infinity dice calculator is designed for speed and clarity. Follow these simple steps:

1. Enter the Number of Dice: In the “Number of Dice (Burst)” field, input the total number of dice you will roll for the skill check.
2. Enter the Target Number: In the “Target Number” field, input the final, modified value your roll needs to be equal to or under. Remember to include all modifiers from range, cover, link teams, and enemy skills beforehand.
3. Read the Primary Result: The large, green-highlighted percentage is your primary answer—the probability of achieving one or more successes.
4. Analyze Key Outcomes: The section below the primary result shows other vital data, such as your chance of scoring a critical hit (rolling your exact Target Number), your chance of complete failure, and the average number of successes you can expect.
5. Review the Distribution Chart and Table: For a deeper analysis, the bar chart and table show the precise probability of every possible outcome, from getting zero successes up to all of your dice succeeding. This is key for understanding variance and planning for best and worst-case scenarios. A good commander always has a backup plan, and this feature of the infinity dice calculator helps you see what those scenarios might be.

Key Factors That Affect Infinity Dice Calculator Results

The results from an infinity dice calculator are highly sensitive to several key factors. Understanding them is vital for effective infinity the game strategy.

1. Target Number (TN): This is the single most important factor. A small +1 or -1 modifier can swing probabilities dramatically. A TN of 10 gives a 50% chance per die, but a TN of 14 increases that to 70%.
2. Number of Dice (Burst / B): Adding more dice provides diminishing returns for achieving *at least one* success but significantly increases the chance of multiple successes. Going from B1 to B2 provides a massive boost, while going from B4 to B5 is less impactful for landing a single hit but greatly increases the average damage output.
3. Critical Hits: The chance of a critical hit (rolling the TN exactly) is always 5% per die (1 in 20). While our infinity dice calculator shows the chance of *at least one* crit, remember that crits have game-altering effects, like cancelling enemy successes in Face-to-Face rolls.
4. Face-to-Face Rolls (FtF): This calculator is for unopposed rolls. An infinity ftf roll calculator is a more complex tool, as you must also account for the opponent’s roll. In an FtF roll, only the highest successful roll matters, and successes can be cancelled, completely changing the math.
5. Order Expenditure: The probability result should be weighed against the cost. Is a 75% chance of success worth your last order? This strategic layer is where the data from an infinity dice calculator becomes tactical wisdom.
6. Saving Throws: A successful hit does not guarantee a wound. The target still gets an ARM or BTS saving throw. Therefore, even with a 95% chance to hit, you must still consider the target’s resilience when assessing the true value of an attack.

Frequently Asked Questions (FAQ)

1. Is this an official Infinity Dice Calculator?

No, this is an unofficial, fan-made tool designed to help players with the game’s probability. It is based on the N4 ruleset but is not endorsed by Corvus Belli.

2. Does this calculator handle Face-to-Face (FtF) rolls?

This specific tool is for unopposed rolls only to keep it fast and simple. Calculating FtF rolls requires more inputs (for the reactive trooper) and a more complex simulation. You would need a dedicated infinity ftf roll calculator for that.

3. Why is the ‘Chance of At Least One Crit’ not just 5% times the number of dice?

Because each roll is an independent event. The correct calculation is 1 minus the probability of *not* rolling a crit on any die. For example, with two dice, the chance of not critting is (19/20) * (19/20). The chance of at least one crit is 1 – (19/20)^2.

4. How should I use the ‘Expected Number of Successes’ value?

This value is an average. It’s most useful for comparing the potential damage output of different weapons or units over time. For example, a B5 weapon with a low TN might have a lower chance to hit than a B2 weapon with a high TN, but its expected successes could be higher, indicating more potential damage if the hits land.

5. Why does the infinity dice calculator have a max Target Number of 20?

In Infinity, a roll of 20 is always a failure, regardless of your Target Number. Even if your modifiers push your skill value above 20, you still fail on a roll of 20, so the effective TN caps out. Our infinity dice calculator respects this rule.

6. Can I use this for other d20 systems?

Yes, as long as the system uses a roll-equal-to-or-under mechanic and doesn’t have other complex rules like exploding dice. This tool is fundamentally a binomial probability calculator for a d20.

7. How are criticals calculated in the probability table?

The main table shows the probability of a number of successes, regardless of whether they are crits or normal successes. A crit is just a special type of success. The “Chance of At Least One Crit” is calculated separately as a key outcome.

8. Where can I find a calculator for ARM/BTS saves?

An infinity arm roll calculator is another specialized tool. The calculation is the same (unopposed roll), but the inputs are different: your ‘Target Number’ would be the enemy’s (Damage – ARM), and you’d roll 1 die.