Bankroll size, variance, return, and risk of ruin are the four variables that determine how a video poker session plays out and how long a player's money lasts.

Each concept affects the others: a higher-variance game requires a larger bankroll; a lower return increases the probability of ruin; a bigger bankroll reduces session risk even when return and variance stay the same.

Understanding how these four elements interact is the foundation of informed video poker play.

The Four Elements Defined

What is Return in Video Poker?

Return is the percentage of total money wagered that a video poker game pays back to the player over time. A 95% return means that for every $100 played through the game, $95 is returned to the player as winnings on average, giving the casino a 5% edge.

This is a long-run average calculated over hundreds of thousands of hands. In the short term, return can vary dramatically. A single royal flush can push a session's return far above the theoretical percentage; an extended run without significant wins can push it well below. Over enough play, actual results tend to converge toward the calculated figure.

What is Variance in Video Poker?

Variance in video poker is a measure of how widely a player's results fluctuate around the expected return. It describes the spread between wins and losses in a given period of play.

Low-variance games produce winning hands frequently and in relatively consistent amounts, so wins and losses tend to balance out over shorter sessions. Jacks or Better is a typical example.

High-variance games concentrate most of the return in rare, high-paying hands, such as four-of-a-kind bonuses or the royal flush. That means long losing stretches punctuated by occasional large wins. Deuces Wild and Double Bonus Poker are typical examples.

What Is a Bankroll in Video Poker?

A bankroll is the total amount of money a player sets aside specifically for gambling. It represents the funds available to sustain play, whether held as cash, stored in a casino safe, or available as a casino line of credit.

In practical terms, bankroll size determines how long a player can remain in action and how much variance they can absorb before running out of funds.

What Is Risk of Ruin in Video Poker?

Risk of ruin is the probability that a player will lose their entire allocated bankroll. It’s expressed as a percentage and can never reach zero, since any finite bankroll carries some chance of being exhausted.

Risk of ruin exists in two forms:

• Session risk of ruin: the probability of losing the bankroll defined for a single session, day or trip.
• Lifetime risk of ruin: the probability of eventual total loss across unlimited play.

On a personal level, risk of ruin also reflects a player's tolerance for loss. A risk-tolerant player might accept a 20% risk of ruin, meaning they are comfortable losing their entire bankroll one in every five sessions. A more cautious player might set their acceptable risk at 1% (one in 100).

How Return Affects Bankroll Size and Risk of Ruin

Return is the single most important factor in determining lifetime risk of ruin. For any game with a return below 100%, lifetime risk of ruin is always 100%. Given enough play, a finite bankroll will eventually be exhausted. Only a game with a return above 100% gives a player any chance of avoiding eventual ruin.

For session play, the relationship is more gradual:

• Return close to 100%: bankroll requirements are lower, and session risk of ruin is reduced because expected losses per session are small.
• Return significantly below 100%: bankroll requirements increase, and session risk of ruin rises, because the player loses more per session on average.
• Return above 100%: bankroll requirements can be minimal, since the long-term expectation is positive, and session risk of ruin is low.

How Variance Affects Bankroll Size and Risk of Ruin

Variance directly affects how much bankroll a player needs to survive the natural swings of a game, even when return is held constant.

Low-variance games produce smaller fluctuations in both directions, so a smaller bankroll is sufficient to ride out losing stretches. High-variance games produce deeper and longer losing runs before the large winning hands arrive, requiring a larger bankroll to remain solvent.

Risk of ruin rises with variance. Because high-variance games expose the player to greater short-term losses, the probability of the bankroll hitting zero before a recovery is higher, even if the game's return is identical to a lower-variance alternative.

How Bankroll Size Affects Risk of Ruin

Bankroll size has the greatest direct impact on the session risk of ruin. A larger bankroll provides more reserves to absorb losing streaks and survive long periods of variance, reducing the probability of ruin in a given session.

For lifetime risk of ruin, bankroll size is secondary to return. No bankroll, however large, eliminates the risk of lifetime ruin when the return is below 100% – it only delays the inevitable.

Risk of ruin is calculated using three inputs: bankroll size, return, and variance. Several calculators are available online.

For games with a return below 100%, only session calculations are possible. For games with a return above 100%, lifetime calculations are also available. Most calculators work in both directions, either outputting a risk percentage from a given bankroll, or calculating the bankroll required to hit a target risk level.

Key Takeaways

• For any return below 100%, lifetime risk of ruin is always 100%, so eventual ruin is mathematically certain.
• Higher variance requires a larger bankroll to achieve the same risk of ruin as a lower-variance game with identical return.
• The session risk of ruin decreases as bankroll size increases; the lifetime risk of ruin is determined primarily by return.
• Risk of ruin can be calculated using three inputs: bankroll size, return, and variance.