The Mathematics of Deuces Wild

Deuces Wild represents one of the most fascinating variants in video poker, offering the only widely-available game with a theoretical return exceeding 100% when played with perfect strategy. The four wild cards fundamentally change both the mathematics and the strategy.

Full-Pay Deuces Wild (100.76%)

The legendary "Full-Pay" Deuces Wild offers a theoretical return of 100.76% with perfect play—meaning the player has a mathematical edge over the house.

The Full-Pay Paytable

HandPayout (per coin)Natural Royal Flush800Four Deuces200Wild Royal Flush25Five of a Kind15Straight Flush9Four of a Kind5Full House3Flush2Straight2Three of a Kind1

What Makes It Special

The 100.76% return depends on several factors:

Natural Royal pays 800:1 (same as Jacks or Better)

Four Deuces at 200:1 provides significant return

Wild Royal at 25:1 hits more often than natural

Low-tier hands (Flush, Straight) pay minimally

The Impact of Wild Cards

Having four deuces as wild fundamentally changes game mathematics:

Frequency Shifts

Hands occur at dramatically different rates:

HandJoB FrequencyDeuces Wild FrequencyThree of a Kind7.44%28.45%Four of a Kind0.24%4.91%Straight1.12%5.78%Flush1.10%2.48%Full House1.15%2.13%

Strategic Implications

The wild cards create counterintuitive plays:

Never hold a single deuce alone—always look for other combinations

Pairs become less valuable—deuces create three-of-a-kind opportunities

Drawing for wilds changes expected values

Natural hands sometimes trump wild ones

Strategy Complexity

Deuces Wild requires significantly more complex strategy than Jacks or Better:

Hands by Number of Deuces

The optimal strategy depends heavily on how many deuces you're dealt:

Four Deuces: Hold all—guaranteed 200:1 payout

Three Deuces:

Hold with any Wild Royal

Otherwise, hold three deuces alone

Two Deuces:

Complex hierarchy of possible draws

Four of a Kind or better—hold

Four to Royal—draw one

Otherwise—hold deuces alone

One Deuce:

Most complex decision tree

Multiple penalty card situations

Dozens of exception cases

No Deuces:

Similar to JoB but with different priorities

Four to Royal beats all pairs

Low pairs much less valuable

Strategy Card Complexity

While JoB strategy fits on a simple card, Deuces Wild requires:

Five separate strategy hierarchies (0-4 deuces)

Dozens of exception cases

Penalty card awareness

Practice for reliable execution

Variance Characteristics

Deuces Wild has distinctive variance properties:

Lower Overall Variance

Despite high jackpot pays, the frequent Three of a Kind (28.45%) creates stability.

Jackpot Distribution

The Royal Flush contributes less to RTP because:

Natural Royal hits ~1 in 45,000 hands

Wild Royal hits ~1 in 555 hands

More return comes from frequent hands

Bankroll Requirements

For recreational play, Deuces Wild is friendlier than high-variance games like Double Double Bonus, requiring smaller bankrolls for equivalent risk of ruin.

Short-Pay Degradation

Casinos modify Deuces Wild paytables to create house edge:

VersionKey ReductionRTPFull PayNone100.76%15/9/4Four of a Kind to 499.73%15/9/4 (NSUD)Not-So-Ugly Ducks99.73%15/8/4Straight Flush to 898.91%13/4Various reductions97.58%10/4Common casino version94.82%

Finding Full-Pay

True full-pay Deuces Wild has become rare:

Once common in Las Vegas

Now typically found only in select casinos

Higher denominations more likely to offer full pay

Some online casinos still offer it

Advantage Play Implications

The 100.76% RTP makes Deuces Wild attractive for advantage players, but with caveats:

Practical Considerations

Strategy mastery required: Errors quickly eliminate the edge

Casino awareness: Casinos know these games favor players

Availability: Finding full-pay is increasingly difficult

Complementary play: Slot club benefits can enhance returns

Historical Context

In the "golden age" of advantage play (1990s-2000s), full-pay Deuces Wild was a staple:

Professional players could expect hourly profit

Combined with slot club points for additional value

Casino comps added further return

Represented true professional gambling opportunity

Why Casinos Offered It

The question arises: why offer a game with negative house edge?

Recreational player errors: Most players don't achieve 100.76%

Traffic generation: Attracts players who also play other games

Slot club offset: Points cost is factored into game economics

High-denomination focus: Better pays at quarters or dollars

Competition: Once standard, removing it risked losing customers

The gradual elimination of full-pay Deuces Wild marks the end of an era when advantage play was a viable profession using video poker alone.