Drawing Odds in Video Poker

Video poker drawing odds describe the possible replacement-card outcomes after you decide what to hold. They are essential to strategy, but they are not strategy by themselves. A hold with more “outs” can still be worth less than a hold that hits less often, because correct play depends on the payout-weighted value of every possible final hand under the exact paytable.

The draw begins with 47 unseen cards

In a standard 52-card video poker game, the initial deal shows five cards. Once those five are known, 47 cards remain unseen from the player’s perspective.

If you discard one card, there are 47 possible one-card replacements. If you discard two, order does not matter: the number of possible two-card draws is the combination C(47,2), or 1,081. The counts grow quickly:

Those combination counts are the foundation of exact video poker analysis. A computer can enumerate every possible replacement, classify the resulting five-card hand and apply the paytable. The best hold is the one with the highest average return across that complete set.

A one-card flush draw shows the basic idea clearly

Suppose your five-card deal contains four hearts and one card of another suit, and you decide to hold the four hearts.

A standard deck contains 13 hearts. You can already see four of them, so nine hearts remain among the 47 unseen cards.

Flush-completing probability = 9 / 47 ≈ 19.15%

That also means about 80.85% of the replacement cards are not hearts.

The 9/47 calculation is useful, but it is not yet a strategy answer. Some of those nine hearts can produce a straight flush or royal flush depending on the ranks held. Some non-hearts can produce a paying high pair. The exact expected value is the average of all 47 final payouts, not simply the chance that the most obvious draw completes.

Straight draws can have four outs, eight outs, or something more complicated

A simple open-ended four-card straight such as 5-6-7-8 can usually be completed by any 4 or any 9. If none of those ranks is already visible among the discarded card, that is eight helpful cards out of 47, about 17.02% for the straight itself.

An inside straight such as 5-6-8-9 needs a 7, normally four cards out of 47, about 8.51%.

But video poker hands often overlap. If the four-card straight is also four to a flush, some cards can make a straight flush. If one of the apparently helpful cards is already present as the fifth dealt card that you plan to discard, the unseen count changes. If the game contains wild cards, the entire classification changes.

So “eight outs” is a starting count, not a universal rule to memorize without looking at the actual five cards.

The discarded cards are known unavailable cards, not cards that return to the draw pool

A common counting mistake comes from thinking that discarding a card puts it back into the deck. In standard video poker analysis, the five dealt cards are already known. Cards you discard are not available as replacements on that draw.

That is why the denominator remains 47 after the initial deal, not 48, 49 or 52.

For example, if your fifth dealt card is one of the ranks that would otherwise help a straight, that specific card is already seen and cannot arrive as a replacement. Exact draw counting has to respect all five original cards, including the cards you do not hold.

“Hit frequency” groups many different final hands together

Players often ask how often a hold “hits.” That question needs a definition.

If you hold four to a flush in Jacks or Better, does a replacement that pairs a high card count as a hit? It produces a paying pair but does not complete the flush. What about a card that completes a straight flush? That is more than the original draw. What about a non-paying low pair in a game where low pairs return nothing?

A strategy engine avoids this ambiguity. It counts each final hand by category and payout.

A useful table for one hold might look conceptually like this:

The expected value comes from multiplying counts by returns, summing them and dividing by the total number of possible draws.

Expected value decides between competing holds

Consider a hand that contains both four to a flush and three high cards. The flush hold may have an obvious 9/47 completion probability. The three-high-card hold may create many different ways to form pairs, two pair, trips, straights or a royal-related result depending on the exact ranks and suits.

You cannot correctly compare the two holds by saying “nine flush outs is more than the number of cards that make a pair.” Their possible payouts differ and their outcome sets overlap in different ways.

For any hold H:

EV(H) = Sum of payouts over all possible draws after H / Number of possible draws after H

If the wager is one credit, EV can be expressed in credits returned per credit bet. If the displayed paytable pays a royal differently at five credits, the analysis must use the wager level actually being considered.

That is why expected value of a hold is the natural companion to drawing odds.

Four to a royal is powerful because payout weight can dominate frequency

A four-card royal draw has only one exact card among the 47 unseen cards that completes the royal flush. That is roughly a 2.13% royal-completion probability on the next card.

That sounds small, and it is. Yet four to a royal is often an extremely valuable draw because a max-coin royal payout is enormous relative to ordinary hands. The other 46 replacement cards can also produce lesser paying results depending on the ranks and game.

This is a perfect example of why the most frequent improvement is not automatically the best hold. A rare result can carry enough payout weight to change the decision.

It is also why four to a royal should be learned as an expected-value concept rather than as a “royals are due” superstition.

Two-card and three-card draws require combinations, not simple out counts

When you draw two cards, there are 1,081 unordered replacement pairs. A strategy calculator evaluates every pair once. Counting one card at a time and multiplying approximate percentages can easily double-count or miss overlapping outcomes.

Three-card draws are even more complex: C(47,3) = 16,215 combinations. A hand may reach the same final category through many rank-and-suit paths.

This is why exact strategy charts are usually generated by exhaustive enumeration rather than by mental arithmetic. The player does not need to memorize 16,215 combinations. The player needs to understand what the chart represents: a complete comparison of all legal holds under a specified game and paytable.

Paytable changes can reverse a close decision

Drawing probabilities come from the deck and hold. Their value comes from the paytable.

Suppose two legal holds have similar outcome distributions. If one hold produces flushes more often and another produces high pairs more often, reducing the flush payout can reduce the first hold’s EV enough to change the correct decision.

Wild-card games make this effect even stronger because hand rankings and payouts differ from Jacks or Better. A Deuces Wild chart cannot be imported into Bonus Poker simply because both games use five-card draws.

Correct video poker strategy is therefore always game-and-paytable specific.

Paytable labels can hide important return differences

Even within one named family, two machines can use different schedules. “Jacks or Better” is not a complete mathematical description. A 9/6 schedule and a weaker schedule reward full houses and flushes differently, which changes overall return and can change borderline hold decisions.

The same is true for Bonus Poker, Double Bonus, Double Double Bonus and wild-card variants.

Before using a strategy chart, verify the exact rows on the machine. Why paytables matter is not an advanced side topic; it is part of the strategy input.

Near misses do not alter the next draw

Drawing odds can create strong emotional reactions because the player can see how close the final hand was. Four to a royal followed by the wrong card feels different from a random losing hand even when both return zero.

That visual closeness does not make the next royal more likely. Each new hand is generated under the game’s approved random process. The correct use of drawing odds is prospective: given these five cards now, which hold has the highest value?

The previous ten misses are not part of that calculation.

For the related misconception, see video poker due to hit myth.

A detailed one-card example shows how overlap must be handled

Suppose you hold 9♥-10♥-J♥-Q♥ and discard an unrelated low card. There are nine hearts left, so nine replacement cards complete a flush or better. But those nine are not all equivalent:

• K♥ completes a straight flush;
• 8♥ completes a straight flush;
• the remaining hearts complete ordinary flushes unless another higher category applies;
• any K of another suit completes a straight;
• any 8 of another suit completes a straight.

If you simply count “nine flush outs plus eight straight outs,” you double-count K♥ and 8♥ because they belong to both sets. The correct category count assigns each final hand to its highest paying category once.

This overlap problem is one reason hand analyzers are so useful for learning.

Casino math does not need to change after you press Draw

The casino earns its edge through the approved game rules, paytable and player errors where strategy matters. It does not need to selectively deny a flush because too many flushes have recently hit.

From the player’s perspective, the useful controls are visible:

• choose the stronger paytable when available;
• use the correct strategy chart for that paytable;
• avoid importing draw logic from a different variant;
• keep denomination and total action within bankroll;
• do not turn a missed draw into evidence that the machine is “cold.”

The deck mathematics already explains why correct draws miss so often.

The practical formula is count first, value second

For a one-card draw:

Probability of a specific outcome set = Helpful unseen cards / 47

For multi-card draws:

Number of combinations = C(47, cards drawn)

For a hold:

Expected Return = Σ(Probability of final hand × Paytable return for that hand)

For the full game under a strategy:

RTP = Long-run expected credits returned / Credits wagered

The sequence matters. First enumerate what can happen. Then apply the paytable. Only then compare holds.

A high hit rate can be comforting and still be mathematically inferior. A low-frequency draw can be correct because its rare outcomes pay enough to compensate. Drawing odds tell you the shape of the opportunity; expected value tells you what it is worth.

Continue with hand frequency tables, why optimal strategy is not intuitive, four to a flush, four to a straight, three to a royal, and four to a royal. These pages turn the combination math into actual hold decisions.