PICKEM POKER ODDS
Pickem Poker Odds: Probabilities and Hand Frequencies
Pickem Poker odds can mean exact completion odds for one visible decision, long-run final-hand frequencies, or the chance of short-session events such as several nonpaying hands in a row.
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The Exact Decision Sample Space
At the historical two-stack Pickem Poker decision point, two fixed cards are visible on the left. Choice A and Choice B are also visible as the exposed card on top of each three-card stack. All four exposed cards are known and unavailable, so 48 unseen cards remain. The selected three-card partial hand then receives two hidden completion cards.
Order does not matter because J♣ followed by 10♣ produces the same final five-card holding as 10♣ followed by J♣. That is why each visible side has 1,128 legal unordered completions, not 2,256 ordered draws.
Three Different Numbers
This page focuses on probability and hand frequency. For the full expected-return and house-edge interpretation, use the RTP and House Edge guide.
Why the Fourth Visible Card Matters
The alternate exposed choice card is not merely ignored. It is known information, and it is removed from the 48-card unseen deck before the selected side is evaluated.
Royal completion still available
Fixed cards: A♣ K♣. Choice A: Q♣. Choice B: 7♦.
For the A♣ K♣ Q♣ side, the only Royal Flush completion is J♣ 10♣. That is exactly 1 completion out of 1,128, or 0.088652%, which is 1 in 1,128.
Royal completion blocked by the alternate choice
Fixed cards: A♣ K♣. Choice A: Q♣. Choice B: J♣.
The Q♣ side cannot complete a Royal Flush because J♣ is already exposed as the alternate choice and is unavailable. The J♣ side cannot complete a Royal Flush because Q♣ is already exposed as the alternate choice and is unavailable.
A three-card Royal category does not automatically guarantee a nonzero Royal Flush completion probability in every exact four-card deal.
Conditional Odds Example: Visible Three of a Kind
Suppose the fixed cards are 9♠ 9♥, Choice A is 9♦, and Choice B is K♣. For the selected 9♠ 9♥ 9♦ side, all 1,128 legal completions divide cleanly into three result types.
One nine remains. Pairing that remaining nine with any of the other 47 unseen cards produces Four of a Kind. Eleven unaffected non-nine ranks have four cards available, creating 11 × C(4, 2) = 66 Full House completions. Only three kings remain because K♣ is the other exposed choice, creating C(3, 2) = 3 additional Full House completions. Total Full Houses: 66 + 3 = 69. Every other completion leaves Three of a Kind.
How the Published Full-Game Sample Space Is Built
The historical full-pay reference distribution uses this analytical sample space:
= 1,326 × 1,225 × 1,128
= 1,832,266,800 analyzed deal-completion outcomes
This treats the two fixed cards, two visible choices, and two selected completion cards as unordered pairs. It is not a count of every possible physical eight-card screen layout. The strategy decision is applied to the visible fixed and choice cards before the selected side's completion is scored.
Full-Pay Final-Hand Distribution
The table below is a published historical full-pay optimal-play reference, not a claim that any current casino offers this table. Frequencies are calculated from exact combination counts, not by inverting rounded display probabilities.
Swipe horizontally to view all columns.
| Final result | Published combinations | Probability | Approximate frequency | Return contribution |
|---|---|---|---|---|
| Royal Flush | 5,208 | 0.000284% | Approximately 1 in 351,818 | 0.3411% |
| Straight Flush | 47,652 | 0.002601% | Approximately 1 in 38,451 | 0.6237% |
| Four of a Kind | 776,112 | 0.042358% | Approximately 1 in 2,361 | 5.0830% |
| Full House | 4,317,408 | 0.235632% | Approximately 1 in 424.4 | 4.2414% |
| Flush | 5,842,860 | 0.318887% | Approximately 1 in 313.6 | 4.7833% |
| Straight | 9,281,412 | 0.506554% | Approximately 1 in 197.4 | 5.5721% |
| Three of a Kind | 54,994,848 | 3.001465% | Approximately 1 in 33.32 | 15.0073% |
| Two Pair | 113,761,152 | 6.208766% | Approximately 1 in 16.11 | 18.6263% |
| Pair of Nines or Better | 418,444,104 | 22.837509% | Approximately 1 in 4.379 | 45.6750% |
| Nonpaying hand | 1,224,796,044 | 66.845944% | Approximately 2 in 3 hands | 0% |
| Total | 1,832,266,800 | 100% | 99.9531% |
Royal Flush is separated from Straight Flush. Pair of Nines or Better means the final hand's highest category is exactly one qualifying pair; Two Pair, Three of a Kind, and stronger hands are not also counted in the pair row. Nonpaying hands include low pairs and no-pair hands.
Exact Hit Frequency
Hit frequency: 607,470,756 / 1,832,266,800 = 33.1540557%
Average interval: 1 / 0.331540557 = 3.016 hands per paying result
About one paying result per 3.016 hands on average does not mean that every third hand pays. A paying-hand frequency is a long-run average over the stated model.
What Most Paying Hands Actually Are
Pair of Nines or Better accounts for approximately 68.883% of all paying final hands. Pair of Nines or Better, Two Pair, and Three of a Kind together account for approximately 96.663% of all paying final hands.
Those three common categories contribute 79.3086 percentage points of the 99.9531% total theoretical return. The Royal Flush contributes only 0.3411 percentage points of return despite its enormous payout. That does not make the Royal unimportant; it shows the difference between a rare high payout and frequent small results.
What "1 in 351,818" Really Means
The Royal Flush count is 5,208 outcomes out of 1,832,266,800 analyzed outcomes. That gives 1,832,266,800 / 5,208 = approximately 351,817.74, displayed as approximately 1 in 351,818. Do not derive this by inverting the rounded six-decimal probability.
Under independent hands and the stated full-pay optimal-play model, the probability of at least one Royal Flush in N hands is 1 - (1 - p)^N, where p = 5,208 / 1,832,266,800.
Playing the average waiting time does not create a 100% chance. At roughly one average interval, the chance is about 63.2%. A Royal Flush is never due, and these figures describe the historical model, not a prediction for one player.
Nonpaying Streaks
Using the published nonpaying probability q = 0.668459443, the probability that the next N hands are all nonpaying is q^N.
These are probabilities for a specified block beginning now. They are not the probability of observing at least one such streak somewhere inside a much longer session. A 33.15% hit frequency does not prevent ordinary clusters of losses.
Standard Deviation and Variance
Using the full-pay outcome distribution and per-credit payout values of 1200, 239.8, 120, 18, 15, 11, 5, 3, 2, and 0, the mean gross return is 0.999531 wager units. The independently calculated standard deviation is approximately 3.8737 wager units per hand.
At a fixed five-credit wager, that corresponds to approximately 19.37 credits of one-hand standard deviation. Standard deviation is not expected loss; it measures the spread of possible one-hand results. Rare large payouts strongly affect this number, so short-session realized return can be far from the theoretical mean.
Why Small Samples Mislead
A few dozen or a few hundred hands mainly test short-term outcomes. They do not verify the game's long-run RTP. Even 10,000 hands have only about a 2.8% chance of containing a Royal Flush under the reference model.
Practice records are useful for tracking decision accuracy. They are not reliable evidence that a published long-run distribution is true or false. No finite sample guarantees that observed results will match the theoretical distribution exactly. Larger samples generally reduce relative sampling variation, but substantial deviations can still occur.
Paytable and Strategy Dependence
The displayed final-hand distribution assumes the historical full-pay schedule and its stated optimal strategy. A reduced payout can change which visible choice has the higher EV, and strategy changes can alter the final-hand distribution.
The physical deck probabilities remain the same, but the optimal decision rule can change. Do not transfer this frequency table blindly to a short-pay version. Use the Paytable Guide, RTP and House Edge, Strategy Guide, and Free Trainer together.
Common Odds Misunderstandings
- Inverting 0.000003 does not produce an accurate Royal frequency because that probability was rounded.
- A three-card Royal has a 1-in-1,128 Royal completion only when both required cards remain unseen.
- A 33.15% hit rate does not promise a payout every three hands.
- A paying-hand frequency is not the same as RTP.
- A rare hand can contribute less total return than a common small hand.
- The hidden cards revealed after the decision cannot be used to judge what was knowable beforehand.
- Two choices in the same strategy-chart row need not have identical exact odds.
- A low pair is a nonpaying final result, even though a low pair can be a strong three-card partial strategy choice.
Sources and Methodology
Published reference: historical full-pay combination counts, probabilities, payout contributions, and the 99.9531% total were checked against Wizard of Odds Pick ’em Poker tables, Henry Tamburin’s Pick ’Em Poker explanation, and Beating Bonuses Pickem Poker reference and calculator context.
PickemPoker.com calculation: percentages from combination counts, reciprocal frequencies, hit frequency, paying-hand shares, Royal cumulative probabilities, nonpaying-streak probabilities, standard deviation, and the visible-three-of-a-kind 1,128-completion example were independently recalculated.
Live status: no historical source proves current casino availability or the live paytable at any casino.