Most matchup numbers online come from simulations. This page goes one step further: the hand below has few enough unknowns that every possible runout can be checked exactly, one by one. Here is the open-ended straight draw against the overpair, enumerated.
| Matchup | Straight draw wins | Overpair wins | Ties |
|---|---|---|---|
| Tc Jd vs As Ac on Qh 9s 4c | 34.2% | 65.8% | 0.0% |
The matchup, defined
An open-ended straight draw is four cards in rank sequence that can complete at either end. An overpair is a pocket pair higher than the board’s top card.
- The straight draw holds Tc Jd. With the Qh and 9s on the board it has nine-ten-jack-queen in sequence: a king completes the king-high straight K-Q-J-T-9, and an eight completes the Q-J-T-9-8 straight, which is queen-high. Eight distinct cards (four kings, four eights) complete it.
- The overpair holds As Ac, a pair of aces above the board’s queen.
- The flop comes Qh 9s 4c.
The model, named
Both hands are known, so 52 - 7 = 45 cards are unseen, and the turn and river can arrive in C(45,2) = 990 possible pairs. All 990 were checked exactly. No simulation noise: the numbers below are the complete count.
The result and the exact decomposition
Checking every runout: the straight draw wins 34.2%, the overpair wins 65.8%, ties 0.0%.
The draw’s wins break into exactly three paths (the enumeration counts each one):
- Straight: 32.7 points. That matches the formula exactly: with 8 straight-completing cards among 45 unseen, the chance that at least one arrives on the turn or river is 1 - (37/45 x 36/44) = 32.7%. When it arrives, the straight always wins here: on a runout that completes the straight, the aces can at best reach two pair or three of a kind, both of which lose to a straight.
- Two pair: about 0.9 points. Rare runouts where the ten-jack pairs up into two distinct pairs while the aces stay below.
- Three of a kind: about 0.6 points. Runouts where the jack or the ten trips up.
Add them: 32.7 + 0.9 + 0.6 = 34.2, the exact total. The overpair takes everything else.
How to use the number
With its premises. If the overpair gets it all in on this flop, it is a two-to-one favorite. From the draw’s side, calling an all-in needs a price of less than 34.2% equity to be profitable in this simplified model, where the all-in closes the betting and both cards come for free. If another bet can happen on the turn, the draw can be priced out of some of its equity, and the calculation must be redone with the new price.
One practical note: 34.2% is the raw two-card equity. It is not the chance of winning any single street’s decision, and it is not a guarantee against folds or raises, which this all-in framing deliberately excludes.
FAQ
Why enumerate instead of simulate?
With 990 possible runouts, an exact count is cheap and has zero sampling error. Simulations approximate the same number; here the number is exact.
Is the straight always good when it completes?
In this matchup, yes. The aces can reach at most three of a kind or two pair here, and every one of those loses to a straight. No runout lets the aces make a full house and still lose to the draw.
Why does the draw win 34.2% if its straight chance is 32.7%?
The straight is the main path but not the only one. About 0.9 points come from two pair runouts and about 0.6 points from trips, all counted in the same enumeration.
Where can I check matchups like this?
A poker odds calculator runs these comparisons on any two hands and board. The hand rankings chart is handy for seeing where each completed hand category lands.
Every number on this page comes from one named model: both hands known, 45 unseen cards, 990 runouts checked exactly.