The odds of flopping a pair with an upaired starting hand is 29% or 1 in 3.45
Pair – Quick Recap
Definition of a One Pair –
Holding two cards of identical rank.
Example – AAXXX
A Pair in Hold’em can be where we hold two cards of identical rank in our starting hand. It can also be if we pair one of our hole cards with one on the board, or we play a Pair on the board. The best Pair in Hold’em is Aces.
Odds of Making a Pair on the Flop
The odds of making a Pair on the flop depend on the type of hand we have.
Assuming two unpaired hole cards, our odds of making a Pair on the flop is 29%.
However, our overall odds of making a Pair with any starting hand is actually 31.1%.
So, why the discrepancy?
Naturally, some of our starting hands will already be pocket Pairs! This means we have guaranteed odds to make a Pair or better. Ignoring any Pairs on the board (we’ll still count our holding as One-Pair in this case), here is the breakdown for pocket-Pairs.
The Pocket Pairs - Breakdown
Weak Pair (below second card on the board) = 41.3%
Mid Pair (above second card on the board) = 23.3%
Over Pair (above top card on the board) = 23.3%
Trips and better = 12%
Naturally, the likelihood of the different types of Pair depends on the exact pocket Pair we hold, since stronger Pocket Pairs flop Over Pairs more frequently.
For example -
KK – Flops an Over Pair 67.3% of the time.
JJ – Flops an Over Pair 36.2% of the time.
88 – Flops an Over Pair 10.2% of the time.
Unpaired Holdings – Breakdown
Bottom Pair = 8.98%
Middle Pair = 10%
Top Pair = 10%
Once again, it heavily depends on the starting hand.
Odds with AKo
Bottom Pair = 0%
Middle Pair = 0%
Top Pair = 29%
Odds with 98o
Bottom Pair = 4.9%
Middle Pair = 15.6%
Top Pair = 8.45%
Odds with 32o
Bottom Pair = 26.9%
Middle Pair = 2.02%
Top Pair = 0%
It really should not come as a surprise that high-card hands are more likely to make top Pairs, mid-card hands are more likely to make Mid Pairs, and low-card hands are more likely to make bottom Pairs.
It’s actually impossible for AKo to flop a second or bottom Pair, think about it!
Odds of Making a Pair on the Later Streets
Let’s imagine we have entirely missed the flop with an unpaired hand and want to know our chances of picking up a Pair on either the turn or river.
At this stage, five cards are already out (the flop plus our two hole cards). There are 47 cards left in the deck, six of which give us a Pair.
Our chances of hitting a Pair on the turn are hence 6/47 = 0.12767 or about 12.8%.
Going from turn to river, there is one less card in the deck, meaning our chances of spiking one Pair on the river with an unpaired hand on the turn are 6/46 = 0.1304 or about 13%
Note that there is a slightly higher chance of spiking from turn to river due to the smaller pool of available cards we are drawing from.
Finally, let’s calculate our chances of hitting going from flop until the river. We do this by calculating our chances of not hitting and then subtracting from 100%.
Chances of not hitting one Pair on the turn = 41/47
Chances of not hitting one Pair on the river = 40/46
Probability of missing on both streets = (41/47) * (40/46) = 0.7586 or about 76%
Our chance of hitting going from flop to river is hence (100% - 76%) about 24%.
Implied Odds Analysis of a Pair
Making a One Pair type holding does not generally guarantee us good implied odds. There are numerous ways that our opponent can improve on the later streets, so we should not assume that we are in for a massive payout when hitting.
On the contrary, one-pair type holdings (especially the lower Pairs) are notorious for generating reverse implied odds. Even if we hit, there is a decent chance we’ll lose additional chips on the later streets if our opponent improves to a better hand.
The good news is that one-pair hands (when made with the board) have 5 outs to make either Two Pair or Trips, and these types of holdings perform reasonably in the implied odds department.
Pocket Pairs have minimal improvement potential, but they occasionally make very strong disguised hands (i.e. sets) which carry excellent implied odds.
Basic Strategy Advice
Don’t go crazy with one Pair, especially when playing with 100bb stacks or more. These hands are relatively easy to be outdrawn and typically should only look to play small or medium-sized pots.
The exceptions are high top Pairs with good kickers and over-pair type hands which may occasionally be good enough to play for stacks, depending on the exact situation.
The odds of flopping a Pair with an unpaired starting hand
Hitting a pair from flop to turn when holding air
Hitting a pair from turn to river when holding air
Hitting a pair from flop to river when holding air