Is Bottom Set more profitable than Top Set?
Does a Set of Twos get paid off more often than a Set of Aces? Barry Carter found out so you don't have to.
In the self study series Barry Carter shows you how he tried to solve a poker problem then consults a coach or solver to get feedback on his method.
Most of the time in this series I try and share a lesson I have learned in poker while trying to fix a leak. Sometimes, however, I just explore something I am curious about.
Today I wondered if having middle or bottom set is actually more profitable than top set. I have a working theory that, although top set is stronger, bottom set is more profitable because you unblock top pair hands, so you will get paid off more often. We all know how tough it is to get the money in the middle when you flop a Set of Aces, after all, but flopping a Set of Twos on an Ace high flop is a dream scenario.
When the gap between cards is wide
I tried this on a number of different flops and preflop ranges. Here is one example, it's A93 rainbow, LJ opens, BTN calls, 40BB effective. This is the LJ post-flop range, from GTO Wizard:
These are the stats for the three sets - we are looking at Equity, Expected Value and Equity Realisation:
| Hand | Equity | EV | EQR |
|---|---|---|---|
| Set of Aces | 97% | 16.47 BBs | 238% |
| Set of Nines | 96.5% | 17.18 BBs | 250% |
| Set of Threes | 93.5% | 15.38 BBs | 231% |
No surprise that Aces has the highest equity because it can obviously beat the other two sets. As suspected Nines is a more profitable hand overall, it makes 17.18 BBs on average and has equity realisation of 250%, compared to the 16.47BBs and 238% of Aces. This confirms what I thought, a Set of Nines has more Ax top pair hands that will pay it off.
Bottom Set, however, is less profitable than Aces and realises equity less well. This surprised me, and I am guessing that it is because this hand can get counterfeited more easily if the flop comes running AA/99/ or A9. It also will be because pocket pairs between Kings and Fours can all spike a better set on the turn or river.
When it's mostly a high card flop
Carrying on the experiment, this is the same set of stats, but on an AQ9r flop:
| Hand | Equity | EV | EQR |
|---|---|---|---|
| Set of Aces | 94.5% | 15.72 BBs | 234% |
| Set of Queens | 94.1% | 16.60 BBs | 248% |
| Set of Nines | 92.9% | 15.80 BBs | 240% |
Both Queens and Nines are more profitable than Aces here and realise equity much better. They have much fewer worries about being counterfeited or a pocket pair spiking a set on the turn or river.
When it's a low flop
This is the same set of stats for a 652r flop:
| Hand | Equity | EV | EQR |
|---|---|---|---|
| Set of Sixes | 93.9% | 17.35 BBs | 260% |
| Set of Fives | 92.5% | 16.27 BBs | 248% |
| Set of Twos | 90.5% | 14.98 BBs | 233% |
This was very interesting. The EV and EQR both decrease in a much more linear way than the other examples. Top set is better on all three metrics than second set, which is much better than bottom set.
This is likely because the EV of all these hands likely come from overpairs, as well as high cards spiking a pair on the turn or river. There isn't much 6x or 5x for top pair to pay off a Set of Twos anyway.
So the takeaway here is that when top pair is quite high up, having 2nd or third set is very profitable because of the greater number of one pair hands that will pay it off. However, when there is a significant gap between the top and bottom card, the profitability diminishes because of the risk of getting outdrawn by the middle portion of Villain's range. When top pair is quite low, it's best to have top set.
All of this is academic because flopping a set does not happen often in poker and you should be prepared to go broke with it most of the time when it does.
Previous self study articles
- Playing against disconnected players
- Overbetting with Ace King
- Why do we check back with Range Advantage?
- Why do I turn top pair into a bluff?
- How I use ICMIZER
- How wide can we go with Antes?
- Why can we bluff missed straight draws more than missed flush draws?
- How to play a strong underpair on a wet board
- How to play a 15BB stack
- How often does Villain have an Ace?
- Why do we not check/raise with the nut flush draw?
- Why do we bet small on the turn?
- When do we open shove the flop?
- The difference between SB and BB defends in single raised pots
- The difference between SB and BB 3-bet pots
How do you study away from the tables? Let us know in the comments:
