Poker — set mining for fun and profit and the rule of 15/25/35
In Texas no limit poker, set mining means to play small pocket pairs (22 through 77) in the hope of making a set (3 of a kind) on the flop and winning a big pot.
These hands are a bit of a lottery ticket. If you have 22 say, then the probability of another 2 coming on the flop is 1 in 8.5 (11.8%). You’ll miss far more often than you will hit, and if you miss you’ll have the very modest 4th pair. On the other hand, if you’re lucky a set is a strong hand!
Humans enjoy buying lottery tickets, so set mining with small pocket pairs is fun. But is it profitable?
What is the rule of 15/25/35?
ChatGPT thinks the rule of 15/25/35 is as follows: the rule of 15/25/35 is a guideline for playing pocket pairs in poker, but it is not necessarily a hard and fast rule that should be followed blindly. The rule suggests that if the cost of calling a preflop raise is less than 15% of your stack, you can call with pocket pairs of 66 and higher; if it is less than 25%, you can call with pocket pairs of 55 and higher; and if it is less than 35%, you can call with pocket pairs of 44 and higher.
Don’t always believe the AI though! The idea that you should play weaker (lower) pocket pairs the more you’re being asked to punt off doesn’t make any sense. This is not the rule of 15/25/35.
Here’s a better definition (http://pokerbug.blogspot.com/2012/06/102030-rule-part-1-what-is-it.html): the 15/25/35 rule is a tool that helps you determine whether you should cold-call a raise preflop with a speculative hand. It’s based solely on effective stack sizes (and therefore implied odds). The 3-part rule states:
- You need at least 15x the bet size in implied odds to call with a small/medium pocket pair
- You need at least 25x in implied odds to call with a suited connector
- You need at least 35x in implied odds to call with a non-suited connector or a suited gapper
The logic behind this is that an important requirement for playing small pocket pairs is that the effective stack needs to be large enough to pay you off if you hit pay-dirt. If you call a 3BB raise pre-flop, then unless both you and villain both have at least 3 * 8.5 = 25.5 BB remaining in your stacks, then your call can’t be profitable (as noted above, you’re only going to have a strong hand 1 in 8.5 times).
We need to allow for the possibility that you don’t always win your opponent’s entire stack, and that you’ll occasionally make your set but lose anyway (viz. if you get ‘coolered’ set-over-set). The old heuristic (prior to about 2012) was that you needed to ensure that the effective stack on the flop was 10 times the amount you needed to call. For suited connectors (e.g. 65 suited), the rule of thumb was 20 times, and for unsuited connectors and suited gappers stacks (even more speculative lottery tickets ..) the remaining stack needed to be 30 times the required call.
This was known as the “10/20/30 rule”. The implicit assumption behind this heuristic was that if you didn’t make your set on the flop then you had no hope of winning, but if you did make your set then players were pretty dumb back in the day and would give you their entire stack every time.
Apparently players are a bit more tricky these days, and Bart Hanson has revised the heuritic to now be the “15/25/35 rule”: to play small pocket pairs profitability the effective stack needs to be at least 15 times your call, to allow for the fact that you’ll only win 60% of villian’s stack on average, if you make your set.
Side-bar on deep stacked spots
The 15/25/35 heuristic (to the extent it’s valid at all) would need to be revised when players are very deep stacked — 200 big blinds (BB) and above.
As a general rule in poker, the deeper stacked we are the more concerned we need to be about low probability / high impact events. When you are very short stacked (say you are down to 10 BB), then top pair is the ‘nuts’! You have the best hand most of the time and if someone has a flush, well, you lose 10BB. When you have a medium stack (50BB to 100BB) you need to pay some attention to the probability that someone has that flush, but if you have a flush then if someone else has a higher flush, well, you lose 100BB. However, if you have 200BB+ you really want to have the Ace high flush, the nut flush!
Similarly in the case of set mining, if you have 22 and you make a set with a 100BB size stack, you really shouldn’t worry about the quite unlikely event of being coolered set-over-set. If that happens, nice hand opponent, you lose 100BB. But if you have 200BB+, you need to start folding out those low pocket pairs in case you get caught set-over-set to an opponent’s higher pocket pair also making a set, which will be extremely expensive in this scenario.
Do GTO solvers validate the 15/25/35 rule?
Game theory optimal (GTO) solvers are frustrating beasts, as the results are very dependent on, and sensitive to, the initial conditions you supply viz. the opening ranges and betting tree. Not like chess engines which simply give you the best move in a given position. That’s probably the subject of a separate blog though. My input using the solver GTO+ assumed that:
- IP and OOP both have the top 50% of starting hands (not very realistic, but good enough for illustrative purposes).
- IP called a $5 bet preflop, there is $10 in the pot on the flop, and no rake.
- No donk betting. One possible betting size (50% of pot) with raises been 50% pot bets as well.
- 37 representative flops.
- Stack sizes on the flop of 50BB, 100BB or 300BB.
The main finding is that the 15* rule for low pocket pairs may be too conservative.
The cells highlighted in green are the ones that are theoretically profitable, where the in position (IP) player’s expected value is >$5 (the amount they had to call pre-flop). The rule of 15 would suggest that small pocket pairs (77 and below) are unprofitable at 50BB, and profitable at 100BB and 300BB, whereas the table suggests that the EV is fairly insensitive to stack size (indeed, is slightly better at 50BB than for 100BB) and that only 22 should be folded preflop.
Where does this EV come from? The following chart shows the EVs ranked from best to worse across the flops, for a particular starting hand 5c5h.
Here’s the same information tabulated for the best 15 flops for 5c5h in the 100BB scenario:
The table shows that the best possible flop is 5s2d2c (a full house), for which IP has 98.34% probability of winning at showdown, and an EV of $27.86 (IP wins the $10 already in the pot and a further $17.86 on later betting streets).
Flops #2 to 7 are all flopped sets; IP has equity >90% and EV of about $20. EV falls sharply after that, and the worst flop (not shown above) is AsJs8s, with 29% equity and an EV of $1. The average non-set EV is about $4. It’s worth noting that if IP ‘gives up’ when they miss making a set, then the average EV across all flops is <$5 and 55 becomes an unprofitable pre-flop call.
This is probably the reason for the discrepancy between the 15/25/35 heuristic and the solver output. Low pocket pairs can be profitable to play, but it requires you to extract a lot of value in the 88% of times that you miss making a set, and this is very difficult if you’re not a computer! You will need to call down in uncomfortable spots, and make some heroic bluffs.
Steve Selbrede has looked at a large database of hands, and found that in practice small stakes players lose EV playing low pocket pairs. 22–77 only made money in this sample if it was a limped flop, but not if the pocket pair holder raised preflop or called a preflop raise.
Recommended calling ranges
Despite my own research above, most computer generated opening calling ranges do not favour playing low pocket pairs, particularly in early position. Consider the following recommended opening range for the LoJack (first to act) in a 6-max cash game, 100BB stack sizes.
Per the chart, the Lojack shouldn’t raise with pocket pairs below 66. The Hijack can however widen their range and raise with 66 and 55 as well, Cutoff can include 44 and 33, and only the Button gets to open with all pocket pairs down to 22 (assuming all earlier players folded). Here’s the opening range for the player in best position, the Button:
More complicated opening ranges that propose a mixed strategy, may recommend raising opening small pocket pairs a small percentage of the time. Here, for example, the LoJack again:
The opening frequency is very similar for the pure and mixed LoJack opening ranges (17.0% vs 17.6%), except that now 55 is opened around half the time and 22 is opened 18% of the time. The EV of opening 22 — 55 is worth zero however, by definition, as the solver mixes between folding and opening the betting. If betting was strictly better than folding it would never fold. The solver therefore (presumably) only plays these for defensive board coverage reasons, so that if the board is mostly low cards the opponents can’t run over you, as you may still have a set. 77 has a positive EV and is 100% opened, the EV is minimal (0.05 BB).
Conclusion
I suspect that many recreational players will continue to try to see the flop with their small pocket pairs, despite what the recommended opening ranges and the emperical evidence says, even if they know it’s negative EV. They’re fun to play. They’re a lottery ticket! I will personally only fold a small pocket pair to a large raise or 3-bet pre-flop.
