3 Hands Versus 6
Fold danglers except maybe on the button
This post is part of me trying to find ways of thinking about PLO without being able to count combos. Thanks to
for the seed of this idea.
Poker players love inventing new games because the current ones aren’t confusing & punishing enough. For the record, my favorite invented game is Oklahoma—3 boards, the lowest card on the board disqualifies that row. If 2 rows have the same low card, they are both disqualified. If all 3 rows have the same low card then the dealer gets the pot. You can play it high-only with 2 cards or high-low with 4.
Anyway, I’ve invented a new game—6 Or 3. In this game preflop you get to choose whether you are dealt 6 hands or 3. Villain also chooses whether to get 6 hands or 3. Then you play holdem as usual.
Imagine being out of position with 3 hands versus a villain with 6. How unprofitable is that situation going to be? You’re crushed.
I’m speaking, of course, about playing PLO hands with danglers. At showdown, you get to confidently turn over one of six hands. How many hands are you going to feel good about when you flip them over?
Take AKQ6. AK—sure, I like showing that down, AQ—sure, KQ—likely sure. Broadway straights or top two pair are going to feel good (depending on the board & the action, natch). A6? Nope. K6, Q6? Nope, not unless you have trips & not even then. If I play AKQ6, I only really get to play 3 hands.
Pairs
Pairs are a tradeoff 🙅🏼. You only get to play 4 hands—AAKQ gives you AA, AK, AQ, & KQ. When you hit a set, though, suddenly your hand’s equity shoots up (at least for the moment). Fewer hands, more good equity when you hit.
This perspective helps me understand why low pairs out of position are unprofitable. If I’m playing 4 hands & big money goes in, someone playing in position with 6 hands has me beat. If they are playing 4 hands then their set is better than mine (no set & they fold). If they are playing 6 hands, my equity on straightening boards is nil.
3 of a Suit
Say I have 3 of a suit, how does that affect my equity? A♥️K♦️Q♥️T♦️ gives me straight equity with AK, AQ, AT, KQ, KT, & QT. I also have nut flush equity with hearts and (less with) diamonds. Add another heart—A♥️K♥️Q♥️T♦️—and I have the same straight equity but less profitability with my flush equity. I’m only really playing one flushing combination even thought I hold 3.
In this scenario I’ll hit flushes less often (because villain has fewer flushes—6.4% to 4.8%) & when I do I’ll be paid less often & less (because villain has lower flushes).
To try to get a sense of the magnitude of the flush over flush effect, let’s say there’s 60 bb left in the stacks with an SPR of 1 going into the river. If we each have 2 hearts & villain has the king, let’s assume they’ll call a pot-size bet because I always bluff the stiff ace. 1 chance in 9 of winning 60 bb = 6.6BB expected value. If I have 3 hearts & they’ll call a half pot bet then I have 1 in 8 chances of 30 bb = 3.7bb in EV. That extra heart costs me half of my river equity (based on these assumptions).
An extra card of a suit is even worse with lower rundown hands. Not only do we hit flushes less often, but when we do & we are in flush-over-flush, we’re more likely to be beaten (villain can have fewer small flushes & so proportionally more larger flushes).
I’ve tended to think of 3 of a suit as not that big a deal, but the equity difference is substantial. I can fold 3 of a suit hands unless I have some or all of:
Straight or pair equity
Position
Nut flush
Conclusion
The good news is that I get to decide whether to play 6 Or 3. In position with good sources of equity then maybe 3 is okay, depending on the villain. If villain is always playing 6, I’m probably still in bad shape but lots of villains choose to play 3 (I did for a while), so it’s okay sometimes.