Notes from the felt · June 2026

Four-card equity, the part hold'em players skip.

Hold'em equity is a number. PLO equity is a shape. A bot that doesn't see the shape is just guessing in a tuxedo.

Here's the thing about PLO. You're dealt four cards. You must use exactly two from your hand and exactly three from the board. That "exactly two" rule is doing more work than people realize, and it's why so many things you know from no-limit stop being true the moment you sit down at a 4-card table.

Why do PLO equities run so close?

In NLH, the strongest preflop matchup — aces vs. random — sits around 85%. In PLO, the strongest possible four-card holding is double-suited A-A-K-K (or similar rundowns with the right backup). Against a random four-card hand, it runs about 70%. Against a tight opening range, you're closer to 60%. That compression is structural: more cards means more hands realize more equity. Nobody is ever drawing dead by the turn the way they often are in hold'em.

For a bot, this matters in two ways. First, the value of a "made hand" decays. Holding the current nuts on the flop in PLO is worth dramatically less than holding the current nuts in NLH — because someone is far more likely to have a 13-card draw that's flipping or ahead. Second, the variance of decisions goes up. Two close calls in a row in NLH might be -2bb either way. In PLO they're closer to -8bb either way. Your bot can be right on average and still tilt the bankroll badly if its equity model is even slightly off.

How does a bot actually compute it?

Three approaches live in the wild, in roughly increasing order of how much they cost to run:

1. Monte Carlo rollout. Deal random runouts a few thousand times, count wins and ties, divide. Cheap, noisy, fine for preflop bucketing.
2. Exhaustive enumeration on truncated boards. For postflop spots with two streets to come, you can enumerate all remaining board cards exactly. Slower per spot but deterministic, which matters when your bot needs to be consistent across re-runs.
3. Abstraction + lookup. The serious solver-style approach. Cluster hands into equity buckets (often hundreds of thousands of them), precompute a strategy, look up the bucket at runtime. The hard part isn't the lookup — it's building an abstraction that doesn't lose information you care about, like redraws.

What about redraws and blockers?

If your bot collapses a hand to a single equity number, it loses the information that decides 80% of close turn spots: the redraw profile. A wrap straight with two extra outs to a flush is not the same as a wrap dry, even when their flop equity against a single hand is identical — because their equity against the opponent's continuing range is wildly different.

Blockers in PLO are denser too. With four cards, you can hold two of the four cards your opponent needs for the nut flush. Holding the bare ace of clubs on a three-club board blocks one nut-flush combo; holding the ace and another club blocks all of them. A bot that doesn't track blocker density gets bluff-caught by hands it should fold and folds hands it should call.

The takeaway

Four-card equity isn't a bigger number. It's a richer object — a distribution over runouts, with redraw and blocker structure baked in. The bots that survive in PLO games are the ones that model that object honestly, not the ones that ported their NLH equity calculator and added two more card slots.

The other half of the story — where these bots actually live and what the ecosystem around them looks like — is over here. Or back to the homepage.