# A guide to the card neighborhoods

The method comes from W. L. Rocha’s **Distance Equilibrium / Distance Structure** material. We found the local PDF *WSRF No-Limit Hold’em: Interesting Unblackboxing Guide Normally Not Addressed So Very Well*, chapters 25–31, together with `texasholdem/LRO_DISTANCE_EQUILIBRIUM.md`, `texasholdem/lro_player.py`, and `CelestialsPartDeux/wsrf-poker/feature_extractor.py`. Their exact local paths and SHA-256 hashes are preserved in [the training receipt](training/report.json). The private PDFs are not copied into the public website.

## A pocket becomes a map

Number the ranks from 2 = 0 to ace = 12. For hole-card values a and b, form:

1. a
2. b
3. (a + b) mod 13
4. |a − b|

Duplicates are one reference point. The distance between rank values r and q is `min(abs(r-q), 13-abs(r-q))`. A rank belongs to the neighborhood of its **closest** reference. The displayed groups are 0 away, 1 away, 2 away, and 3 or more away. The last group may include larger actual distances; the rank tiles show the exact step count.

For 7♥ 6♥, the values are 5 and 4. References are 5, 4, 9, and 1, corresponding to ranks 7, 6, J, and 3. Every rank can now be placed relative to those anchors. This compact representation makes it easier to see patterns across the deck.

The guide names the combined 0–1 neighborhood “LIKELY.” This game counts its actual size after removing your known cards. It does not substitute one fixed percentage for every pocket. The probability of a group, the probability of a particular card, and the chance of winning a showdown are different quantities.

## The moving-reference variation

The guide also describes LRO, “Last Reference Observed.” Before the flop, use the hole cards. On the flop, use its second and third cards. On the turn, use the third flop card and turn. On the river, use the turn and river. The selector lets you compare this with the hole-card map. Only already revealed cards are used.

## What the three games let you explore

- **Distance Draw:** play a full heads-up Hold’em hand, compare your neighborhood map with the adviser, and reflect on the size and timing of a choice. You can watch a model and nudge its caution.
- **River School:** estimate showdown share or the price of a final all-in call. Exact answers appear after your choice; the optional adviser is a trained approximation.
- **Pocket Studio:** choose two cards from six. The four unchosen cards return to the unseen deck. Build a strong pocket, leave room for a turn improvement, or reverse the challenge and seek the weakest one.

The method is presented as a useful way to investigate and communicate card relationships. Our [fresh training and ablation results](TRAINING.md) report what the experiments establish, including where additional playing edge was not established. The game does not award automatic strength bonuses for being near a reference rank.

## Hold’em rules used

Two hole cards, a three-card flop, one turn, and one river; your best five of the seven available cards determine the showdown. The button posts the small blind, acts first preflop, and acts last after the flop. Betting implements checks, calls, folds, full minimum raises, short all-ins, uncalled-chip refunds, and split pots. See Wikipedia’s [Texas hold’em overview](https://en.wikipedia.org/wiki/Texas_hold_%27em) and [heads-up poker overview](https://en.wikipedia.org/wiki/Heads-up_poker).

This is a static play-chip table with no clock. A hand stays in the open page; a fresh match resets the stacks. The three stack variations are 25, 100, and 200 big blinds. The bot has no privileged card inputs.