Omaha Two HorizonsLANTERN MIXED TABLES

LANTERN MIXED TABLES

Omaha Two Horizons

A high road. A low road. A chance to scoop.

Lars Rocha

♦

Sixteen pages of play, patterns,
worked hands, and discoveries.

A dedicated WSRF companion.
Your pace. Your possibilities.

Omaha Two HorizonsDiscoveries

Discoveries

Your first invitation

Explore both directions, count distinct low ranks, and look for hands that can earn the whole pot.

Use exactly two private cards and three board cards for each five-card hand. High and low may use different combinations. A qualifying low contains five distinct ranks from ace through eight. A qualifying low shares the pot with high; otherwise high receives the whole pot.

Take your seat with Fern and familiar AI company. The room offers heads-up or six-seat play, automatic next hands, adjustable pace, practice peeks, a visible WSRF tree, a Monte Carlo playground, and a notebook that keeps your place. Choose Gentle company while learning the rhythm, then explore Seasoned or Sharp whenever you feel ready.

Start by naming the game and the legal five-card construction. Then count the players still active and read the amount needed to continue. Those small observations give the coach’s estimate a useful setting. The worked pages that follow preserve their cards, assumptions, and numerical receipts so you can explore the same question again.

Omaha Two HorizonsDiscoveries

Discoveries

A rhythm you can follow

The room keeps the chip arithmetic close to the action.

At this tableHow it works
Starting stack2,000 free play chips at each seat
SeatsHeads-up or six seats
Blinds / antesSmall blind 10; big blind 20
BettingSmall increment 20; large increment 40.
Street rhythm20 on preflop/flop; 40 on turn/river in limit play.
Limit capFour full bets per street, including the opening bet.
Short all-insA full increment reopens raising under this room’s house rule.
Split-chip orderThe high half receives an odd split chip. Tied shares award odd chips clockwise from the stored button.

These are the room’s declared house settings. A short stack contributes its available chips, and side pots keep each contribution matched to the players eligible for it. A returned unmatched contribution stays separate from a contested pot. Opening the Coach or Options panel holds the action while you explore.

A fixed amount makes the price easy to follow. Use the current street’s increment and the chips already in front of you when reading a raise-to amount.

Omaha Two HorizonsDiscoveries

Discoveries

See the five-card construction

The cards make the idea concrete.

A♣2♦K♥K♠

The community board

3♣4♦5♥Q♠9♦

Your four private cards offer six pairs to try. On the river, the five community cards offer ten three-card selections. The evaluator checks the sixty legal combinations, keeping the best result for the direction being compared. The illustration gives one concrete path through that menu.

Try covering the worked answer and pointing to the five chosen cards. Then name one different final card that would invite a new construction. A concrete card change is a useful way to connect imagination with the rules.

Omaha Two HorizonsDiscoveries

Discoveries

A little map of possibility

One away, two away, three away—and a clear reference frame.

23456789TJQKA♦DISTANCE MAP

LIKELY · 10/13 near ranks

Moving references: 5 · A · 4 · J

48 unseen cards.
Bucket counts: 14 / 23 / 7 / 4

Distance mean 1.02 · SD 0.88

The pocket map uses your first two dealt cards. In an Omaha hand these are an explicit pair of anchors inside the four-card pocket; the hand evaluator still explores all legal two-card choices. In a stud hand they are the first two private cards. The moving map uses the latest two community cards or your latest two exposed stud cards once they are available.

The map’s circular ranks run from 2=0 to A=12. The reference expressions use the two anchors, their sum modulo thirteen, and their absolute difference. Near means distance zero or one. Seven or more near ranks gives LIKELY; six or fewer gives UNLIKELY. Both labels receive balanced examples in each newly trained model.

Known-card counts include your own cards and every publicly exposed card, including cards shown by a folded stud opponent. That keeps the remaining physical-card counts connected to what you can actually observe. The game-specific hand ranking and the map each describe their own part of the hand.

Omaha Two HorizonsDiscoveries

Discoveries

A few habits worth keeping

Let the game’s special character guide your attention.

See two complete constructions

Build the high hand and the low hand as separate five-card selections. Each construction uses two private cards and three board cards. The same private pair may work for both, or a different pair may serve each direction. Writing both selections out makes the split-pot structure tangible.

Count distinct ranks for low

A low draw grows through distinct ranks. Start with the low ranks you hold, then look for distinct board ranks that complete a five-card selection. If the board repeats a rank already central to your plan, take a fresh look at all six private pairs. Another pair may provide a useful route.

A scoop brings the horizons together

A scoop means receiving the whole contested pot. In a split game that can happen through winning both halves, or through high when the hand finishes with high taking the entire award. A hand with meaningful high and low potential creates several ways to reach that satisfying result.

Give each share its own denominator

Suppose a 200-chip pot splits into two 100-chip halves. One player wins high alone, while two players tie low. The high winner receives 100 and each low winner receives 50. The tied low is a quarter of the whole pot. Your WSRF target uses these fractions directly, so a split is represented by the share actually earned.

Omaha Two HorizonsWorked hands

Worked hands

Worked hand 1 · Omaha 8

Follow the cards, then discover the estimate.

YOUR CARDS
5♥A♥3♥9♣
COMMUNITY BOARD

The flop is ahead.

StreetOpponentsPotCallMade hand
preflop13010High card · Low possibilities ahead
A view of the spotValue
Moving rank zoneLIKELY · 10/13
WSRF pot share54.8%
Monte Carlo share55.2%
95% sampling interval54.0% – 56.5%
Whole-pot frequency39.3%
Sample count4,096
ActionPolicy score
Call 100.273
Fold0.000
Raise to 40-0.161

This independently generated teaching hand preserves your own cards and every exposed card, then samples the remaining cards uniformly. Fractional ties and split pots contribute the share actually earned. The interval describes sampling uncertainty under that model; the forest’s estimate is a separate learned prediction.

Compare the action scores with the call price and the active field. They express the explicit betting policy’s use of the learned share, rather than a fitted chip-return forecast. Opening a tree lets you follow the card features that helped produce the share estimate.

Study fixture omaha8-1 · 4,096 samples · Independent namespace mixed-guide-independent. Cards, seeds, and measurements are preserved in the study receipt.

Omaha Two HorizonsWorked hands

Worked hands

Worked hand 2 · Omaha 8

Follow the cards, then discover the estimate.

YOUR CARDS
2♠K♥6♦A♠
COMMUNITY BOARD
4♦A♥6♠
StreetOpponentsPotCallMade hand
flop514020Two pair · Low possibilities ahead
A view of the spotValue
Moving rank zoneLIKELY · 10/13
WSRF pot share23.4%
Monte Carlo share26.3%
95% sampling interval25.5% – 27.2%
Whole-pot frequency3.3%
Sample count4,096
ActionPolicy score
Call 200.084
Fold0.000
Raise to 40-0.243

This independently generated teaching hand preserves your own cards and every exposed card, then samples the remaining cards uniformly. Fractional ties and split pots contribute the share actually earned. The interval describes sampling uncertainty under that model; the forest’s estimate is a separate learned prediction.

Compare the action scores with the call price and the active field. They express the explicit betting policy’s use of the learned share, rather than a fitted chip-return forecast. Opening a tree lets you follow the card features that helped produce the share estimate.

Study fixture omaha8-2 · 4,096 samples · Independent namespace mixed-guide-independent. Cards, seeds, and measurements are preserved in the study receipt.

Omaha Two HorizonsWorked hands

Worked hands

Worked hand 3 · Omaha 8

Follow the cards, then discover the estimate.

YOUR CARDS
T♣A♥A♣3♦
COMMUNITY BOARD
K♣2♠8♦4♠
StreetOpponentsPotCallMade hand
turn1400One pair · 8–4–3–2–A
A view of the spotValue
Moving rank zoneLIKELY · 9/13
WSRF pot share56.2%
Monte Carlo share76.8%
95% sampling interval76.0% – 77.7%
Whole-pot frequency54.6%
Sample count4,096
ActionPolicy score
Check0.005
Bet 40-0.153

This independently generated teaching hand preserves your own cards and every exposed card, then samples the remaining cards uniformly. Fractional ties and split pots contribute the share actually earned. The interval describes sampling uncertainty under that model; the forest’s estimate is a separate learned prediction.

Compare the action scores with the call price and the active field. They express the explicit betting policy’s use of the learned share, rather than a fitted chip-return forecast. Opening a tree lets you follow the card features that helped produce the share estimate.

Study fixture omaha8-3 · 4,096 samples · Independent namespace mixed-guide-independent. Cards, seeds, and measurements are preserved in the study receipt.

Omaha Two HorizonsWorked hands

Worked hands

Worked hand 4 · Omaha 8

Follow the cards, then discover the estimate.

YOUR CARDS
8♥5♥3♦K♦
COMMUNITY BOARD
A♠T♣2♥2♦5♣
StreetOpponentsPotCallMade hand
river516040Two pair · 8–5–3–2–A
A view of the spotValue
Moving rank zoneUNLIKELY · 6/13
WSRF pot share7.5%
Monte Carlo share2.8%
95% sampling interval2.5% – 3.2%
Whole-pot frequency0.0%
Sample count4,096
ActionPolicy score
Fold0.000
Call 40-0.150
Raise to 80-0.475

This independently generated teaching hand preserves your own cards and every exposed card, then samples the remaining cards uniformly. Fractional ties and split pots contribute the share actually earned. The interval describes sampling uncertainty under that model; the forest’s estimate is a separate learned prediction.

Compare the action scores with the call price and the active field. They express the explicit betting policy’s use of the learned share, rather than a fitted chip-return forecast. Opening a tree lets you follow the card features that helped produce the share estimate.

Study fixture omaha8-4 · 4,096 samples · Independent namespace mixed-guide-independent. Cards, seeds, and measurements are preserved in the study receipt.

Omaha Two HorizonsWorked hands

Worked hands

Worked hand 5 · Omaha 8

Follow the cards, then discover the estimate.

YOUR CARDS
7♥A♣J♥J♣
COMMUNITY BOARD

The flop is ahead.

StreetOpponentsPotCallMade hand
preflop13010High card · Low possibilities ahead
A view of the spotValue
Moving rank zoneLIKELY · 9/13
WSRF pot share55.4%
Monte Carlo share60.0%
95% sampling interval58.7% – 61.3%
Whole-pot frequency45.7%
Sample count4,096
ActionPolicy score
Call 100.279
Fold0.000
Raise to 40-0.151

This independently generated teaching hand preserves your own cards and every exposed card, then samples the remaining cards uniformly. Fractional ties and split pots contribute the share actually earned. The interval describes sampling uncertainty under that model; the forest’s estimate is a separate learned prediction.

Compare the action scores with the call price and the active field. They express the explicit betting policy’s use of the learned share, rather than a fitted chip-return forecast. Opening a tree lets you follow the card features that helped produce the share estimate.

Study fixture omaha8-5 · 4,096 samples · Independent namespace mixed-guide-independent. Cards, seeds, and measurements are preserved in the study receipt.

Omaha Two HorizonsWorked hands

Worked hands

Worked hand 6 · Omaha 8

Follow the cards, then discover the estimate.

YOUR CARDS
T♣K♣J♣5♠
COMMUNITY BOARD
Q♠4♦T♠
StreetOpponentsPotCallMade hand
flop514020One pair · Low possibilities ahead
A view of the spotValue
Moving rank zoneLIKELY · 10/13
WSRF pot share18.0%
Monte Carlo share18.7%
95% sampling interval17.6% – 19.7%
Whole-pot frequency13.7%
Sample count4,096
ActionPolicy score
Call 200.030
Fold0.000
Raise to 40-0.317

This independently generated teaching hand preserves your own cards and every exposed card, then samples the remaining cards uniformly. Fractional ties and split pots contribute the share actually earned. The interval describes sampling uncertainty under that model; the forest’s estimate is a separate learned prediction.

Compare the action scores with the call price and the active field. They express the explicit betting policy’s use of the learned share, rather than a fitted chip-return forecast. Opening a tree lets you follow the card features that helped produce the share estimate.

Study fixture omaha8-6 · 4,096 samples · Independent namespace mixed-guide-independent. Cards, seeds, and measurements are preserved in the study receipt.

Omaha Two HorizonsPractice

Practice

Six discoveries to keep

Affirmative questions, with the reason beside each answer.

Omaha Two HorizonsTraining

Training

Meet your new forest

Actual pytoolzx / WSRF fitting, with the measured results beside it.

GameSelected fitPositionsTraining showdownsTest MAE
Omaha 8full6,144786,4326.04 pp

Each game receives 6,144 training positions, with 128 independently sampled showdowns at every position. Six equally represented pools combine opening, middle, and closing play with LIKELY and UNLIKELY moving-map labels. Private and public suit counts, exposed-board strength, and rank geometry give the forest a richer view. The fitted object is pytoolzx.wsrf.WSRFRegressor, and pytoolzx.indexrng.Index supplies independently named seed streams.

Compact and full forests are compared on 768 validation positions. The smaller validation error chooses the serving forest before a fresh 1,536-position test is evaluated. Validation labels use 384 samples; test labels use 512. MAE is the average absolute difference in estimated pot share, expressed here in percentage points.

Game / seats / practice styleHandsBB / 100Approx. 95% interval
Omaha 8 / 2 / calling51243.233.6 to 52.7
Omaha 8 / 2 / random51252.533.1 to 72.0
Omaha 8 / 2 / selective51242.926.2 to 59.6
Omaha 8 / 6 / calling1,53632.017.8 to 46.1
Omaha 8 / 6 / random1,53645.126.3 to 64.0
Omaha 8 / 6 / selective1,53651.117.2 to 85.0

The complete-hand benchmark rotates the trained policy through every seat of each fresh deck. Its intervals use deck averages to respect the relationship between seat rotations. These named local practice styles define the scope of the measurements. The full receipt preserves every game, table size, and opponent row.

Omaha Two HorizonsPractice

Practice

Make the table your own

A practice path you can enjoy returning to.

Begin with a comfortable rhythm

Choose Gentle company and a relaxed pace. Leave automatic next hands enabled if you enjoy a continuous session, or choose each new hand yourself. The panel controls hold your exact place whenever you open an explanation.

Give one hand a question

Choose a question you can inspect: can this card complete the construction, can this price be expressed as a pot share, or can the tree show which input it used? The worked answer becomes useful when you can point to its reason on the table.

Explore with a practice peek

A peek makes the opposing cards visible for your exercise. The model continues to use its own cards and public observations, so its estimate stays comparable before and after your peek. The notebook marks that hand as practice and preserves the result.

Let the forest take a turn

The WSRF partner option lets the trained adviser play your seat using the explicit betting policy. Pause on a street that interests you and open the tree. Watch mode is a way to explore the model’s choices; your own chair is ready whenever you switch back.

Keep a story to return to

Download a notebook from Options. It includes the deal and action sequence needed for exact replay, along with stacks, funding, completed hands, and HUD totals. Restore it in the same game and table size. A saved story can make the next visit feel like a continuation.

Omaha Two HorizonsReference

Reference

Your pocket reference

Useful terms and a path to the underlying work.

TermMeaning at these tables
Pot shareThe fraction of a contested pot earned, including splits
ScoopThe whole contested pot comes to one player
Bring-inThe opening stud contribution selected by the door-card rule
CompletionBringing an opening stud contribution to the full small bet
Exposed cardsCards visible to everyone, retained as known cards
WSRF poolOne of six opening/middle/closing × LIKELY/UNLIKELY groups
Policy scoreThe explicit action comparison built around the learned equity
NotebookYour local saved deal, actions, stacks, and history

VPIP counts voluntary entries on the opening street; OR counts opening raises or completions. AF divides bets plus raises by calls. WTSD counts showdowns among hands reaching the first draw street. WSD counts showdowns winning any contested pot, including ties. Read each percentage together with its completed-hand sample count.

Explore the background for this variant in Wikipedia’s limit omaha eight-or-better overview. The room’s specific stakes, cap, reopening, and odd-chip conventions are declared on page 3. The examples, exercises, UI, and training experiment in this guide are original to Lantern Poker.

Explore the worked-hand receipt, complete-hand match table, and training and reproduction notes. Return to the Omaha Two Horizons table whenever you are ready.