LANTERN MIXED TABLES
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.
Discoveries
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.
Discoveries
The room keeps the chip arithmetic close to the action.
| At this table | How it works |
|---|---|
| Starting stack | 2,000 free play chips at each seat |
| Seats | Heads-up or six seats |
| Blinds / antes | Small blind 10; big blind 20 |
| Betting | Small increment 20; large increment 40. |
| Street rhythm | 20 on preflop/flop; 40 on turn/river in limit play. |
| Limit cap | Four full bets per street, including the opening bet. |
| Short all-ins | A full increment reopens raising under this room’s house rule. |
| Split-chip order | The 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.
Discoveries
The cards make the idea concrete.
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.
Discoveries
One away, two away, three away—and a clear reference frame.
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.
Discoveries
Let the game’s special character guide your attention.
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.
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 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.
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.
Worked hands
Follow the cards, then discover the estimate.
The flop is ahead.
| Street | Opponents | Pot | Call | Made hand |
|---|---|---|---|---|
| preflop | 1 | 30 | 10 | High card · Low possibilities ahead |
| A view of the spot | Value |
|---|---|
| Moving rank zone | LIKELY · 10/13 |
| WSRF pot share | 54.8% |
| Monte Carlo share | 55.2% |
| 95% sampling interval | 54.0% – 56.5% |
| Whole-pot frequency | 39.3% |
| Sample count | 4,096 |
| Action | Policy score |
|---|---|
| Call 10 | 0.273 |
| Fold | 0.000 |
| 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.
Worked hands
Follow the cards, then discover the estimate.
| Street | Opponents | Pot | Call | Made hand |
|---|---|---|---|---|
| flop | 5 | 140 | 20 | Two pair · Low possibilities ahead |
| A view of the spot | Value |
|---|---|
| Moving rank zone | LIKELY · 10/13 |
| WSRF pot share | 23.4% |
| Monte Carlo share | 26.3% |
| 95% sampling interval | 25.5% – 27.2% |
| Whole-pot frequency | 3.3% |
| Sample count | 4,096 |
| Action | Policy score |
|---|---|
| Call 20 | 0.084 |
| Fold | 0.000 |
| 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.
Worked hands
Follow the cards, then discover the estimate.
| Street | Opponents | Pot | Call | Made hand |
|---|---|---|---|---|
| turn | 1 | 40 | 0 | One pair · 8–4–3–2–A |
| A view of the spot | Value |
|---|---|
| Moving rank zone | LIKELY · 9/13 |
| WSRF pot share | 56.2% |
| Monte Carlo share | 76.8% |
| 95% sampling interval | 76.0% – 77.7% |
| Whole-pot frequency | 54.6% |
| Sample count | 4,096 |
| Action | Policy score |
|---|---|
| Check | 0.005 |
| 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.
Worked hands
Follow the cards, then discover the estimate.
| Street | Opponents | Pot | Call | Made hand |
|---|---|---|---|---|
| river | 5 | 160 | 40 | Two pair · 8–5–3–2–A |
| A view of the spot | Value |
|---|---|
| Moving rank zone | UNLIKELY · 6/13 |
| WSRF pot share | 7.5% |
| Monte Carlo share | 2.8% |
| 95% sampling interval | 2.5% – 3.2% |
| Whole-pot frequency | 0.0% |
| Sample count | 4,096 |
| Action | Policy score |
|---|---|
| Fold | 0.000 |
| 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.
Worked hands
Follow the cards, then discover the estimate.
The flop is ahead.
| Street | Opponents | Pot | Call | Made hand |
|---|---|---|---|---|
| preflop | 1 | 30 | 10 | High card · Low possibilities ahead |
| A view of the spot | Value |
|---|---|
| Moving rank zone | LIKELY · 9/13 |
| WSRF pot share | 55.4% |
| Monte Carlo share | 60.0% |
| 95% sampling interval | 58.7% – 61.3% |
| Whole-pot frequency | 45.7% |
| Sample count | 4,096 |
| Action | Policy score |
|---|---|
| Call 10 | 0.279 |
| Fold | 0.000 |
| 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.
Worked hands
Follow the cards, then discover the estimate.
| Street | Opponents | Pot | Call | Made hand |
|---|---|---|---|---|
| flop | 5 | 140 | 20 | One pair · Low possibilities ahead |
| A view of the spot | Value |
|---|---|
| Moving rank zone | LIKELY · 10/13 |
| WSRF pot share | 18.0% |
| Monte Carlo share | 18.7% |
| 95% sampling interval | 17.6% – 19.7% |
| Whole-pot frequency | 13.7% |
| Sample count | 4,096 |
| Action | Policy score |
|---|---|
| Call 20 | 0.030 |
| Fold | 0.000 |
| 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.
Practice
Affirmative questions, with the reason beside each answer.
Training
Actual pytoolzx / WSRF fitting, with the measured results beside it.
| Game | Selected fit | Positions | Training showdowns | Test MAE |
|---|---|---|---|---|
| Omaha 8 | full | 6,144 | 786,432 | 6.04 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 style | Hands | BB / 100 | Approx. 95% interval |
|---|---|---|---|
| Omaha 8 / 2 / calling | 512 | 43.2 | 33.6 to 52.7 |
| Omaha 8 / 2 / random | 512 | 52.5 | 33.1 to 72.0 |
| Omaha 8 / 2 / selective | 512 | 42.9 | 26.2 to 59.6 |
| Omaha 8 / 6 / calling | 1,536 | 32.0 | 17.8 to 46.1 |
| Omaha 8 / 6 / random | 1,536 | 45.1 | 26.3 to 64.0 |
| Omaha 8 / 6 / selective | 1,536 | 51.1 | 17.2 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.
Practice
A practice path you can enjoy returning to.
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.
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.
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.
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.
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.
Reference
Useful terms and a path to the underlying work.
| Term | Meaning at these tables |
|---|---|
| Pot share | The fraction of a contested pot earned, including splits |
| Scoop | The whole contested pot comes to one player |
| Bring-in | The opening stud contribution selected by the door-card rule |
| Completion | Bringing an opening stud contribution to the full small bet |
| Exposed cards | Cards visible to everyone, retained as known cards |
| WSRF pool | One of six opening/middle/closing × LIKELY/UNLIKELY groups |
| Policy score | The explicit action comparison built around the learned equity |
| Notebook | Your 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.