Stacked symbols: why they make wins rarer but bigger
Stacking a symbol on a reel strip cuts how often it shows but fills more rows when it does. On an invented 30-stop strip, 60% of windows fall to 26.7%.
Brasslight SlotsBlog
Notes on how these games actually work: paytables, odds, strategy, and the maths underneath.
Bridge, stance and a straight stroke: cueing basics
Why a 1 or 2 degree error in the cue's line is enough to miss a pot: the geometry of the bridge, stance and stroke, with the miss distances worked out.
8ballsSit and Go payouts: what a 50/30/20 split means for your play
In a 50/30/20 Sit and Go, chips are not prize share. With stacks of 5,000, 3,000 and 2,000 the chip leader's equity is 38.4% of the prize pool, not 50%.
Omaha PokerMinimum defence frequency: what a bet size asks you to call
Minimum defence frequency is pot ÷ (pot + bet): the share of your range that must continue. A half-pot bet asks for 66.7%; pot odds ask a hand for 25%.
Holdem CoachFives and Threes with partners: the four-player game
How the four-player partnership game works: partners opposite, 7 tiles each, no boneyard, one shared score to 61, and the tactics that follow from it.
Fives and Threes DominoesDiesel or electric: how modern trains get their power
Diesel-electric trains carry a power station on board; electric trains take power from a wire or rail, from 750 V DC up to 25 kV AC.
Valley RailHolding a lone deuce in Deuces Wild
With one deuce and nothing else useful, you keep the deuce alone and draw four. What that draw makes, and which suited pairs are strong enough to join it.
Video PokerThe dead man's hand: aces and eights and other named hands
Aces and eights is plain two pair: 1,584 of 2,598,960 five-card hands, 1 in 1,641. Hickok's 1876 hand, its disputed fifth card, and other named hands.
Poker vs DealerBoost pressure: what a pound of boost adds
At sea level each psi of boost packs in about 6.8% more air before heat. 15 psi gives a pressure ratio of 2.02, but compression heat takes a large share back.
Pink Slip KingsReduced motion: why some players switch animations off
Screen motion can cause dizziness and nausea for some people. What reduced-motion settings are, what WCAG says about animation, and what a calmer design swaps.
Big Ben BlocksBetting with the count: how a true-count bet ramp works
A bet ramp ties bet size to the Hi-Lo true count. With each +1 worth about 0.5% and a 0.5% house edge, break-even is near +1. A 1 to 8 unit ramp, worked.
Blackjack CoachFive-card Charlie: a house rule and what it would be worth
A five-card Charlie wins any hand of five cards that has not bust. How rare that is, why a third of such hands still lose, and what the rule is worth.
Blackjack 21 Big Cards OfflineWhy trains can't stop quickly: braking distance explained
Steel wheels on steel rail grip far less than rubber on road, so a train at 120 km/h needs about 800 m to stop where a car needs about 80 m.
Valley RailPenalty cards: when a discard changes the right hold
On 9/6 Jacks or Better, suited J-T beats K-J (0.497 to 0.486) until a spade sits among the discards. Then K-J wins, 0.486 to 0.480. Counted draw by draw.
Video PokerFrom one-armed bandit to video slot: a short history
Four dates show how slots changed: the 1890s Liberty Bell, 1963's Money Honey, the 1976 video slot and the 1984 virtual reel patent, with the odds each allowed.
Brasslight SlotsPool and snooker: how the two games differ
Pool and snooker compared: table size, ball size and count, how each game is scored, what a foul costs, and where the 147 maximum break comes from.
8ballsTrips, boats and wheels: poker's hand nicknames explained
Trips is three of a kind (54,912 hands), a boat is a full house (3,744), a wheel is A-2-3-4-5 (1,020 plus 4 steel wheels). Each nickname, counted.
Poker vs DealerBlockers in Omaha: what holding the nut card tells you
On a three-heart flop 20.9% of opponent hands hold a flush. Each heart in your four cards removes some, and the ace of hearts removes every nut flush.
Omaha PokerContinuation bets: why the preflop raiser bets the flop
A continuation bet follows a preflop raise. Two unpaired cards miss the flop 67.6% of the time, and a half-pot bluff only needs b/(p+b) = 33.3% folds.
Holdem CoachLong suits: why many of one number controls the line
Each number is on 7 of the 28 tiles. How often a 7-tile hand holds 4 or more of one, and how the rest of the suit shrinks for your opponent.
Fives and Threes DominoesDrag racing classes: from bracket racing to Top Fuel
How drag racing is organised: heads-up pro classes like Top Fuel and Pro Stock, versus bracket racing with a dial-in, handicap start and breakout rule.
Pink Slip KingsTap to place: playing a block puzzle without dragging
Dragging a piece across a 9x9 board hides the target under your finger. Why tap-to-place helps, what WCAG 2.2 says, and how many placements a piece has.
Big Ben BlocksWhere blackjack's house edge comes from, rule by rule
Blackjack's house edge is a sum of small rule effects. Acting first costs about 8%; 3:2 naturals, surrender and deck count move it. Each rule priced in points.
Blackjack 21 Big Cards OfflineDeck penetration: why a count needs cards dealt
Penetration is how much of the shoe is dealt before the shuffle. The same Hi-Lo running count of +4 is a true count of +0.9 at 25% dealt and +4 at 83%.
Blackjack CoachWestminster to Piccadilly: the places behind the levels
Big Ben Blocks runs its Adventure levels from Westminster to Piccadilly. Here is what stands at each end, with the dates that are well established.
Big Ben BlocksStiff hands against a 2 to 6: why you stand on 13 to 16
Against a dealer 2 to 6, basic strategy stands on hard 13 to 16. The dealer busts 35.4% to 42.3% of hands and hitting loses more. Plus the hard 12 exception.
Blackjack CoachHow a random number generator picks each spin
A slot spin starts with a pseudo-random number generator: a seed, a state, and a rule that turns each number into a reel stop. A 16-stop worked example.
Brasslight SlotsPocket geometry: why a fast ball misses a pocket it should make
A 4.5 in corner pocket gives a 2.25 in ball only a 2.25 in window straight on, and none at 60 degrees. Add pace and the jaws turn more shots away.
8ballsPat hands: how often five cards need no exchange
A pat hand uses all five cards: straight or better. Exactly 19,716 of 2,598,960 deals qualify, 0.76%, or about one hand in 132.
Poker vs DealerRundowns: why connected four-card hands play well in PLO
A rundown such as 9-8-7-6 makes a straight by the river 27.5% of the time, against 11.4% for K-9-5-2, and it is only 1.04% of starting hands.
Omaha PokerLight rail and trams: how they differ from main-line trains
Trams drive on sight at about 750 V DC; UK main lines signal trains apart and use 25 kV AC. A typical tram stops in 39 m, a 100 mph train in about 2 km.
Valley RailThree-betting: when to re-raise instead of calling
A 3-bet is the re-raise of an open. See why QQ+ and AK is 34 combos, 2.6% of 1,326, and how risk/(risk + reward) gives the folds a 3-bet bluff needs.
Holdem CoachHeavy tiles: when to get rid of high-spot dominoes
Six of the 28 dominoes carry 9 or more spots, 61 of the set's 168. Why that weight matters when you go out first, and when to hold a heavy tile.
Fives and Threes DominoesEighth mile or quarter mile: how the two distances compare
A quarter mile is 1,320 ft (402.3 m) and an eighth is 660 ft (201.2 m). Why the eighth-mile ET is not half, and the 1.55 to 1.57 rule for converting it.
Pink Slip KingsTwo pair in Double Bonus Poker: why it pays only even money
Double Bonus pays two pair 1, the same as a pair of jacks. Holding it is worth 1.766 coins per coin bet, and a lone pair of aces is almost level at 1.763.
Video PokerDoubling down: one card, twice the bet
Doubling down doubles your bet for exactly one more card. See why the one-card limit exists, when it pays, and how house rules change the move.
Blackjack 21 Big Cards OfflineTurbo and auto spin: what speed changes and what it doesn't
Faster spins mean more spins per hour, not better or worse odds per spin. In an example, 4 times the spin rate uses 4 times the coins per hour at the same RTP.
Brasslight SlotsSafety play: when not potting is the better shot
A safety is a legal shot played to leave your opponent nothing. In an illustrative example, a 30% pot beats the safety only if a miss leaves them a hard shot.
8ballsBreak-even odds: what a 3-to-1 payout needs you to win
A payout of N-to-1 breaks even when you win 1 time in N+1. At 3-to-1 that is 25%, which a flush draw (19.15%) misses and an improving pair (28.71%) clears.
Poker vs DealerCounterfeiting in Omaha Hi-Lo: when the board kills your low
A board card that matches your low card counterfeits it. Holding two low cards you miss a low the board shows 40.9% of the time; holding three, 15.1%.
Omaha PokerLevel crossings: how automatic barriers know a train is coming
Track circuits, axle counters and treadles detect a train, and the strike-in point is set by distance = speed × warning time: 27 s at 100 mph is about 1.2 km.
Valley RailHow often each hand lands in Jacks or Better
After the draw, jacks or better lands about one hand in 4.7 and a royal one in 40,400. Each row of 9/6 Jacks or Better, and what it adds to the 99.54% return.
Video PokerThe blinds and the button: how forced bets drive the action
The small and big blind sit left of the button and post 1.5 big blinds a hand. See who acts when before and after the flop, and the heads-up exception.
Holdem CoachFives and Threes against All Fives: two ways to score
All Fives scores only on multiples of five. Fives and Threes also scores threes. Both systems compared total by total, with the points for each.
Fives and Threes DominoesWeight transfer: why a car squats at the launch
Accelerating moves load from front to rear: ΔW = m·a·h ÷ L. For a 1,500 kg car at 1 g that is 278 kg, which helps rear-drive and hurts front-drive.
Pink Slip KingsSmall pairs: when to split twos, threes, fours and sixes
Twos and threes split against a dealer 2 to 7, sixes against 2 to 6, fours only against 5 and 6 when doubling after a split is allowed. Here is why, and what changes without it.
Blackjack CoachWhy the player acts first, and why that is the house's edge
You finish your hand before the dealer plays, so if you bust, the dealer's cards no longer matter. Copy the dealer exactly and that one rule costs you about 8% of every bet.
Blackjack 21 Big Cards OfflineInside the Great Clock: how pennies keep Big Ben on time
A pendulum with a 4-second period is 3.97 m long, and one old penny on its tray makes the Great Clock gain 0.4 seconds a day. The physics, worked through.
Big Ben BlocksThrowing all five away: when Jacks or Better says redraw
On 9/6 Jacks or Better, redrawing all five from 3-5-7-9-T returns 0.358 coins per coin bet. Keeping the ten returns 0.325. Here is the count.
Video PokerMidnight UK time: GMT, BST and when the clocks change
UK midnight is 00:00 GMT (UTC+0) in winter and 00:00 BST (UTC+1) in summer. The clocks go back on 25 October 2026. See what it means in other time zones.
Big Ben BlocksLeft to right: why a ways win must start on reel one
In a ways slot a symbol pays only if it runs unbroken from reel one. Counting examples show how one missing cell turns 81 ways into none.
Brasslight SlotsRailway time: how trains standardised the clocks
Local noon moves 4 minutes per degree of longitude. See how that gap, about 10 minutes at Bristol, pushed railways to one standard time.
Valley RailCombination shots: potting one ball off another
A combination pots one ball by driving another into it. Aim errors multiply across the gap: a 1 mm slip becomes about 5 degrees on the second ball at 300 mm.
8ballsCard removal: how the cards you can see change your odds
Every visible card leaves the unseen pile. A flush draw of 9 in 47 (19.15%) falls to 17.39% if another spade shows, and rises to 19.57% for any other card.
Poker vs Dealer1,326 starting hands, 169 types: counting Hold'em combos
C(52,2) = 1,326 two-card hands collapse to 169 types: 13 pairs at 6 combos, 78 suited at 4, 78 offsuit at 12. Card removal then changes the counts.
Holdem CoachStarting with 6, 7, 8 or 9 tiles: what hand size changes
A bigger starting hand shrinks the boneyard from 16 tiles to 10 and cuts the chance of holding no tile for a number from 14.4% to 4.3%.
Fives and Threes DominoesFive-Card Omaha: what a fifth hole card changes
A fifth hole card gives you 10 two-card pairs instead of 6 and 100 possible hands at showdown instead of 60, but you still play exactly two. Counted exactly.
Omaha PokerThe 60-foot time: why the first 18 metres decide a run
The first 60 feet (18.29 m) are 4.5% of a quarter mile, yet a slow launch is carried to every later line. A 2.0 s 60-foot time means about 0.93 g on average.
Pink Slip KingsSoft and hard hands: how an ace changes value mid-hand
An ace counts as 11 until that would bust you, then as 1. See why a soft hand cannot bust on one hit, and how often a hit turns soft 13 to 21 into a hard total.
Blackjack 21 Big Cards OfflineDoubling 9, 10 and 11: the hard totals worth doubling
Basic strategy doubles hard 9 against a 3 to 6, hard 10 against a 2 to 9 and hard 11 against a 2 to 10. Here is why each line sits where it does.
Blackjack CoachWhy the fifth coin matters: the royal flush bonus at max bet
On a casino-style 9/6 Jacks or Better table the royal pays 250 per coin for one to four coins and 800 at five. That jump is worth about 1.2 points of return.
Video PokerWhat a multiplier does to a ways-to-win payout
A multiplier scales the pay per way, not the number of ways. Worked through with hypothetical pay values: one cell, the whole win, and stacked multipliers.
Brasslight SlotsTunnel or cutting: how engineers take a line through a hill
A cutting's volume grows with the square of its depth, a tunnel's only with its length. Work out where the break-even depth falls, with an example.
Valley RailRacing for pink slips: where the name came from
A pink slip is the ownership paper for a car. Racing for pink slips meant the loser handed over the title and the car. Here is where the term comes from.
Pink Slip KingsPool table sizes: 7, 8 and 9-foot tables compared
Compare 7, 8 and 9-foot pool tables: playing surface in inches, the 2:1 ratio, how many balls fit across, and how much room each table needs around it.
8ballsDanglers: why a disconnected fourth card weakens a hand
A dangler is a fourth Omaha card that cannot join a straight with the other three. Count how often J-T-9-3 makes a straight by the river against J-T-9-8.
Omaha PokerThe Illustrious 18: count-based plays worth learning first
The Illustrious 18 are the Hi-Lo plays where the true count changes basic strategy: insurance at +3, 16 against 10 at 0, 15 against 10 at +4, and 15 more.
Blackjack CoachDirty outs: discounting cards that also help your opponent
A dirty out completes your hand and your opponent's better one. Dropping two of eight outs cuts a turn draw from 17.4% to 13.0%, below a 16.7% price.
Holdem CoachPlaying to 61: how pub dominoes borrowed the cribbage board
Fives and Threes targets of 61, 121, 181 and 241 are cribbage board lengths: 60 holes a lap plus one. What each target means for the number of scoring turns.
Fives and Threes DominoesFive-card draw: where the oldest form of poker came from
Early poker used 20 cards and four players. What is documented about the road to five-card draw, and which dates stay uncertain.
Poker vs DealerUndo, hints, rotate and bomb: when a puzzle aid is worth it
Block puzzle aids cost coins, so use them where the grid says they pay. On a 9x9 board, one hole blocks 3 of 27 groups and turning an L adds 192 places.
Big Ben BlocksThe dealer's peek: why blackjack is checked before you play
With an ace or a ten showing, a dealer who peeks checks for blackjack before you act. See the 30.87% and 7.72% odds, and what the check saves a double.
Blackjack 21 Big Cards OfflineWhy no suit outranks another in poker
Poker ranks hands by card rank, never by suit. Each suit has 13 cards and 1,287 five-card combinations, so none is rarer and equal hands split.
Poker vs DealerTurbo or supercharger: two ways to force air in
Both pack more air into the cylinders. At 1 bar of boost the absolute pressure doubles, 1.013 to 2.013 bar, but the air heats up, so an intercooler matters.
Pink Slip KingsReel strips and stops: where a slot's reels land
A reel strip is an ordered list of stops. One random number picks a stop per reel, and a symbol's chance is its count over the strip length. A 20-stop example.
Brasslight SlotsThe physics of the break: momentum through a rack
Why a square hit on the head ball breaks best: equal-mass collisions pass momentum straight on, the cue ball stops, and gaps in the rack waste the energy.
8ballsQuartering in Omaha Hi-Lo: how half a pot can lose chips
Quartering in Omaha Hi-Lo means getting a quarter of the pot. With 2 or 3 players putting in equal amounts, that is less than you put in, so you lose chips.
Omaha PokerNever split tens: why a 20 beats two fresh hands
A pair of tens is a 20, and a 20 wins 76% to 86% of the time against a dealer 2 to 9. Splitting it trades that for two hands that are worth far less.
Blackjack CoachSuited high cards: when two beat three in Jacks or Better
On 9/6 Jacks or Better, holding suited Q-J is worth 0.610 coins per coin bet. Adding an offsuit king to hold K-Q-J is worth 0.515. Here is the count.
Video PokerSet mining: the odds of flopping a set with a pocket pair
A pocket pair flops a set or better 11.8% of the time, about 7.5 to 1 against. That is why set mining needs a stack 15 to 20 times the call.
Holdem CoachDrawing from the boneyard in Fives and Threes
Rules for drawing differ between tables. Counting tiles gives the chance a draw is playable: 60% with two different ends, 30% when both ends match.
Fives and Threes DominoesConed wheels: how a train steers itself round a curve
A train has no steering wheel. Tapered wheel treads let the wheelset find the right path round a curve. See the geometry and a 500 m worked example.
Valley RailEdges first: where to place pieces on a 9x9 grid
A straight five has 90 places on a 9x9 grid, but only 2 cover a corner and 10 cover the centre. Count them to see why edges are the place to park pieces.
Big Ben BlocksPushes in blackjack: what happens when you tie the dealer
A push returns your stake: no win, no loss. See which ties count, why a bust never pushes, and how often standing on 20 meets a dealer 20.
Blackjack 21 Big Cards OfflineWhy drag racers do a burnout before every run
A burnout heats the tyres and cleans the tread. Worked example: raising grip from 0.8 to 1.0 cuts a 3,000 lb car's 60-foot time from 2.80 s to 2.44 s.
Pink Slip KingsThree of a kind: exchange one card or two?
Three of a kind drawing two cards makes a full house 66 in 1,081 and quads 46 in 1,081. Keeping a kicker and drawing one gives 3 in 47 and 1 in 47.
Poker vs DealerSplitting nines: why you stand on 18 against a 7
A pair of nines splits against most dealer cards but stands against a 7. The dealer's final totals show why: 18 beats a 17, and a 7 makes 17 most often.
Blackjack CoachNear misses: why a symbol just off the line counts for nothing
A symbol one reel short of a ways-to-win line pays nothing. With invented odds, four matching reels in five miss 60% of the time. The sums are shown.
Brasslight SlotsSingle track and passing loops: running trains both ways
One track, two directions. See how a section's running time caps the trains per hour, why one passing loop doubles it, and how tokens kept trains apart.
Valley RailBank shots: angle in, angle out, and where it fails
A bank shot follows the mirror rule: angle in equals angle out. Reflect the pocket across the cushion, aim at the image, and see why speed and spin spoil it.
8ballsPaired boards in Omaha: when the nut flush loses to a full house
Once the board pairs, even the ace-high flush can lose. Count exactly how many opponent hands make a full house and how often a board pairs by the river.
Omaha PokerHolding two pair in Jacks or Better: what the draw is worth
On a 9/6 Jacks or Better paytable, holding two pair and drawing one card is worth 2.60 coins per coin bet. Breaking it for a high pair is worth 1.54.
Video PokerDominated hands: why ace-nine struggles against ace-king
Ace-nine shares an ace with ace-king and wins only about 24% against it, 26% with chops. Against king-queen the same hand is a 58% favourite.
Holdem CoachBlocking in Fives and Threes: playing to deny a score
Your move decides which ends the opponent faces. A worked example compares scoring 3 and risking 8 with scoring 0 and risking 2, with the arithmetic.
Fives and Threes DominoesDealer stands on soft 17: what the rule changes for you
Whether the dealer hits or stands on soft 17 moves the house edge by about 0.2 points in six decks. See how it reshapes the dealer's totals and your plays.
Blackjack 21 Big Cards OfflineKeeping a 3x3 box empty: room for the awkward piece
A 3x3 square has 49 places on an empty 9x9 grid, and nine well-spread blocks can remove every one. Count which cells cost the most room.
Big Ben BlocksTwo pair on the draw: how often it becomes a full house
Hold two pair and exchange the fifth card: 4 of 47 unseen cards make a full house, 8.51%, about 10.75 to 1 against. One pair drawing three manages 1.02%.
Poker vs DealerHit frequency: why most slot wins are smaller than the bet
A made-up slot hits on 43.6% of spins, yet only 13.6% return more than the stake. Hit frequency and RTP are different numbers, and the sums show why.
Brasslight SlotsPower-to-weight ratio: why a lighter car runs quicker
Quarter-mile time scales with the cube root of weight per horsepower, so 10% less weight is only about 3.4% quicker. Worked examples with the Hale/Fox formulas.
Pink Slip KingsThrow: why cut shots need a touch of overcut
Ball-to-ball friction throws the object ball a few degrees off the line of centres. Over a metre, 2 degrees is 3.5 cm, so cut shots need a little extra cut.
8ballsDouble-suited hands: what two suits add before the flop
Count the five ways a four-card Omaha hand can be suited, then see why double-suited hands make a flush by the river twice as often as single-suited ones.
Omaha PokerHow a steam locomotive turns coal into motion
Coal heats water, the steam pushes pistons, and rods turn the wheels. Follow the chain link by link, and work out the pull of a typical two-cylinder engine.
Valley RailSuited or offsuit: how much a matching suit adds in Hold'em
Suited cards are 4 of the 16 combinations of a non-pair. They flop a flush 0.84% of the time and add about 4 points of equity, not enough to save a weak hand.
Holdem CoachFour to a royal: when to break a made flush or straight
In 9/6 Jacks or Better, four to a royal returns about 18.4 coins per coin bet, against 6 for a made flush. The exact counts, and the one made hand you keep.
Video PokerEvery scoring end total in Fives and Threes, 3 to 20
Nine end totals between 3 and 20 score in Fives and Threes. Each one with its points, the ends that make it, and why 16, 17 and 19 never pay.
Fives and Threes DominoesDoubling soft hands: ace-two to ace-seven explained
Soft hands from ace-two to ace-seven double only against a weak dealer card. Here is the six-deck chart and the reason each cell is what it is.
Blackjack CoachPlaying Time Attack: block puzzle choices against a clock
Big Ben Blocks has a three-minute Time Attack with no aids. Use line counts and fixed placements on the 9x9 grid to decide fast and avoid holes.
Big Ben BlocksWhy tens make up almost a third of a blackjack deck
Sixteen of 52 cards count ten, 30.8% of the deck. That one fact sets the dealer's hole card, the stiff hands, how often you get 20 and a natural.
Blackjack 21 Big Cards OfflineStandard gauge: why most railways run on 1,435 mm
Standard gauge is 4 ft 8½ in, or 1,435 mm. It came from colliery wagonways, beat Brunel's 7 ft ¼ in broad gauge, and still shares the world with five others.
Valley RailScatter symbols: the odds of three on five reels
If each reel shows a scatter with probability 0.2, three or more across five reels turn up 5.79% of the time. Here is the binomial maths, step by step.
Brasslight SlotsThe 30-degree rule for a rolling cue ball
A rolling cue ball leaves a cut shot about 30 degrees off its line. The maths gives 33.7 degrees for a half-ball hit, and 27 to 34 across the common cuts.
8ballsWhy pocket aces are weaker in Omaha than in Hold'em
Aces win about 85% against a random Hold'em hand but only about 65-70% in Omaha. Count why: four-card hands pair, draw and connect far more often.
Omaha PokerLow pair or four to a flush: the Jacks or Better call
In 9/6 Jacks or Better, four to a flush returns 1.15 to 1.34 coins per coin bet and a low pair returns 0.82. The counts behind that gap, and where each sits.
Video PokerImplied odds: when a call pays off on later streets
A flush draw on the turn is 19.6% against a 25% price. Implied odds tell you the gap: you must win another 55.6 on later streets to break even.
Holdem CoachHard 16 against a dealer 10: why hitting is the lesser evil
Hard 16 against a dealer 10 loses about 54 bets in 100 whether you stand or hit. Surrender, at 50, is cheaper still. Here is the working.
Blackjack CoachDrawing one card to a flush: nine outs from 47 cards
Hold four cards of one suit and replace the fifth: 9 of the 47 unseen cards finish the flush, a 19.15% chance, or about one attempt in five, and 80.85% of the time you miss.
Poker vs DealerThe Christmas tree: pro tree and sportsman tree starts
A sportsman tree runs three ambers 0.5 s apart, then green. A pro tree lights all three together, then green 0.4 s later. Here is how R/T reads on each.
Pink Slip KingsInside a double-six set: 28 tiles and 168 spots
A double-six set holds 28 tiles, 7 doubles and 168 spots. Each number sits on 7 tiles and 8 ends, and a total of 6 is the most common.
Fives and Threes DominoesOther players at the table: do their cards hurt you?
Another player's hit never changes your expected result. Every unseen card is equally random, so the player who took the dealer's bust card cost you nothing.
Blackjack 21 Big Cards OfflineBig Ben is a bell: the facts behind the name
Big Ben is the Great Bell, not the clock or the tower: cast in 1858, about 13.7 tonnes, cracked and rehung. The tower, the dials and the chimes in numbers.
Big Ben BlocksThe order to learn video poker variants in
Jacks or Better first, then Bonus Poker, Double Bonus and Deuces Wild last. What each step reuses from the one before, and what you have to unlearn.
Video PokerTwenty-one, pontoon and blackjack: how the games differ
Blackjack, pontoon and vingt-et-un all aim at 21 but differ in who sees what, who wins ties and what a natural pays: 2:1 in pontoon, 3:2 in blackjack.
Blackjack 21 Big Cards OfflineRailway towns: how a station made a village grow
Crewe, Swindon and Wolverton were hamlets or small market towns before the railway. What a station and a works did to them, with figures from the 1860s.
Valley RailThe 90-degree rule: where the cue ball goes after a stun shot
After a stun shot the cue ball leaves along the tangent line, 90 degrees from the object ball. Here is why, how the speeds split, and how spin bends the path.
8ballsWhy the second-best flush is a trap in Omaha
A king-high flush looks strong, but Omaha opponents hold four cards each. Count how often one of them has the ace-high flush, from 1 to 8 opponents.
Omaha PokerHow a pick bonus works, and why the picks are already decided
In most pick bonuses the prize is drawn by the RNG when the bonus triggers, and the taps only reveal it. A worked example shows the expected value and why choice cannot help.
Brasslight SlotsPocket pair against two overcards: the coin flip that isn't
Pair against two overcards is called a coin flip. Computed over every board, it runs from 46.0% (22 v JTs) to 57.2% (QQ v AKo); only 22 v AKs is level.
Holdem CoachHard 12 against a 2 or 3: why basic strategy says hit
Standing on 12 against a dealer 2 or 3 feels safe, but basic strategy hits it. Here is the 30.8% bust risk, the dealer's bust rates and why 4, 5 and 6 differ.
Blackjack CoachCounting tiles in Fives and Threes: what they cannot hold
Every number sits on exactly seven tiles of a double-six set. Count yours, count the line, and a draw tells you which tiles your opponent cannot hold.
Fives and Threes DominoesShapes as well as colours: block puzzles for colour-blind players
In a 9x9 block puzzle a line clears by being full, not by matching colour. About 8% of men and 0.5% of women are colour-blind; here is how to read the board.
Big Ben BlocksWhen to shift: why the best shift point is past peak torque
Shift where wheel force in the next gear equals wheel force in this one. In an example engine that is 6,898 rpm, 1,900 rpm past peak torque.
Pink Slip KingsIs the ace high or low? The ace in five-card poker
In five-card poker the ace is high, except in the wheel A-2-3-4-5, the lowest straight. Q-K-A-2-3 is no straight, and there are exactly 10 straight ranks.
Poker vs DealerThree of a kind: how each video poker variant treats it
Three of a kind pays 3 in Jacks or Better, Bonus Poker and Double Bonus, but 1 in Deuces Wild. What each paytable makes of the hand, and why you keep the three.
Video PokerSlot RTP and volatility: what each number measures
Three toy slots all return 96% yet behave very differently. RTP is the long-run average; volatility is the spread, and the maths shows how to tell them apart.
Brasslight SlotsWhat a six-deck shoe changes compared with a single deck
A six-deck shoe adds roughly half a point to the house edge over one deck. Card removal, pairs and dealer naturals shift by far less than most players expect.
Blackjack 21 Big Cards OfflineHorsepower and torque: how to read a dyno chart
Horsepower is torque times rpm divided by 5,252, so the two curves always cross at 5,252 rpm. An example engine shows what each line means for acceleration.
Pink Slip KingsWraps: how an Omaha straight draw can have 20 outs
A wrap uses two hole cards to connect with the flop in several ways. Count the 20 outs in T-9-6-5 on 8-7-2, and see what the draw is really worth.
Omaha PokerHow railway bridges carry a load: four designs
Beam, arch, truss and suspension bridges all carry weight to the ground in different ways. Here is how each works and why heavy railways avoid suspension spans.
Valley RailReading the board: the best five cards from seven
A Hold'em hand is the best five of seven cards, 21 possible combinations. Ten use both hole cards, ten use one, and one plays the board alone.
Holdem CoachAiming with the ghost ball: cut angle and ball overlap
How the ghost-ball method turns a pot into a single aiming point, and how cut angle maps to the fraction of the object ball your cue ball covers.
8ballsDoubles at an open end in Fives and Threes
A double at an open end counts both its spots in Fives and Threes. Laying a double on a matching end adds that many spots to the total. Here is what it does.
Fives and Threes DominoesBreaking ties in five-card poker: high cards and split pots
Hands in the same category are settled card by card, highest first, and suits never count. There are 7,462 distinct strengths; exact ties split the pot.
Poker vs DealerFrom Tetris to Sudoku: where the 9x9 block puzzle comes from
The 9x9 block puzzle takes its pieces from Tetris and polyominoes and its board from Sudoku. The counts of shapes, cells and lines show how they differ.
Big Ben BlocksLate surrender: the hands worth giving up on
Late surrender hands back half your bet. Basic strategy uses it on hard 16 against 9, 10 and ace, and on hard 15 against 10, because those lose more than half.
Blackjack CoachWhy practising video poker offline teaches more
Video poker results are too noisy to teach strategy: 400 hands swing about 88 bets against an expected loss under 2. Practise where you can check each hold.
Video PokerWhy a slot is never due: independent spins explained
A 1-in-100 feature misses 100 spins in a row 36.6% of the time, and after any drought the expected wait is still 100 spins. Here is the maths of independence.
Brasslight SlotsHow a low hand is made in Omaha Hi-Lo, and what 8 or better means
A low in Omaha Hi-Lo is five different cards of 8 or lower, exactly two from your hand and three from the board. Ace is low, and A-2-3-4-5 is the best.
Omaha PokerThe odds of improving a pair when you exchange cards
Hold a pair and exchange the other three cards, and you improve 28.7% of the time: two pair 16.0%, trips 11.4%, a full house 1.0%, four of a kind 0.28%.
Poker vs DealerFrom coal mine to power station: how freight chains work
A 1 GW coal power station burns roughly 9,000 to 10,000 tonnes a day, about one unit train. The arithmetic, and why bulk freight suits rail.
Valley RailWhy position matters: one hand from an early and a late seat
Position decides how many players act after you: 8 from under the gun, 2 from the button. At a nine-handed table that changes which hands are safe to play.
Holdem CoachChoosing your opening tile in Fives and Threes
Fourteen of the 28 tiles score as an opener, for 1 to 4 points. The 6-3 scores 3 and hands back 8. Which openers are worth leading, and which are not.
Fives and Threes DominoesLaunch RPM: between wheelspin and bogging down
A launch is limited by grip, not power. Worked example: 3,000 lb, 50% on the rear tyres, grip of 1.0 gives 0.625 g and a 2.44 s 60-foot time; spin costs 0.36 s.
Pink Slip KingsCue-ball spin explained: topspin, backspin and sidespin
How tip height sets topspin and backspin, why 2/5 of the ball's radius gives natural roll, and what sidespin does through squirt and throw.
8ballsHoles and islands: why a fragmented board ends a block puzzle
An empty cell with no empty neighbour only takes a one-cell piece. Count placements and pocket sizes on a 9x9 grid to see why fragments end block puzzles.
Big Ben BlocksInsurance: why it loses unless you are counting
Insurance pays 2:1, so it breaks even only when tens make up one third of the unseen cards. A fresh shoe sits near 31%; a Hi-Lo true count of about +3 reaches it.
Blackjack CoachSplitting pairs: why you always split aces and eights
Sixteen is the worst total in blackjack, and a pair of eights is exactly that. Split them and the aces: each new hand starts from a total that cannot bust.
Blackjack 21 Big Cards OfflineHow a wild changes the count on a ways-to-win slot
A wild adds one to a symbol's count on its reel, so the ways total jumps as a product. It can also bridge an empty reel and lengthen the run.
Brasslight SlotsWhy a flush beats a straight: the rankings follow the odds
In five-card poker there are 5,108 flushes and 10,200 straights, so the flush is about twice as rare. Each rung of the hand ranking is the next rarest.
Poker vs DealerWhat a machine's hold percentage does and does not tell you
Hold is the share of coins in that a machine keeps. On 9/6 Jacks or Better the paytable says 0.46%, but over 100,000 hands the measured figure wanders by about 1.4 points either way.
Video PokerSoft 18: how to play ace-seven against every dealer card
Ace-seven is the one hand that stands, doubles and hits depending on the dealer's card. Here is the full six-deck chart and the numbers behind each choice.
Blackjack CoachHow to work out a pot-sized bet in Pot-Limit Omaha
A pot-sized raise in PLO is your call plus the pot after that call. Worked example: a bet of 100 into 100 can be raised to 400.
Omaha Poker9-ball rules: lowest ball first, and what counts as a foul
How 9-ball works: the diamond rack, the lowest-ball-first rule, the fouls that give ball in hand, the push out, and why the 9 wins from any legal shot.
8ballsHow railway signals keep trains apart
Signals split the track into blocks so only one train occupies each. Braking distance grows with the square of speed, and that sets how far apart they sit.
Valley RailThe rule of 2 and 4 in Hold'em, and where it goes wrong
Multiply outs by 2 on the turn and by 4 on the flop. It is close for small draws, but with 15 outs the rule of 4 reads 60% against a true 54.1%.
Holdem CoachGear ratios and final drive: what gearing does to a quarter mile
Final drive multiplies every gear. A 4.10 instead of 3.42 gives 20% more force at the wheels but cuts road speed at any revs by 17%, and can run out of revs.
Pink Slip KingsWhy 15 is the best total in Fives and Threes
Fifteen scores 8 points in Fives and Threes and no other total passes 6. It is also rare: only two pairs of open ends make it. Here is why, with the counts.
Fives and Threes DominoesSetting up double clears on a 9x9 block grid
A double clear is two gaps filled by one piece. Count the gaps, subtract any shared cell, and you know the exact shape you need and how full the board must be.
Big Ben BlocksHow the dealer plays, and how often each up-card busts
The dealer has no choices: draw to 16, stand on 17. That fixed rule makes a 6 bust 42.3% of the time and a 10 only 21.2%, in a six-deck game.
Blackjack 21 Big Cards OfflineWhy railways follow rivers: gradients and the ruling grade
A steel wheel grips a steel rail with only a fraction of the train's weight, so every climb cuts the load an engine can pull. That is why early lines hugged river valleys.
Valley RailWhat 243 ways to win means, and how it differs from paylines
243 is 3 to the power of 5, every left-to-right path through a 5×3 grid. Wins are counted by multiplying symbol counts on adjacent reels.
Brasslight SlotsReading a drag racing time slip: reaction time, ET and trap speed
A time slip splits one pass into reaction time, incremental ETs and speeds. ET does not include your reaction, so the quicker car can still lose the race.
Pink Slip KingsProgressive jackpots and the point where a machine turns positive
An 8/5 Jacks or Better machine returns 97.30% with a 4,000-coin royal. The meter has to reach about 8,700 coins before correct play breaks even, not the 9,400 that simple arithmetic suggests.
Video PokerExactly two from your hand: the Omaha rule that fools new players
In Omaha every hand is exactly two hole cards plus three from the board. Five worked examples of hands that look made and are not, and how to read a board.
Omaha PokerWhy every cell on a 9x9 block grid belongs to three lines
A 9x9 block grid has 27 clearable groups: 9 rows, 9 columns and 9 boxes. Every cell sits in exactly one of each, so every block you place feeds three.
Big Ben BlocksPot odds in Texas Hold'em: working out whether a call pays
A call pays when your chance of winning beats the call divided by the final pot. A half-pot bet needs 25%; a flush draw on the turn is 19.6%.
Holdem CoachHi-Lo counting: running count and true count explained
Hi-Lo gives every card +1, 0 or −1. The running count tracks what has gone; dividing by decks left turns it into a true count you can compare.
Blackjack CoachHow Fives and Threes scoring works, with worked examples
Fives and Threes scores the two open ends: a total divisible by 3 scores a third, by 5 a fifth, and 15 scores both for 8. Every total, worked out.
Fives and Threes DominoesHow rare each five-card poker hand is
There are 2,598,960 five-card hands. Half of them are high card, 42% hold one pair, and a royal flush is 4 of them: one deal in 649,740.
Poker vs Dealer8-ball rules: the open table, groups and the 8 ball
How standard 8-ball works: the rack, a legal break, why the table stays open after the break, how groups are decided, and the shots that lose on the 8 ball.
8ballsWhy blackjack paying 3:2 matters more than any other rule
A natural turns up once every 21 hands in a six-deck shoe. Cutting its pay from 3:2 to 6:5 adds about 1.36 points to the house edge, more than every other common rule change put together.
Blackjack 21 Big Cards OfflineHow shuffling works in a digital card game
A 52-card deck has about 8 × 10⁶⁷ orderings. Fisher–Yates reaches every one of them in 51 swaps — and the one-line variant that looks identical makes some orderings 25% more likely than others.
Video PokerCommon video poker myths, and what the maths says instead
A machine that has gone 40,000 hands without a royal flush still offers the same one-in-40,000 on the next one — and more than a third of machines will do exactly that. Six beliefs, and the arithmetic that replaces them.
Video PokerReading a Deuces Wild paytable
Eight numbers, and only the middle ones move. Full-pay Deuces Wild is 25-15-9-5-3-2-2-1 at 100.76%, and the row to check first is four of a kind: it lands about once every fifteen hands.
Video PokerFull-pay machines and why they became hard to find
Full pay is the top of a known ladder, not a compliment: 9/6 Jacks or Better returns 99.54%. A coin off the full house costs 1.15 points and a coin off the flush 1.10 — exactly how often those hands land.
Video PokerBankroll and session length: how far a fixed stack actually goes
The house edge says a 1,000-coin stack covers 43,800 hands. Half of real sessions at that stack are over inside 6,540. Session length is set by the ratio of stack to bet, and by nothing else.
Video PokerHow video poker differs from poker at a table
Same 52 cards, same hand rankings, and almost nothing else in common. The machine holds no cards, so hand strength is absolute, there is no fold, and all 2,598,960 deals get played out.
Video PokerMachines that pay on kings instead of jacks
Moving the minimum paying pair from jacks to kings halves how often it lands — 13.00% of deals becomes 6.50% — and takes about ten points off the return. That is why these machines carry a joker.
Video PokerWhy a kicker never helps
Keeping an ace alongside your trips or your pair costs between 0.11 and 0.60 coins a hand, and the loss is the same whichever high card you keep. Holding one every time it is available gives up 5.59 points of return.
Video PokerWhy an inside straight draw is worth exactly half an outside one
Eight cards complete an open-ended four-card straight and four complete a gutshot, so one is worth 0.68 coins and the other 0.34. A gutshot with no high cards in it is worth less than throwing all five cards away.
Video PokerFive Play: what multi-hand does to your bankroll, and what it doesn't
Multi-hand changes neither the return nor the correct holds. It splits one stake across independent draws, which cuts the swing per coin by 55% on a drawing hand and by nothing at all on a pat one.
Video PokerWhy the royal flush is worth two percentage points of the return
One hand in 40,000 pays 800 per coin. That single row carries 1.98 of the 99.54% return on 9/6 Jacks or Better, and the machine you actually experience returns 97.6%.
Video PokerWhat variance actually means at a video poker machine
Return says where a machine ends up; variance says how far it wanders on the way. Over 1,000 hands of 9/6 Jacks or Better the likely swing is thirty times the expected loss.
Video PokerBonus Poker and Double Bonus: what the bigger quads cost you
Both variants pay far more for four of a kind than Jacks or Better. Bonus Poker charges for it at the full house; Double Bonus halves two pair, which changes how you play.
Video PokerHow to read a video poker paytable
The two rows that decide whether a Jacks or Better machine returns 99.5% or 97.3%, and why betting five coins is not optional.
Video PokerJacks or Better strategy, ranked
A simplified hold-priority list for 9/6 Jacks or Better, plus the four mistakes that cost the most.
Video PokerWhy Deuces Wild breaks your Jacks or Better instincts
Four wild cards change which hands are worth keeping. What a pair is worth, why three of a kind is the new baseline, and what to do when you are dealt a deuce.
Video Poker