Click a spot, then pick a card below. Click a filled spot to change it; right-click to clear it.
Opponents
Pairs on the diagonal, suited hands (s) above it, offsuit (o) below. Drag to paint.
Preflop charts
A simple reference: the strongest hands for each seat at a 6-player table, ranked by all-in equity against a random hand. Not solver output.
Pick your two cards to start.
Equity
–
Win – Tie – Lose –
What you end up with
Outs
Fold, call or raise?
Simple model
EV in chips, from now on. Assumes a call ends the betting and a raise is folded to or called, never re-raised. Real hands have more streets and choices: use it to see how the pieces fit, not as a solver.
Game theory
Table rules
–
House edge: how much of each bet the casino keeps on average when you play perfect basic strategy.
Best play
Your cards
Dealer shows
Strategy chart
Pick a hand, or press Deal to practise.
Trainer
Dealer
You
Card counting
Running0
True0
Decks left6
Your edge now–
The Illustrious 18
Hi-Lo: 2 to 6 count +1, 7 to 9 count 0, tens and aces −1. True count = running count ÷ decks left. Each +1 moves about 0.5% of edge to you (a rule of thumb).
Why it works
Every blackjack choice has an exact expected value (EV): what it wins or loses on average per unit bet. The app computes it from the cards left in the shoe, card by card for the dealer. Basic strategy is just the choice with the highest EV.
The house edge comes from one rule: if you bust, you lose even if the dealer busts later. Good play cuts the edge to under half a percent with good rules. Counting finds the moments when the leftover cards favour you.
Kuhn poker: poker with 3 cards
Exact
The smallest real poker game, small enough to solve perfectly. The deck is just a Jack, a Queen and a King (King beats Queen beats Jack). Two players each get one card and put 1 chip in the pot.
Player 1 checks (bets nothing) or bets 1 chip.
If player 1 bet, player 2 calls (puts in 1 too) or folds (gives up the pot).
If player 1 checked, player 2 checks (show cards, higher wins) or bets, and then player 1 calls or folds.
Mathematicians found the perfect way to play it in 1950. It shows why even perfect players bluff.
Play the perfect player
Perfect player
Pot: 2 chips
You
Press Deal to play a hand against perfect play.
The perfect strategy
Nash equilibrium
How often to do each thing with each card. Nobody can win more against it by playing differently.
Any rate from 0% to 33% is perfect, as long as player 1 also bets the King 3 times as often and calls with the Queen a bit more.
Why bluffing works
If you only bet with good cards, your bets give your hand away and nobody pays you. Bluffing sometimes with your worst card keeps the other player guessing, so they have to call sometimes, and then your King gets paid.
The perfect player bluffs just enough that calling and folding are worth exactly the same to you. Pick a mistake to see what it costs:
Your five cards
Jacks or Better: you get 5 cards, keep (hold) any of them, and the rest are replaced. Then you're paid by the table. A pair of jacks or better is the smallest win.
Pay table
Return with perfect play–
Pays are per coin bet (the royal's 800 is the 4,000-coin jackpot for a 5-coin bet). Returns are the published full-game results for perfect play, from the Wizard of Odds; the best hold for each hand is worked out here exactly.
Pick five cards, or press Deal.
Best hold
Exact
How it works
There are 32 ways to choose what to hold (including keeping nothing). For each one the app deals every possible replacement from the 47 cards left, up to 1.5 million of them, adds up the payouts and divides. The hold with the highest average is the best play.
Surprises it finds: keep a small pair over three cards to a straight flush, and throw away a flush you've already made when you hold four to a royal.
Your hand
Face-up card
Best melds
Deadwood –
Found exactly by trying every way to split your cards. Aces are low (A-2-3 is a run, Q-K-A isn't).
Pick your 10 cards, or press Deal.
What to do
Heuristic
Deadwood is exact. Which card to throw, whether to take the face-up card, and when to knock use rules of thumb good players use; gin rummy is too big to solve perfectly here.
How gin rummy works
Each player has 10 cards. On your turn, take the face-up card or the top of the pile, then throw one away. You're trying to group your cards into melds: sets (3 or 4 of a rank, like 9 9 9) or runs (3 or more in a row in one suit, like 4♥ 5♥ 6♥).
Cards not in a meld are deadwood and count against you (aces 1, pictures 10). With 10 or less you can knock to end the hand; with 0 you go gin for a bonus.
Your cards
Your hand
Cut card
How cribbage scoring works
You're dealt 6 cards and throw 2 into the crib, a bonus hand for the dealer. Then a card is cut (the starter) and shared by everyone. Your 4 cards plus the cut score points for fifteens (cards adding to 15), pairs, runs (3 or more in a row), flushes and nobs (the jack of the cut's suit).
Pick the six cards you were dealt, or press Deal.
Best throw
Exact average
Hand: the exact average over all 46 possible cut cards. Crib: the exact average over every 2 cards the other player could throw and every cut, treating their throw as random (real players throw better, so treat it as a guide). As dealer the crib is yours; otherwise it counts against you.
Card Solver