Minimum 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%.
Continuation 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.
Three-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.
The 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.
1,326 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.
Dirty 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.
Set 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.
Dominated 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.
Suited 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.
Implied 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.
Pocket 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.
Reading 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.
Why 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.
The 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%.
Pot 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%.