The 21 Outs UTH Trainer

Ultimate Texas Hold’em decision trainer with dealer-out counting and exact river odds — built on the Wizard of Odds strategy, Stephen How’s refinements, and the Wizard of Vegas “21 outs” thread.
Dealer
Board
Your hand
Mistake log

Strategy reference

Everything the trainer grades against. The pre-flop and flop decisions follow the Wizard of Odds basic strategy; the river is graded by exact enumeration of all 990 dealer hands, with the 21-outs rule shown as the human-speed heuristic.

Pre-flop — raise 4× or check

Raise with any of the following, otherwise check. Raising 3× is never correct.

  • Any pair of 3s or better (pocket deuces: check)
  • Any ace
  • King — any suited king, or K5 offsuit and better
  • Queen — Q6 suited or better, Q8 offsuit or better
  • Jack — J8 suited or better, or JT offsuit

“It’s really important to raise your 4x preflop opportunities. The ‘play’ bet is where you make all your money.” — Stephen How, discountgambling.net

Flop — bet 2× or check

If you checked pre-flop, bet with any of the following, otherwise check:

  • Two pair or better
  • A hidden pair — any pair using at least one hole card — except pocket deuces
  • Four to a flush including a hidden 10 or better of that suit

“Two pair or better” misleads in two spots where most of the hand is the board’s, and the trainer grades them by exact EV instead:

  • Trips on the board — the trips are everyone’s, so it’s a pure kicker battle. Bet 2× only with a top-three kicker (at most two ranks, ignoring the board’s rank, can out-kick you) — e.g. J or better on AAA, Q or better on 888. The third-best kicker is nearly a coin-flip; anything lower checks. Pocket pairs (a full house) and quads still always bet. (Compare the river rule below: 4th-nut kicker calls 1×.)
  • Tiny pocket under a paired board — pocket 2s or 3s below both the board’s pair and its side card (22 on Q-Q-7, 33 on T-T-4) check: almost any dealer pair beats that two pair. Pocket 4s or better, or a pocket over the side card, still bet.

Stephen How’s finer-grained flop strategy adds: bet nut kickers on paired boards, open-ended straight draws when both hole cards beat an 8, and 4th-nut-or-better flush draws. The trainer grades against the simpler Wizard rules above, plus the trips-board kicker rule.

River — bet 1× or fold: counting the dealer’s outs

Bet with a hidden pair or better. Otherwise count the single cards (“outs”) that would let the dealer beat you, and bet when fewer than 21 outs beat you; fold at 21 or more. When you can’t even out-kick the board (you play the board), the Las Vegas Advisor card tightens this to fold at 18+ outs.

Counting quickly. Every unpaired board rank gives the dealer 3 pairing cards, and every rank above your kicker adds 4 more (3 if it’s on the board). The board pattern sets the base:

Board textureBase outsKicker that plays (no higher card showing)
Unpaired board15King
One pair11Queen
Two pair (5th card above the low pair)7Jack
Trips7Jack
Two pair (5th card below both pairs)4Ten
Four of a kind3Seven — and see the exception below

Succession rule (odiousgambit): each board card that outranks the listed kicker moves the requirement down one — on an unpaired board a King plays; with an Ace showing a Queen plays; with Ace and King showing a Jack plays, and so on.

Exceptions from the thread:

  • Never play a bare kicker into a board 4-flush or open-ended 4-straight — fold.
  • A 3-flush or 3-straight on the board is worth roughly one extra out (runner-runner); a 4-flush or 4-straight means you count every completing card as an out.
  • Quads on the board: call very liberally. With QQQQ2 and 7-high you face 24 outs, but the Blind pays 10:1 on four of a kind, so you risk 1 unit to win about 14 — call. Exact EV, not the out count, decides these; the trainer computes it.
  • The true break-even is between 20 and 21 outs (unJon), and a weak second kicker can shade a borderline count — but not in a simple strategy.

Stephen How’s kicker view of the same rule: unpaired board — 2nd-nut kicker (nut kicker if a flush is possible); one-pair board — 3rd-nut kicker; two-pair board — 5th-nut if the top pair is 7s or better, else 4th-nut; trips board — 4th-nut; quads board — 8th-nut suffices.

Why 21? — teliot’s derivation

Folding costs 2 units (Ante + Blind). Calling risks 1 more to win 1–2. With N single-card outs, the chance the dealer hits one is roughly

p = N/45 + (45−N)/45 × (N+4)/44

— first card an out, or first card whiffs and the second hits an out (the +4 covers the dealer pairing their own first card, plus runner-runner). Calling beats folding when p < 3/4, i.e. when you win at least 25% of the time. Solving the quadratic N² − 85N + 1305 > 0 gives N ≤ 20.1 — so you call with 20 or fewer outs, fold at 21+.

Payouts, qualification, and house edge

The dealer needs a pair or better to open (qualify). If the dealer doesn’t open, the Ante pushes; Play and Blind still have action. Ante and Play pay 1:1. The Blind pays only when your winning hand is a straight or better, otherwise it pushes on a win:

Winning handBlind pays
Royal flush500 to 1
Straight flush50 to 1
Four of a kind10 to 1
Full house3 to 1
Flush3 to 2
Straight1 to 1
Anything lessPush

House edge: 2.19% optimal (≈0.53% element of risk); the Wizard’s simple strategy gives up little — about 2.43% house edge, 0.58% element of risk. The trainer’s bankroll figure is in units of one Ante.