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Strategy & rules lab

Right play. Right rules.

Strategy is conditional. Select the table rules first, then use the chart that actually applies.

Blackjack basic strategy

Multi-deck blackjack

These charts maximize expected value for a 4–8 deck game with dealer peek. Blackjack pays 3:2. Splitting aces receives one card. No re-splitting aces is assumed.

Common multi-deck variants:
H HitS StandD DoubleDs Double; otherwise standP SplitR Surrender

Hard totals

Player2345678910A
8 or lessHHHHHHHHHH
9HDDDDHHHHH
10DDDDDDDDHH
11DDDDDDDDDH
12HHSSSHHHHH
13SSSSSHHHHH
14SSSSSHHHHH
15SSSSSHHHRH
16SSSSSHHRRR
17SSSSSSSSSS
18+SSSSSSSSSS

Soft totals

Player2345678910A
A,2HHHDDHHHHH
A,3HHHDDHHHHH
A,4HHDDDHHHHH
A,5HHDDDHHHHH
A,6HDDDDHHHHH
A,7SDsDsDsDsSSHHH
A,8SSSSSSSSSS
A,9SSSSSSSSSS

Pairs

Player2345678910A
2,2PPPPPPHHHH
3,3PPPPPPHHHH
4,4HHHPPHHHHH
5,5DDDDDDDDHH
6,6PPPPPHHHHH
7,7PPPPPPHHHH
8,8PPPPPPPPPP
9,9PPPPPSPPSS
10,10SSSSSSSSSS
A,APPPPPPPPPP

Underlying math

For each state, the recommended action is the legal action with the highest conditional expected value: EV(action | player cards, dealer upcard, rules). Dealer completion probabilities and player draw outcomes are evaluated over the remaining-card distribution. Composition-dependent exceptions can occur; this is total-dependent basic strategy.

Chart scope: These are 4–8 deck, dealer-peek, 3:2 charts. Do not use them for 6:5 blackjack, European no-hole-card games, Spanish 21, Blackjack Switch, or other variants with materially different rules.
Ultimate Texas Hold’em

Decision strategy by street

The strength of the hand is only half the decision. The permitted multiplier shrinks from 4× preflop to 2× on the flop and 1× on the river.

Lower card →
High2345678910JQK
AYYYYYYYYYYYY
KYYYYYYYYYYY
QNNNNSSYYYN
JNNNNNNSSY
10NNNNNNNN
9NNNNNNN
8NNNNNN
7NNNNN
6NNNN
5NNN
4NN
3N
Y Always raise 4×S Raise 4× if suitedN Check

Pairs: raise 3-3 or higher; check 2-2. “Suited” means both hole cards share a suit.

2× · Flop

Raise with

  • Two pair or better
  • A hidden pair, except pocket deuces
  • Four to a flush with a ten-or-higher hole card

Otherwise check and retain the 1× river option.

1× · River

Raise with

  • Any pair or better
  • Or fewer than 21 unseen dealer hole cards that beat your hand

Fold weaker hands once the dealer-out count reaches 21.

Why the thresholds work

The decision compares the incremental EV of betting with checking or folding across all compatible dealer hole cards and remaining community cards. The 4× chart is a compact near-optimal boundary; the river dealer-out test preserves card-removal information that a simple hand-rank chart loses.

Three Card Poker

The Q-6-4 decision line

For the standard Ante/Play game, make the Play wager with Q-6-4 or better. Fold anything lower.

Always playPair or better · any K-high · any A-high · Q-7-x+
BoundaryPlay Q-6-4 or better
FoldQ-6-3 or lower · Q-5-x and below

Underlying math

The threshold comes from enumerating possible dealer three-card hands after removing the player’s cards, applying the dealer qualification rule, and comparing the EV of making the Play bet with the certain loss from folding. Pair Plus is resolved independently and does not change the Ante/Play decision.