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Play chips1000
Rounds0
Strategy match–
Dealer's exact final-hand odds for this up-card
Deal a hand. The same odds stand as columns on the board behind the table.
Educational probability tool. Play chips have no cash value and this is not betting advice: with any strategy the house keeps a small edge.
Hands0
Won0
Lost0
Pushed0
Net units0
EV / bet–
House edge–
± 2σ–
Net units over time
Measured house edge (%) with ±2σ band
The table above replays a sample hand from the run about twice a second.
Dealer lab: measured vs exact
Pick the dealer's up-card and deal the dealer's hand over and over. Solid columns on the board are what the simulation measures, the translucent blue columns are the exact probabilities from the recursion D(s) = Σ p(r)·D(s+r).
Numerical checks (run in your browser)
Each check compares an exact calculation with the simulator. About 3 seconds.
Basic strategy chart (6 decks, dealer stands on 17, double after split)
The science
- Basic strategy is the move with the highest expected value (EV) for every player hand against every dealer up-card. It only needs cards you can see.
- Dealer odds. With independent draws, P(10-value) = 4/13, every other rank 1/13, and the dealer's final-total distribution obeys
D(s) = Σr p(r)·D(s+r)until the total reaches 17. A 6 busts 42.3 % of the time, a 10 only 21.2 %. - Standing EV on total t:
EV = P(bust) + P(d < t) − P(d > t). Hard 16 vs 10 gives −0.576 standing and −0.569 hitting: the worst hand in the game. - House edge = −(mean net result) ÷ (initial bet). Perfect play under these rules leaves about 0.4 %. One hand has σ ≈ 1.15 units, so n hands measure the edge only to ±2.3/√n (±0.73 % at 100 000 hands).
- Hi-Lo count. 2–6 count +1, 7–9 count 0, 10–A count −1; true count = running count ÷ decks left. A high count means the remaining cards are rich in tens and aces. Scaling the stake with it can shift the long-run result slightly, but the effect is far smaller than the noise unless millions of hands are played.
- Simplifications. Fixed rule set (S17, DAS, split to 4 hands, one card on split aces, no surrender, dealer peeks). Exact checks use the infinite-deck limit, good to a few thousandths. The 3D table is a visualisation of the same engine as the 2D page; it adds nothing to the odds. Educational only, not a way to make money.