21st Century Blackjack is a patented game resembling traditional blackjack.
The main deviation from blackjack is that the best hand in 21st Century
Blackjack is 22, and the game is played with jokers (wildcards).
My simulations show that with a basic (non-counting) strategy, the bank
has a .6% edge over the player. 21st Cenuty Blackjack is played in
California card rooms, where patrons may bet as either the player or the
banker. The card rooms typically charge a significant "collection"
per hand played, which is at least 1% of the action.
The purpose of this webpage is to present a comprehensive computer-generated
anaylsis of Basic Strategy and the resulting expectation values (EV).
Please comment to the author linked at the bottom of the page.
Rules
A = 1 or 10, as in regular BJ.
A "natural" is AA or A+joker or joker+joker; A joker + anything else is
a hard 22.
A "natural" beats all other hands.
The Player must hit 12 or less.
The Player must stay on hard 20 and up, and on hard/soft 21, 22.
The Player may double down on 11 or 12, and draw up to two cards.
The Banker must hit soft 18 or less.
The Banker must stay on hard 18 or more.
A dealer natural and banker natural push.
When the bank and player both bust, the player pushes when less than the
dealer, else the player loses.
If the bank shows a joker upcard, the player may not draw.
Optimal Strategy
A program (BasicStrategy.c) was used to
determine optimal strategy w/o counting. This program determined
the optimal stragegy tables (Optimal.txt).
Also, the expectation values for the optimal strategy was output by the
program.
The expectation values (EVs) for hard total hands are given in HardTotalEV.txt
and are given for soft totals in SoftTotalEV.txt.
Further, the expectation values for double-down hands are given in DoubleDownEV.txt.
For example, if a player is dealt a hard 14 vs. a dealer 8 upcard, his
EV is -.198 (he is expected to lose 19.8 cents to the dollar) and following
Basic Strategy, he must hit. If however, he gets a 5 for a total
of 19 (i.e., he got lucky), his EV is now +.355, and he now expects to
receive $1.35 for each dollar of his bet. On the other hand, if he
got a 4 instead, and stays on 18, his EV would be -.138 (he is expected
to lose 13.8 cents per dollar bet).
Another program (Simulator.c) then used
the automatically generated tables, and computed the banker's advantage
to be .6%.
An example run of 1000 hands (examples.txt)
is given to check the program.
Conclusions
Of course, the player should follow the Basic Strategy. The player
is already giving .6 cents / dollar to the bank. When he does not
follow Basic Strategy, he is giving up the additional amounts as tabulated in HardDecisionMistakes.txt
and SoftDecisionMistakes.txt . Generally, players make the
mistake of staying when they should be hitting. In this case, the
tables can be read directly to determine the average amount of extra money they
are giving to the bank. (E.g., staying on a hard 18 against a banker
A upcard is giving the banker an additional 6 cents per dollar.) In the case where
the player hits when he shouldn't, his average cost for this mistake is
also read directly from the table. (E.g., hitting a hard 15 against
a banker 7 upcard is giving an additional 5.4 cents per dollar to the bank.) However,
if the player does not bust on the incorrect hit (i.e., he got lucky!),
then of course he has paid nothing to the bank, and will end up with a
better hand that has a greater probability of winning. The cost of
any subsequent mistake can be read from the tables as just described.
The bank has a .6% edge over the player, and the house takes a collection
> 1%.
