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Expctation Online Blackjack Games

B. interactive Approximation

( l ) Evaluate dealer probabilities for each of 55 subdecks (the 55 interactive combinations). Then average these to find the 10 single card removals and full-deck figures, from all of which the appropriate parameters may be generated. This preliminary work would presumably take about six times as long as in A(1), but only 1/55th as long as exact determination of dealer probabilities for all 3,000 subsets.
(2) Proceed as in A(2).

i present here, for the standard Las Vegas strip single-deck games where the dealer stands on soft 17 (but which is hardly ever offered), a comparison of results and computer times on the CSUSacramento VAX computer

A confession is in order here: Because it was easier to cannibalize one computer program from another, the dealer's probabilities ire actually evaluated 11 times in A(i) and 66 times in B(1) and no averaging took place. Thus the running times of Methods A and B could have been marginally reduced even further, perhaps 2 and 20 seconds respectively.

A few examples of individual player expectations with optimal strategy for specific hands will be presented here for dealer up cards of 2 and 9 to suggest the degree of accuracy engendered by the approximations.
it is not a coincidence that two-card standing expectations are precise for Method B since exact dealer probabilities would have been calculated for removal of the player's two cards. Generally the approximations are at their poorest for small up cards like the 2 and for hands with doubled expectations. There is also a subtlety (discussed at greater length in page Tilve) when the dealer up card is a ten or ace that the approximations are somewhat blunted because the effects of removal do not quite precisely sum up to zero, due to conditioning on the fact that the dealer does not have Online Blackjack Games.

If no one else has bet yet, you need not bet to remain in the hand. You can say "check," (sometimes players rap the table with their knuckles to indicate a check) and this passes the betting opportunity along to the next player, clockwise. If no one bets on that betting round, the next card is dealt; if this happens on the final betting round, hands are exposed to determine the winner. If you check and someone else bets, you can then opt either to call, raise, or fold. Many beginning players forget about the checking option and automatically fold if they don't want to bet. Hold onto your cards until/unless someone else bets.
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