While craps is my game of choice at casinos, I occasionally will sit down at a blackjack table just to slow the night down a little bit. And from years of playing, I’m quite familiar with the strategy chart, which should maximize your chances to win based on your cards and the dealer’s up card. For those not familar, here is an example of chart.
But I think that the underlying assumption when using this chart is that you have no knowledge of any other cards that have been used, or are being used, from the shoe. But the fact is that you’re usually playing with several other players and are able to see their 2 cards, along with your 2 cards and the dealer’s up card. No matter how minimal, these other cards change the conditional probability of your next potential card. Of course, if you’re able to remember all of the cards from previous hands you can gain a big advantage. This is known as card counting and is very difficult to do. But my point is that even the cards that are in plain sight on any given hand should be able to help you. Clearly, having 6-8 decks in a shoe reduces this potential impact. But still…
Is there anyone who actually does this? As a simple example, let’s say you’re playing on a table with 6 other players. if your two cards total 15, and the dealer has 7 showing, the chart advises you to hit. The assumption is that the probability of your next card being a 2, 3, 4, 5 or 6 is enough to maximize your odds against an X-7 hand (X is the unknown dealer’s card). But let’s just say that all of the other players’ cards are all between 2 and 6. Thus, you have 12 fewer 2’s through 6’s available to help your hand. In a 6-deck shoe, 12 of the 30 cards that might help you are already gone. At this point, maybe the odds change and maybe you really shouldn’t hit that 17. I’m just curious if anyone accounts for these other cards when they play. If so, are there any rules of thumb that you follow?
Second question: Another underlying assumption that seems to prevail at a blackjack table is that the dealer’s hidden card is a 10. Since 5 of the 13 cards have a value of 10, it has the greatest probability of coming up at any given time. But if you assume that X is always a 10, then shouldn’t you also assume your next card is also always a 10? Thus, shouldn’t you always stand on anything higher than 11, assuming you don’t have a “soft” total or an available split?