I saw this thread in the pit, and strangely enough it’s exactly what I was discussing with some colleagues over lunch this week.
I should point out these are smart people - we’ve had intelligent discussions on probability and other mathematical topics before. One of them is also an avid gambler. We got to talking about the notion that people will often berate an inexperienced gambler for “taking the card that would have busted the dealer”. I asked them to explain rationally, leaving superstition aside, how this could be.
He came up with an explanation that I had a hard time refuting: suppose the dealer has a “bust” card. Most casinos have a rule like “the dealer has to draw to 17”. So if the dealer has a “6” showing, and he’s forced to draw, the most likely outcome is 6…16…26 (bust). Or at least, that he’ll bust. Now, there are more 10s / face cards in the pack than anything else. By taking an extra card, you’re actually more likely to remove one of the 10s, since it’s the commonest value, thereby fractionally decreasing the odds that the dealer will bust.
I worked through the following example in my head: suppose the dealer has 16 showing. Let’s say for simplicity there are only 5 cards left - 3 10s, and 2 non-10s. If I take one, I’m most likely to get one of the 10s, leaving the dealer with 50-50 odds of busting (since 2 10s and 2 non-10s remain). If I don’t take one, the dealer has a 60% chance of busting - 3 10s, 2 non-10s. Therefore, by taking a card, I’m “helping” the dealer by decreasing his chances of busting. Of course, the card I take could be a non-10, thereby hurting the dealer, but since there are overall more 10s in the pack I’m more likely to get a 10.
So, where’s the fallacy here? I know that nowadays casinos use multiple decks, continuous shuffling and other methods to deter card-counting and such - does that negate this reasoning?
Let’s look at the **actual maths ** of your statement ‘there are more 10s / face cards in the pack than anything else’.
There are 4 10s and 12 face cards in a pack. This makes 16 in all. There are 52 cards in a pack. Therefore there are 52-16=36 other cards.
So there are less 10s / face cards in the pack than anything else’.
Therefore if you take one, you are fractionally increasing the odds that the dealer will bust.
Let’s say ‘for simplicity’ that there are only 13 cards left - 4 10s and 9 non-10s. Exactly the same proportion as in the full deck.
Carry on!
And also, a dealer cannot have a 16 showing. He or she can have a 6 showing, but not 16. As stated above, it is more likely that the dealer has less than 16, as there are more non-10 cards in the deck than 10s. By stating “the dealer has 16 showing” you’re limiting the example to a very small sample of the actual possibilities and are in fact “stacking the deck” for your argument.
If I take a card, 60% of the time I help the dealer by 10%, (as the dealer’s odds of busting move from 60-40 to 50-50), and 40% of the time I hurt the dealer by 20% (as the dealer’s odds move from 60-40 to 80-20). In other words, taking a non-bust card from a deck stacked with bust cards hurts the dealer far more than taking a bust card from the same deck helps the dealer.
I suspect that in the end it all balances out, but I’m not sure how to demonstrate that mathematically.
(a) Suppose the dealer does not have a bust card, what happens then?
(b) Suppose the card “taken” is not a 10?
(d) How likely are these to occur? (hint, as pointed out b is > 50%)
In fact, if you work through all the possibilities and the probabilities of them happening, you will find (wonder of wonders), that it doesn’t matter in the slightest whether the player takes a card or not. That’s why when you look at the strategy cards for blackjack, they don’t say things like “If the player before you has drawn a four, then…”, or “if they next player has a 17 showing, make sure to draw an extra card” – because it’s completely irrelevant.
In fact, it marginally helps everyone at the table. If you are a card counter, and other players take extra cards, that gives you extra information that can be used.
It isn’t really a question of probabilities after the amateur has drawn a card.
Say the dealer had 16, showing 6, and there was one of each card left. All the experienced players will sit because as others have pointed out anything over 5 busts the dealer.
If the amateur draws in this situation and draws anything over a 5 then he has taken the card that would have bust the dealer.
Before the newb decides what to do, you want to be able to say if he should or should not draw a card. So, ask yourself what are the odds of the the first card being drawn being one that will bust the dealer.
OK, now what are the odds that the second card will be one to bust the dealer? As you can see, since you have no knowledge of what order the remaining cards are in, it is just as likely that the first or second cards will bust the dealer, making the choice of the newbie irrelevant.
Not true, he has taken** a ** card that would have busted the dealer. The next card may also be a bust card.
If the amateur draws in this situation and drawa a 5 or under then he **has not ** taken the card that would have bust the dealer.
To say the dealer has 16, showing 6, is unfair - we do not have ESP. You just know the dealer has 6, you don’t know it’s a bust card. Suppose the dealer has a 2-9, that changes the odds.
I also find it hilarious that the term “amateur” is being thrown around. Anyone who believes this “you took my card” stuff seems like the amateur from where I sit.
But it is relevant. By taking the card, the newbie has altered the result. It doesn’t matter that the probabilities are: taking the card makes a difference in how the hand plays out.
Consider: Dealer shows 6. Newbie picks a 10. Dealer picks a 4. Obviously, the fact that the newbie took that card made a big difference in the hand.
Now, before the newbie draws the card, probability is a factor. You can argue that before he draws, the probability is the same. But after the cards are drawn by both the newbie and the dealer, it’s not a matter of probability any more. We know what cards were played, and if the newbie’s play did indeed make a difference in the outcome. Even if the probability before the play shows no effect, the actual results clearly do.
Note that if the newbie picks, and the dealer still busts, the players aren’t going to complain. So the fallacy is simply that players complain about the results, not the probability. But the results clearly indicate that, in any particular deal, the newbie’s action can make a difference.
Well of course the newb’s actions CAN make a difference, and probably WILL make a difference. The point is that this difference is just as likely to be good as it is to be bad.
So, though you can blame him after a hand that ends badly because of his draw, it is no way his fault. Heck if you want to take the attitude that he srewed up the hand, you should keep your eye out for when the same situation saves you (which will happen just as often) and tip him as a consolation for irrational critiques on other hands.
Sure, but isn’t the reverse situation just as often possible? Dealer shows a 6. Newbie picks a 4 and stands. Dealer draws the 10 and busts?
Of course every play affects the outcome of the game; I don’t think anyone is arguing that. It’s just that to blame the newbie on stealing the dealer’s card is rather stupid, when the newbie may just as well be winning hands for the team by busting the dealer.
Chuck, I’m a little unclear if this is directed at me. I meant relevant in the sense of relevant to probabilities and strategy. If you are going to yell at a player for the particular card they happened to draw, that’s just plain stupid. I assume the OP meant that the player should not draw the card in the first place. The complaint is about “taking the card”, I asume it’s the action of taking when he ‘shouldn’t’ve’.
Or Poker players for going all in with a pair of aces when someone else gets a straight.
To really analyze this situation, there is critical information missing from the OP. What is third base’s hand? If he has 10-10 and splits (or some other such nonsense, like standing on A-A), then yes, this is a horrible play (I’ve been told that it’s mathematically the worst play in the game). If he has 8-8, then the proper thing to do is split. If the hand is a 12, then he should stand. Depending on the hand, one can determine the best hand mathematically, however, such calculations are always taken into the long term.
(where “N” = “non-busting card for dealer”; “B”=“busting card for dealer”)
Of these, the first four show no difference in results: whether or not the “amateur” draws, the dealer will get the same result. Results 5, 6, and 7 show the amateur drawing a bust card and thereby leading the dealer to draw a nonbust card. Results 8, 9, and 10 show the amateur drawing a nonbust card, and thereby leading the dealer to show a bust card.
Although there are faulty premises in the OP, if we accept those premises, I think we still end up with an equal chance that the dealer draws a bust card, no matter what the “amateur’s” actions are.
Why? The choice by the newbie clearly affected the result of the hand. So why is it stupid to point out that, by making that choice, he cost the others a win?
And if the newbie’s choice still resulted in the dealer going bust, the other players are not going to complain about it. They may not like the strategy, but by winning the hand, the others will be OK with it.
You can argue the odds, but the fact remains that in that one particular hand, the newbie’s action made a difference. And if the difference is involves the dealer not going bust, it was the newbie’s actions that made that difference.
If the probabilities are the same, though, then the newbie has still made a stupid move. The only way it would be smart would be if the newbie could demonstrate an actual edge by taking the card. If you’re in a situation where the best odds to win are to see if the dealer goes bust (and a dealer showing 16 surely fits that), then it is poor play to draw a card.
It was directed to the general thread. And you don’t yell at the player for choosing a particular card; you’re yelling at him for choosing to draw in the first place. Again, in a situation where not drawing is the smart play, then drawing is stupid, no matter the actual result.
Let’s be clear about the point here: I’m not asking, “is there an optimal strategy for maximizing one’s chances in blackjack?”. I’m asking, can one of the players at a table, by sub-optimal play, adversely affect the chances of the other players? This is a purely mathematical question - which means that you can’t say, “Well, once he’s taken the card and we know what all the cards are, of course we can see that he affected play.” We are trying to figure out if the “newbie” could reason beforehand, with no clairvoyance, just the rules of probability, that it’s a bad idea to take a card, in that it would hurt the other players.