Expected Value
  • Expected Value (EV) is defined as the amount you can expect to win/lose per bet. (After about a million hands!) Thus if you bet $1.00 on a hand with an expected value of .17 you would expect to win .17 cents. This happens to be the expected value if you hit the hand, per the Bjmath tables, of 6,3 vs a dealers 5. So far so good. However, if you double that hand the expected value goes to .266081 or rounded to .27. Thus, per the table your EV is now 27 cents per 1.00 bet. Note .27 is about a 58% gain from .17. (It is not double)
    Question: If you have the same cards whether you hit (take one card) or double (take one card) why does the EV change? In fact, if you hit you can take a second card, so it seems that if anything, the EV of a double should be less than the EV of hitting? If the EV is in some way depended on the bet why does it not double? What is the logic of it only rising 58% and not a 100%?
  • Sage, I think you understand the situation better than you think. When you double, you give up the right to additional cards. So if you catch a 2, you're stuck with 11. Clearly, this is a big disadvantage, and it happens 1/13 of the time. This is why your EV does not double, and only goes up 58%.

    The EV is based on the initial bet, if you look at some of the more stupid moves (e.g. doubling 20vA), you'll see an EV with an absolute value greater than 1 (e.g. -1.71). So your inital bet of $1, turns into a loss of $1.71. This is done so you can multiply all the EVs by their probabilities, add them all up, and end up with the EV for the game. (this won't actually work unless you adjust for the dealer checking the hole card with a T or A - I've tried it. :wink:) It also makes it easier to see when doubling and splitting are better moves.
  • Thanks Mr Ed. OK Got it, Now let’s do some second guessing.… In reviewing the tables, it looks like BS stand/ hit/double/split rules are based upon picking the most positive EV of the four choices, regardless of how small the difference. Thus you can be doubling your bet (risking twice your money) and only end up with a slight increase in EV. Not sure I would do that in my non BJ life. If I double my investment, I would expect a double of the return, not some fraction of the investment. Anyway onward…..
    Let’s look at some of the “proper” BS moves:
    A4 vs 4. BS says DD, EV of hitting is .059395; EV of doubling is .062389.
    So first thing it’s about a breakeven bet. I’m only getting .002994 more $$ if I double my $1.00 investment (bet). So for the extra $1.00 invested, I’m getting less than a 1 cent return?? Does not look like a good idea. But BS says do it because the DD EV is .002994 positive. Conclusion: My kitchen arithmetic says this is not a good double!!
    Look at A7 vs a 3. DD is the correct BS, the EV is only .17933. So I get an extra 18 cents for risking an extra $1.00??
    In looking at the tables (all possible BJ hands with 6 decks) you can find a number of “questionable” BS moves, Lots of $$ risk on a DD for a very small gain?
    Wonder if a review of the split, hit/stand BS rules would yield the same close bets?
  • Sage, interesting topic you brought up.

    Let me start by saying that you must realize that BS is based on the longterm and based on millions of hands & that is how BS comprised the BEST way to play each and every single hand. Even though the difference is very minute in some cases, you must realize that a better move, is still a better move, no matter if it's gonna make you a winner 67% of the time (Doubling 11v6) or 0.000000000000000000001% of the time.

    Also, since you're sounding doubtful, would you rather play a losing move, one contrary to Basic Strategy or one that you know is the correct play? The answer should be obvious.

    Hope you understand what I'm saying. Let me know if I can clear anything up for you.
  • Sage: There is not much to add to what "BUG" has said because he
    is addressing the actual play environment. EV and ODDS help us to
    better understand the game; just how close the game is. It's a natural
    feeling to want to carry that over into game situations, but you just can't
    do that. B/S, or changes to it as a result of observations and/or count
    systems, are proven concepts that we must adhere to if we are to have
    any chance to win. Another thing to take into consideration as regards
    EV is the outcome of playing sessions. If your a small better, the EV for
    your session, just might pay for the gas that got you to the casino, but not
    much else. Typically, that is not how things work and most sessions will
    not be anywhere near some calculated amount. You will win or lose in
    "chunks" and if you make the right play everytime, your chance to win
    is improved considerably.

  • Last time I went to the Casino, here in town, I bought a used BJ deck and inside was a BS card. The Casino’s wants you to play BS! Why?? Well look at some of the DD %’s. Take 6,4 vs 8, EV of hitting is .19962, (19.96%) or 20 cents per $1 bet. BS says DD, then the EV is .291603, but that’s after any extra $1.00 bet, so on the $2.00 total bet, the 29 cents win is 14.5%. So if you double down, the total win % goes down. Well, if it goes down for me, then it goes up for the Casino. Thus the Casino makes more money if I double down on this hand…… Thus there are some marginal BS bets that may not be worth doubling the risk, by doubling the bet. Unless, you are keeping track of the cards and know the high value cards will be coming out. My point is that BS is very useful for the card counter, but all the BS rules (some of the DD on 9’s and some soft doubles) may not be the best for the casual weekend player that does not track the cards. Look at A4 or A5 vs 4. BS is DD, gain is 7% & 6% for a 100% bet increase. No wonder the Casino’s like BS, DD!! So in some cases maybe you should just hit the hand not DD???
  • Sage, You are correct, there are some bad doubles where you should
    just hit rather than double. Example: 9vs2, 9vs7, 11vsA, A7vs2, etc.
    In this case the B/S player has the edge if he dbls., but he makes more
    money if he hits. Later on the odds change because of the count and now
    the counter sitting next to him starts to double these hands. Does that
    make B/S wrong or any less right? I don't think so...........................

  • Sage, nothing personal but it sounds like you've been reading some bogus blackjack books... listen to what people here are trying to tell you. Basic Strategy is the foundation on which all successful BJ play is based - you must trust and follow it or you're going to pay, literally.

    Don't equate blackjack with a stock investment where you're constantly weighing risk vs reward; the basic strategy is the proven best plays over millions/billions of simulated hands - even though the math seems counter-intuitive at times. Since the plays are proven winners (i.e. win the most money or lose the least money), the risk piece has essentially been removed and the EV points you to the correct play.

    Of course its also true that since we don't play the million/billion hands ourselves the EV numbers will not hold perfectly true. Some plays will work out a little better for you and some will be a little worse... but don't use the kitchen math to try and figure which ones or you'll end up just another sloppy bj player.
  • Sage, you have some good insights about the risk/reward trade off, but keep things in perspective. If you are investing your life savings, you will be very concerned about risk, because it would be devastating if you lost your life savings. If you buy (one) lottery ticket, you can certainly afford to lose it all, but you gain the chance at a huge return.

    If you (foolishly) have a bet on the table that makes you uncomfortable, than certainly hit, rather than double - but by definition, your bet is too big. But by hitting, you give up on EV. For the A4v4 example, you give up 0.3% of your bet, when you hit, rather than double. Doesn't seem like much? Consider that the house advantage for BS is about 0.5%, and like you noticed, casinos are giving away BS cards.

    You are thinking, "by doubling, I am investing $2, by hitting I am investing $1". But the EV tables show you "If you double, you can make an extra 0.3 cents." Our goal is not to achieve the highest rate of return, but it is to achieve the highest dollar amount of return. So don't over-analyze the situation.

    Having said all that, there are certain situations that are just so close, that your original thought makes sense: e.g. A2v5. I did the numbers a few posts ago and I think the advantage was something like 1 bet after a million hours of play. So feel free to hit A2v5.

    At a +5 count, the correct move with 10v10 is to double. Well, here's where I get squeemish - I have my max bet out and I just hit that hand. Other hands with +4 counts, I wait until the advantage is a little bigger at +5 before I use them.

    My point is that you should carefully pick which BS plays you ignore, and when you do, understand that in the long run, you are leaving money on the table.

    p.s. Look carefull at that BS card - I would suspect that it contains errors.
  • This is an interesting thread. Thanks to everyone contributing. I am not a statistician, but I am reasonably comfortable with numbers. so I guess i that regard I'm an "average Joe". To me, black jack is a skill and a game. If there is a more superstitious group than gamblers, I've yet to see it, (include traders in the subset of gamblers). Many will agree that someone who walks by and throws down money in the middle of a hot table and walks away pisses most of us off, even though we know objectively that his action be shown to affect our hands. That's the subjectivity of the beast.

    I play about 300 hours a year, much of it heads up. This is alot by recreational standards, but nothing compared to the number of hands needed to reach "long term" probabilities. My point is that money management may be as important to long term success as skill. So in the situation of the marginal dd, even though I know the correct ("flawless") bs play, if I have an uncomfortably large amount of money up, the tables cold, someone new has just sat down, the dealer has just changed and burned a card, my drink is late, I'm out of cigarettes, my girl friend has just left me, the plane is leaving in 45 minutes, and I'm down 200 units for the trip, I might just hit that hand and feel ok about it. If some of you think that makes me a fool, I'm ok with that too.
  • If you re-read these post, you'll see a common threat running thru
    our discussions. It's "money" and we need to work on that because
    our judgement is impaired.
  • Sometimes by pushing things to an extreme I can understand concepts better. The books say you will win 43.31% of the hands, lose 47.89% and push 8.8%. This is hands won, not the $$ won. BS is all about total $$ won. Say we have a new player, he plays the BS hit/stand/splits perfectly, but never DD. What happens?? Will his hands "won" ratio go up? "Yes" but since he will have bet less overall $$ his win and loss extremes will be less. So he has won more hands at the table, and also reduced the swings in his bank roll. He will go home with less $$ on a good day and with less $$ loss on a bad day. In short he has reduced his standard deviation, because his average bet is less. He can play with a smaller bankroll. Comments?? (Note, I am not recommending this approach, just want to understand the numbers better!!)
  • You got it.

    And he could reduce his bankroll requirement to zero, if he didn't play at all :wink:
  • Ray-

    Your "judgment is impaired" response, caught me off guard. Can you explain please? I'm here to learn.
  • Larz177, Money matters in most gambling situations and BJ is no
    exception. The importance of hitting that 16 vs 10 when your down
    to your last chip or making that three card split with a couple of DD's
    thrown in are good examples. These are difficult times for the majority
    of the population. We know what is right or wrong, but tell that to the
    feelings of going home with empty pockets if you lose. Is it possible to
    overcome those tendencies? Well, yes for a few, but for the majority,

  • Ray-

    Yes, money does matter. Isn't that obvious? I have posted several times about money management. However, I do firmly believe that the game has a certain feel and rhythm that can be used to advantage. I was speaking generally only of the extremely marginal dd situation. I took your impaired judgement comment badly. There are enough ridiculous personal attacks on this board, and I won't do anything to further the situation.


  • Larz177, I understand. If you have played for a few years you have seen
    those situations play-out day after day. That's just the way it is. May the
    rhythm of the game make you a winner........................................

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