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Thread: Easy Question Re: Player Advantage and Average Bet Size

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    Easy Question Re: Player Advantage and Average Bet Size

    Hello all,

    A simple question I should know the answer to:

    One of Norm's calculators asks for 4 pieces of data such as "player advantage" and "average bet size" and "number of hands played" and "desired outome in units," I believe.

    I am getting 'tripped up' with advantage vs. E.V., I think. For example, if a card counter says she has a .4% advantage, doesnt that mean she can expect to profit, over the long run, about $.40 per $100 that she wagers?

    If that is true, lets say she manages to generate the .4% advantage with a $10 - $40 bet spread.

    BUT WOULDN'T HER ADVANTAGE CHANGE BASED ON HER BET SPREAD? In other words, if she applied her same count system but used a $10 - $60 spread instead of a $10 - $40 spread, wouldn't her advantage increase (along with her variance)?

    So, are variance and an insufficient bankroll, along with heat from pit personnel, the 'only' things stopping counters from using, say, in the above example, a $10 - $120 bet spread?

    So, with Norm's calculator, isn't what one enters for 'player advantage' contingent upon what she enters for "average bet size?"

    Finally, if I can predict the presence of an Ace with an average accuracy of 11.46%, that does NOT mean that my advantage (just when predicting Aces and therefore not taking into account flat betting the 'rent bets) is 11.46%, correct? Rather my advantage is about .(1146 X .51) + (-.005 X 'I forget'), or about 5.00%, correct? If that is indeed correct, is there a term for the .1146?

    Thank you all in advance!
    Last edited by Overkill; 03-13-2021 at 10:25 PM. Reason: Clarification

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    Quote Originally Posted by Overkill View Post
    Hello all,

    A simple question I should know the answer to:

    For example, if a card counter says she has a .4% advantage, doesnt that mean she can expect to profit, over the long run, about $.40 per $100 that she wagers?
    ...

    Finally, if I can predict the presence of an Ace with an average accuracy of 11.46%, that does NOT mean that my advantage (just when predicting Aces and therefore not taking into account flat betting the 'rent bets) is 11.46%, correct? Rather my advantage is about .(1146 X .51) + (-.005 X 'I forget'), or about 5.00%, correct? If that is indeed correct, is there a term for the .1146?
    On your first question, the 0.4% advantage is specific for your counting system and bet spread. Player’s advantage varies a lot from hand to hand, that is why we can win.
    On your second question, your advantage is 0.1146*0.51-0.1146*0.34.
    Last edited by aceside; 03-14-2021 at 07:49 AM.

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    Overkill - yes, heat and bankroll considerations drive most betting strategies that you will develop. In some cases limitations like table limits come into play as well.

    Aceside not sure i am following your logic - where does the .34 come from? i would have computed the edge as (.1146*.51) - ((1-.1146)*0.005) - do the math and its about a 5.4% edge overall - nice game for the overkill.

    Cohiba

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    Quote Originally Posted by Cohiba View Post
    Overkill - yes, heat and bankroll considerations drive most betting strategies that you will develop. In some cases limitations like table limits come into play as well.

    Aceside not sure i am following your logic - where does the .34 come from? i would have computed the edge as (.1146*.51) - ((1-.1146)*0.005) - do the math and its about a 5.4% edge overall - nice game for the overkill.Cohiba
    Discussions like this are pointless--and the math is basically wrong--without being much more specific about the assumptions. When someone says he can predict an ace coming with 11.46% average accuracy, what, exactly, does that mean? Does it mean that, playing alone, you can call the ace for your hand only with that accuracy, or does it mean that you can call an ace coming for the next round and that you don't know if it will go to you or the dealer (aceside's somewhat arbitrary assumption)? Obviously, there's an enormous difference in how the calculation would then proceed. And, of course, no mention is made of how many player hands there are, which affects the probability of whether the dealer will get the ace or not.

    Don

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    Quote Originally Posted by DSchles View Post
    Discussions like this are pointless--and the math is basically wrong--without being much more specific about the assumptions. When someone says he can predict an ace coming with 11.46% average accuracy, what, exactly, does that mean? Does it mean that, playing alone, you can call the ace for your hand only with that accuracy, or does it mean that you can call an ace coming for the next round and that you don't know if it will go to you or the dealer (aceside's somewhat arbitrary assumption)? Obviously, there's an enormous difference in how the calculation would then proceed. And, of course, no mention is made of how many player hands there are, which affects the probability of whether the dealer will get the ace or not.

    Don
    I totally agree with Don.

    Let me just answer Cohiba's question to me. The 34% is the dealer's advantage when she gets this marked ace.
    In another thread, Cohiba also asked me why I didn't switch to Zen count. That is because I play side bets like king's bounty and lucky ladies, and also because Zen is not accurate for Stand-17 games.

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    Quote Originally Posted by aceside View Post
    I totally agree with Don.
    Now you've got me worried.

    Don

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    Quote Originally Posted by DSchles View Post
    Now you've got me worried.

    Don
    No worries. I am asking Cohiba to help sim this proposal:

    Consider a 6-deck shoe with strip rules to play solo using the Kelly bet spread. When TC>+1 and ace density>4 per deck, I play one blackjack hand; when TC>+1 and ace density<4 per deck, I play two blackjack hands.

    Do you think this sim is valid? And doable?
    Last edited by aceside; 03-15-2021 at 09:28 PM.

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    1) To clarify, there are several opportunities within 6-deck shoes that I have proclaimed "the very next card will be an Ace" with the above-mentioned accuracy with a small sample of one player playing two hands against the dealer (6 deck shoe) as well as a small sample of one player varying from one to three hands per round throughout a 6-deck shoe.

    I have not been recording the outcome of the hands, only the outcome of whether I have been successful in predicting that the next card will be an Ace or not. For example, I am correct in my prediction about 11 times out of 100, whereas chance would dictate a correct prediction once out of 10? (2, 3, 4, 5, 6, 7, 8, 9, 10, A)? Ace prediction attempts.

    Given that clarification, is not Cohiba's math (above) correct? Further, how is the possibility of the dealer getting THE Ace I predicted not already factored in to the .51 figure? In other words. when someone says he has, for example, a .42% advantage counting cards, then he has a .42% advantage counting cards. Simulations yield that number, correct? We don't subtact from the .42% the possibilities of the dealer receiving the 'good cards' that the player was hoping for - it's 'built in' already, right?

    But I guess wiith Ace prediction that is not the case, or at least that is not the case with Ace prediction with, say, less than 3 or so other players other than I at the table to 'catch' a 'late' Ace that we don't want the dealer to get?

    So, I still need to subtract as Cohiba did above, correct? And then the NEXT STEP is to subtract the likelihood of the dealer winning the hand based on getting 'my' Ace, or just the likelihood of the dealer getting 'my' Ace, or just the dealer winning the hand?

    2) And what about my question above regarding average bet size and advantage. For example, Don: On page 24 of your book you give the reader some very useful information - "For a given bankroll, and a given advantage at a specific true count, an optimal bet is determined by multiplying the bankroll by the edge (in percent) and dividing the outcome by the variance (Griffin prefers the average squared result of a hand of blackjack, but the difference is slight) of hands played at the particular true. According to Stanford Wong..."

    But how does one calculate, without the aid of a computer, the edge or advantage (percent)? Isn't the edge a function of average bet size? If so, it seems mathmatically improper to have one variable (edge or advantage) in a formula (optimal bet formula) be dependent on another variable (average bet size) within the same formula? Where have I gone astray, oh Wise Ones??

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    Quote Originally Posted by aceside View Post
    Do you think this sim is valid? And doable?
    Virtually any sim that you can think up is "doable." But, no, I don't think the proposal is valid, and it won't lead to anything meaningful or worthwhile.

    Don

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    Quote Originally Posted by Overkill View Post
    I have not been recording the outcome of the hands, only the outcome of whether I have been successful in predicting that the next card will be an Ace or not. For example, I am correct in my prediction about 11 times out of 100, whereas chance would dictate a correct prediction once out of 10? (2, 3, 4, 5, 6, 7, 8, 9, 10, A)? Ace prediction attempts.
    No, of course not. Chance would predict one out of 13. There are four tens!

    Quote Originally Posted by Overkill View Post
    Further, how is the possibility of the dealer getting THE Ace I predicted not already factored in to the .51 figure?
    It most certainly is NOT! When we say that knowing a player hand will contain at least one ace is worth 0.51% to the player, no assumption at all is made concerning the dealer's hand. The assumption is that his hand will contain random cards.

    Quote Originally Posted by Overkill View Post
    But I guess with Ace prediction that is not the case, or at least that is not the case with Ace prediction with, say, less than 3 or so other players other than I at the table to 'catch' a 'late' Ace that we don't want the dealer to get?
    That's why I mentioned the assumptions that either are or aren't being made. If you know the arrival of an ace is imminent, but you could be off by one, thereby giving that ace to the dealer rather than to yourself, then that is very harmful. Because, if the dealer has an ace in his hand, then he has a 0.34% edge over the player, whose hand now becomes the random one.

    Quote Originally Posted by Overkill View Post
    So, I still need to subtract as Cohiba did above, correct?
    Yes. Or, so it seems to me. And, again, that edge is 0.34% for the dealer.

    Quote Originally Posted by Overkill View Post
    But how does one calculate, without the aid of a computer, the edge or advantage (percent)?
    What need do you have to do that? There are two ways to calculate anything in blackjack: simulation of combinatorial analysis. And, while virtually everything can be done by the former, not everything can be done accurately by the latter. So, your need to do things "without the aid of a computer" makes little sense to me.

    Edges at various true counts can be calculated irrespective of bet sizes at those edges. Factoring in the latter gives you a global advantage for the entire endeavor, but you start with the local edges and then proceed from there. I can list the edges at each true count for a given game and set of rules without ever enunciating a bet size at those levels. Then, once you furnish bet sizes, and necessary frequencies, you establish an average bet and an overall edge for the approach you're using.

    Don

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    Ok, thanks so much, Don (and others). Your last paragraph really helps. What I meant by "without the aid of a computer" is: What are the 'longhand' formulas for finding edge and for finding EV?

    EV (Expected Value), or expected profit, is expressed as a dollar amount. It is derived by multiplying number of hands X average bet size X average advantage, correct? E.g., 100 hands X $10 X 3.5% = $35. (However. this of course does not take into account volatility (variance).).

    1) But how does one calculate advantage? I had thought it was number of dollars won or lost ÷ total amount bet. E.g., $90 won in one Blackjack flat betting session ÷ $900 = 10% Average Advantage or Global Advantage.

    2) But is this also how one would, without the benefit of a simulator, derive row 4 "Advantage (percent)" of Table 2.3. (p. 23) of your book?

    As you see in 1) above, I did indeed use a dollar amount to find my average advantage. But, Don, didn't you say above that for a card counter, LOCAL edges for various counts can be calculated IRRESPECTIVE of bet sizes at those counts.

    3) So, what is the formula for calculating a local edge? Does it have to do with (Heaven help me) win rate?

    The source of my confusion may lay in local edge vs. global edge.

    Finally, and I may be getting ahead of mysef now because I haven't yet seen your answers to my above questions, but

    4) Please assume a flat bettor has a local edge of 1.0% for hands 1 and 2 and 3 and 4 and 5 and 6, and for hands 7 - 36 , she has a local edge of 3.0%. What is her global advantage? Is it (.01 X 6) + 5(.03 X 30) = .06 + 4.5 = 5.1. Now we divide 5.1 by 2 and arrive at 2.55% global advantage? Is that correct for this flat betting example that does not take into account bet size changing at various counts?

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