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Thread: PaddyBoy: How to calculate your edge.

  1. #1
    PaddyBoy
    Guest

    PaddyBoy: How to calculate your edge.

    Not a BJ question but advantage play,sort of.
    It is from who wants to be a millionaire.

    If i was at 64,000$ and only the 50/50 option left i always said would go for it as you risk 32,000 but can rise by 64,000.A 2/1 payoff for a even money chance.

    So for a 2/1 payoff in any play you should have more than a 33.33% chance of winning,you have a 50% of winning so is this a 16.66% advantage?

    Now if this is a 16.66% advantage and lets say you are broke before the game,are you mad to take the 50/50 as you are betting half your Bankroll? And thereby seriuosly overbetting?


  2. #2
    Geoff Hall
    Guest

    Geoff Hall: Re: How to calculate your edge.

    > If i was at 64,000$ and only the 50/50
    > option left i always said would go for it as
    > you risk 32,000 but can rise by 64,000.A 2/1
    > payoff for a even money chance.

    In fact the payoff is even greater as you may know the answer to the next question (actually you may know the next 4 answers and end up with $1M).

    I would go for 50-50 regardless of my financial status as the gains are too tempting.

    Best regards

    Geoff


  3. #3
    Don Schlesinger
    Guest

    Don Schlesinger: Re: How to calculate your edge.

    It's not as simple as you make it out to be.

    First, in your discussion, you neglect the fact that, should you get the right answer, you continue and may win hundreds of thousands of dollars more. It isn't an "either/or" proposition, and the total of all possibilities to win money has to be considered.

    Second, no two people's utility functions are identical. To a risk-averse individual, losing the $32,000 that is in hand may be intolerable. To a more aggressive player, going "with the edge" is clearly the proper move.

    Don

  4. #4
    Geoff Hall
    Guest

    Geoff Hall: Re: How to calculate your edge.

    > It's not as simple as you make it out to be.
    > First, in your discussion, you neglect the
    > fact that, should you get the right answer,
    > you continue and may win hundreds of
    > thousands of dollars more.

    Keeping it simple, if the probability of you knowing the answers to the next questions is 50/50 then the 'Gamble' is worth an extra $250,000 on top of the $32,000 gained by guessing. So you would end up, on average, with $314,000 instead of $32,000.

    Even if the probability of you knowing the answer, was 10/1, for each question that followed, you would still gain an additional $15,600 on average i.e. overall win of $79,600 instead of $32,000.

    Of course, in England, you could always hire someone with a bad cough :-)

    Best regards

    Geoff

  5. #5
    Paddyboy
    Guest

    Paddyboy: Ok forget about millionaire

    Ok forget about it being millionaire.
    Lets us just say it is on any 2/1 payoff for a 50/50 chance.
    I just want to know what your advantage is and how much of your BR you should bet

    > Keeping it simple, if the probability of you
    > knowing the answers to the next questions is
    > 50/50 then the 'Gamble' is worth an extra
    > $250,000 on top of the $32,000 gained by
    > guessing. So you would end up, on average,
    > with $314,000 instead of $32,000.

    > Even if the probability of you knowing the
    > answer, was 10/1, for each question that
    > followed, you would still gain an additional
    > $15,600 on average i.e. overall win of
    > $79,600 instead of $32,000.

    > Of course, in England, you could always hire
    > someone with a bad cough :-)

    > Best regards

    > Geoff

  6. #6
    Geoff Hall
    Guest

    Geoff Hall: Re: Ok forget about millionaire

    > Ok forget about it being millionaire.
    > Lets us just say it is on any 2/1 payoff for
    > a 50/50 chance.
    > I just want to know what your advantage is
    > and how much of your BR you should bet

    OK, let's assume that you can either take $50,000 or gamble 50/50 and end up with either $25,000 or $100,000.

    Overall, if you gamble, then you would 'average' $62,500, a 25% advantage.

    Putting this into perspective, if you knew that 1 of the next 2 cards, in a game of Blackjack, was definately an Ace, this would give you roughly a 25% edge over the house by betting both boxes.

    The question is, with infinite table limits, how much would you bet ?

    Don answers this by stating that it depends on :-
    a) The amount of available financing the person has.
    b) The type of person placing the bet and whether they are 'safe' bettors or 'reckless' bettors, or somewhere in between.

    If you gave 1000 people a hypothetical $50,000 bankroll and asked them how much they would stake then you would get a variety of answers. Don and Karel had a past thread looking at the mathematical analysis of how much to bet in relation to the advantage at hand, but I'm not sure how to retreive this information.

    Even with a 99% edge, would you risk the whole of your bankroll at 2/1 ???

    Best regards

    Geoff

  7. #7
    PaddyBoy
    Guest

    PaddyBoy: Re: Ok forget about millionaire

    >Overall, if you gamble, then you would 'average' >$62,500, a 25% advantage.

    Can you tell me how to arrive at this number.Can you give me a formula?ie if chance of winning is 40% and you get paid 3/1 what is edge.
    I just want a formula to arrive at my edge.

    > OK, let's assume that you can either take
    > $50,000 or gamble 50/50 and end up with
    > either $25,000 or $100,000.

    > Overall, if you gamble, then you would
    > 'average' $62,500, a 25% advantage.

    > Putting this into perspective, if you knew
    > that 1 of the next 2 cards, in a game of
    > Blackjack, was definately an Ace, this would
    > give you roughly a 25% edge over the house
    > by betting both boxes.

    > The question is, with infinite table limits,
    > how much would you bet ?

    > Don answers this by stating that it depends
    > on :-
    > a) The amount of available financing the
    > person has.
    > b) The type of person placing the bet and
    > whether they are 'safe' bettors or
    > 'reckless' bettors, or somewhere in between.

    > If you gave 1000 people a hypothetical
    > $50,000 bankroll and asked them how much
    > they would stake then you would get a
    > variety of answers. Don and Karel had a past
    > thread looking at the mathematical analysis
    > of how much to bet in relation to the
    > advantage at hand, but I'm not sure how to
    > retreive this information.

    > Even with a 99% edge, would you risk the
    > whole of your bankroll at 2/1 ???

    > Best regards

    > Geoff

  8. #8
    Geoff Hall
    Guest

    Geoff Hall: Re: Ok forget about millionaire

    > Can you tell me how to arrive at this
    > number.Can you give me a formula?ie if
    > chance of winning is 40% and you get paid
    > 3/1 what is edge.
    > I just want a formula to arrive at my edge.

    You are basically using the expected outcome of numerous trials in order to calculate your expectation of a single event.

    So, for your example above, (40% win at 3/1), to calculate your edge :-

    Let's say that you either keep $20,000 or can gamble and end up with either $10,000 (lose) or $60,000 (win at 3/1).

    If you don't gamble then your expected amount is obviously $20,000.

    If you do gamble then 60% of the time you will end up with $10,000 and 40% of the time you will end up with $60,000.

    Now take, say, 100 trials :-

    Not gambling = $2,000,000 (=$20,000 per single event).

    Gambling = (60 X $10,000) + (40 X $60,000) = $600,000 + $2,400,000 = $3,000,000 (= $30,000 per single event).

    So, gambling, in this example, will gain you an extra $10,000 from just keeping the $20,000 by not gambling.

    Therefore your increase from $20,000 to $30,000, in expected return, gives you an edge of

    10,000/20,000 X 100 = 50% edge. (increase/initial amount X 100)

    Hope this helps

    Geoff

  9. #9
    PaddyBoy
    Guest

    PaddyBoy: Re: Ok forget about millionaire

    >Let's say that you either keep $20,000 or can >gamble and end up with either $10,000 (lose) or >$60,000 (win at 3/1).

    If you bet 20000 at 3/1 wont you end up with 80,000,Your winnings and the initial bet.This is the way it works in my bookies anyway

    > You are basically using the expected outcome
    > of numerous trials in order to calculate
    > your expectation of a single event.

    > So, for your example above, (40% win at
    > 3/1), to calculate your edge :-

    > Let's say that you either keep $20,000 or
    > can gamble and end up with either $10,000
    > (lose) or $60,000 (win at 3/1).

    > If you don't gamble then your expected
    > amount is obviously $20,000.

    > If you do gamble then 60% of the time you
    > will end up with $10,000 and 40% of the time
    > you will end up with $60,000.

    > Now take, say, 100 trials :-

    > Not gambling = $2,000,000 (=$20,000 per
    > single event).

    > Gambling = (60 X $10,000) + (40 X $60,000) =
    > $600,000 + $2,400,000 = $3,000,000 (=
    > $30,000 per single event).

    > So, gambling, in this example, will gain you
    > an extra $10,000 from just keeping the
    > $20,000 by not gambling.

    > Therefore your increase from $20,000 to
    > $30,000, in expected return, gives you an
    > edge of

    > 10,000/20,000 X 100 = 50% edge.
    > (increase/initial amount X 100)

    > Hope this helps

    > Geoff

  10. #10
    Geoff Hall
    Guest

    Geoff Hall: Re: Ok forget about millionaire

    > If you bet 20000 at 3/1 wont you end up with
    > 80,000,Your winnings and the initial
    > bet.This is the way it works in my bookies
    > anyway

    I was using the same basis that you quoted from your first thread :-

    ..."If i was at 64,000$ and only the 50/50 option left i always said would go for it as you risk 32,000 but can rise by 64,000.A 2/1 payoff for a even money chance."...

    Best regards

    Geoff

  11. #11
    Don Schlesinger
    Guest

    Don Schlesinger: Re: Ok forget about millionaire

    Sorry that the above response wasn't clear to you. Here's an easy way to understand what your edge is in such a situation. Winning 40% of the time means winning four times out of 10, or two times out of five. Suppose you bet 1 unit on each of five plays. Each time you win you will receive your wager plus three additional chips. Since you will then have four chips in front of you on two different occasions, that means that you will have a total of eight chips having started with only five. You win three chips on average for every five chips that you bet. This of course translates into a 60 percent advantage for the player.

    Can we find a formula to summarize the above? Yes, surely we can. Suppose we elet p = the probability of winning. If there are no ties, then 1-p = the probability of losing. Suppose, further, that we let x = the odds-to-one payoff when we win. In this case p = 40%, 1-p = 60%, and x = 3.

    Then your edge is simply the amount you win multiplied by the probability of winning minus the probability of losing. In this case, we have three times 40% - 60% = 120% - 60%, = 60%, which is your edge in this proposition.

    Let's try another one to make sure you understand. Suppose I win 30 percent of the time and get paid at 4-to-1 odds when I win. What is my advantage? Well, four times 30% -70% = 50%, which is your edge. Let?s try this in the original way I explained this to you. Suppose you play 10 times betting one chip each time. You will win three times, on average, and when you do you will find that you have your original bet + 4 winning chips for a total of five in front of you. Do this three times and you will have 15 chips in front of you, having begun with only 10. Your win is 5 out of 10 or 50%.

    Hope this clears things up for you.

    Don


  12. #12
    PaddyBoy
    Guest

    PaddyBoy: Clear as crystal now ! *NM*


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