Snyder/McDowell? A middle-road approach

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Snyder/McDowell? A middle-road approach

Posted By: Zenfighter
Date: Thursday, 3 February 2005, at 12:00 p.m.

Player's first cards expectations.

Rules: 6dks, das, spl3, nrsa BSE = - 0.41%

1) 100 bets predicting aces by pure guess.

1st Card EV (%) Random Occur. Product

A 50.79 .0769230769 3.9069230769
T 14.34 .3076923080 4.4123076923
9 - 0.87 .0769230769 -0.0669230769
8 - 8.31 .0769230769 -0.6392307692
7 -17.94 .0769230769 -1.3800000000
6 -20.76 .0769230769 -1.5969230769
5 -19.66 .0769230769 -1.5123076923
4 -17.55 .0769230769 -1.3500000000
3 -15.22 .0769230769 -1.1707692308
2 -13.13 .0769230769 -1.0100000000

1.0000000001 - 0.4069230769

EV = - 0.41%

Thus, a player who bets on aces at random by pure guess will face a negative expectancy in the long run,
that equals his standard off the top disadvantage with the rules in question.

2) 100 bets predicting aces with BJAP’s methods. Success = 13%; Failures = 87% The dealer doesn’t get any of the extra key(s) aces, only his random ones (.0769). Here the 87 of the failures shall be shared among the other 12 cards, hence 87/12 = .0725

McDowell: The player expect to get the Ace “on purpose” 13 times in every one hundred attempts. This will be true at a full table, where the dealer has a little chance of getting the ace “by accident.”

1st Card EV (%) Adjusted Occur. Product

A 50.79 .1300000000 6.602700
T 14.34 .2900000000 4.158600
9 - 0.87 .0725000000 -0.063075
8 - 8.31 .0725000000 -0.602475
7 -17.94 .0725000000 -1.300650
6 -20.76 .0725000000 -1.505100
5 -19.66 .0725000000 -1.425350
4 -17.55 .0725000000 -1.272375
3 -15.22 .0725000000 -1.103450
2 -13.13 .0725000000 -0.951925

1.0000000000 2.535525

EV = 2.54%

Total cost for the 87% of the failures = - 4.067175 = - 4.07%

Here, is where McDowell’s targeted equation 7-3 seems to have underestimated the real cost of the failures (while betting on predictive aces only). By assuming a simplified mathematical formulae, obviously what you get is an inflated EV = 3.85%, which is not the case, as you can see from the above table. (Even if the dealer doesn’t get any of the key(s) predicted aces)

3) 100 bets on predictive aces. Player and dealer will share the extra key(s) aces.

Here again 90/12 = .0750 is the adjusting occurrence for the player’s failures.

1st Card EV(%) Adjusted occur. Product

A 50.79 .1000 5.07900
T 14.34 .3000 4.30200
9 - 0.87 .0750 -0.06525
8 - 8.31 .0750 -0.62325
7 -17.94 .0750 -1.34550
6 -20.76 .0750 -1.55700
5 -19.66 .0750 -1.47450
4 -17.55 .0750 -1.31625
3 -15.22 .0750 -1.14150
2 -13.13 .0750 -0.98475

1.0000 0.87300

Total improvement over random distribution = 0.8730 + 0.41 = 1.283%

Dealer’s advantage as a function of his first card.

1st Card EV( %) Adjusted occur. Product

A 34.17 .1000 3.41700
T 17.32 .3000 5.19600
9 4.11 .0750 0.30825
8 -5.76 .0750 -0.43200
7 -14.46 .0750 -1.08450
6 -23.58 .0750 -1.76850
5 -20.33 .0750 -1.52475
4 -16.28 .0750 -1.22100
3 -12.63 .0750 -0.94725
2 -9.27 .0750 -0.69525

1.0000 1.24800

Total improvement over random distribution = 1.248 – 0.41 = 0.838%

Thus the final EV = 1.283 – 0.838 = 0.445

EV = 0.45%

Moral? You should avoid the utmost a heads up game while using these techniques.

Obviously the player’s final expectation as a function of 1,2,3,4,5,6 or 7 players is:

EV = Sum Ei {for i = 1 to 7}/7

This is a figure between 1 and 2 percent. An elementary mathematical interpolation between both extremes should convince even an obtuse disbeliever.

At least I haven’t see any evidence whatsoever to support the notion that McDowell’s math is full of errors and his conclusions are worthless, as by a carefully reading from the American expert Arnold Snyder’s review, one would probably infer.

With 3 or 4 predictive bets per hour, don’t quit your daily job anyway, if you are planning to use this technique as a solo weapon, I mean. :-)

On the other hand, McDowell’s book looks to me an innovative and groundbreaking piece of work. His scholarly approach to the subject is really fascinating. The dubious inferences of equation 7-3 should be evaluated with a little more of benevolence. JMO.
Sincerely

Zenfighter

Messages In This Thread

Snyder/McDowell? A middle-road approach (views: 1896)
Zenfighter -- Thursday, 3 February 2005, at 12:00 p.m.
- Still not right (views: 1321)
  ET Fan -- Thursday, 3 February 2005, at 4:37 p.m.
- Thankyou Zenfighter! (views: 620)
  Myooligan -- Thursday, 3 February 2005, at 5:12 p.m.
  - Re: You're welcome (views: 678)
    Zenfighter -- Thursday, 3 February 2005, at 7:19 p.m.
    - Re: You're welcome (views: 581)
      Myooligan -- Thursday, 3 February 2005, at 7:49 p.m.
    - Sorry, no. Look at it this way: (views: 658)
      ET Fan -- Thursday, 3 February 2005, at 8:19 p.m.
      - Re: Oops (views: 584)
        Zenfighter -- Friday, 4 February 2005, at 6:19 a.m.
        
        A Very Simple Solution (views: 620)
        ET Fan -- Friday, 4 February 2005, at 2:08 p.m.
- My own calculation ... (views: 592)
  ET Fan -- Friday, 4 February 2005, at 2:52 a.m.
  - Re: My own calculation ... (views: 624)
    Zenfighter -- Friday, 4 February 2005, at 3:58 a.m.

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Message: > Player's first cards expectations. > Rules: 6dks, das, spl3, nrsa BSE = - 0.41% > 1) 100 bets predicting aces by pure guess. > 1st Card EV (%) Random Occur. Product > A 50.79 .0769230769 3.9069230769 > T 14.34 .3076923080 4.4123076923 > 9 - 0.87 .0769230769 > -0.0669230769 > 8 - 8.31 .0769230769 -0.6392307692 > 7 -17.94 .0769230769 -1.3800000000 > 6 -20.76 .0769230769 -1.5969230769 > 5 -19.66 .0769230769 -1.5123076923 > 4 -17.55 .0769230769 -1.3500000000 > 3 -15.22 .0769230769 -1.1707692308 > 2 -13.13 .0769230769 > -1.0100000000 > 1.0000000001 - > 0.4069230769 > EV = - 0.41% > > Thus, a player who bets on aces at random by pure > guess will face a negative expectancy in the long run, > that > equals his standard off the top disadvantage with the > rules in question. > 2) 100 bets predicting aces with BJAP’s methods. > Success = 13%; Failures = 87% The dealer doesn’t get > any of the extra key(s) aces , only his random ones > (.0769). Here the 87 of the failures shall be shared > among the other 12 cards, hence 87/12 = .0725 > McDowell: The player expect to get the Ace “on > purpose” 13 times in every one hundred attempts. This > will be true at a full table, where the dealer has a > little chance of getting the ace “by accident.” > > 1st Card EV (%) Adjusted Occur. > Product > A 50.79 .1300000000 > 6.602700 > T 14.34 .2900000000 > 4.158600 > 9 - 0.87 .0725000000 > -0.063075 > 8 - 8.31 .0725000000 > -0.602475 > 7 -17.94 .0725000000 > -1.300650 > 6 -20.76 .0725000000 > -1.505100 > 5 -19.66 .0725000000 > -1.425350 > 4 -17.55 .0725000000 > -1.272375 > 3 -15.22 .0725000000 > -1.103450 > 2 -13.13 .0725000000 > -0.951925 > 1.0000000000 > 2.535525 > > EV = 2.54% > Total cost for the 87% of the failures = - 4.067175 > = - 4.07% > Here, is where McDowell’s targeted equation 7-3 seems > to have underestimated the real cost of the failures > (while betting on predictive aces only). By assuming a > simplified mathematical formulae, obviously what you > get is an inflated EV = 3.85%, which is not the case, > as you can see from the above table. (Even if the > dealer doesn’t get any of the key(s) predicted aces) > > 3) 100 bets on predictive aces. Player and dealer > will share the extra key(s) aces. > Here again 90/12 = .0750 is the adjusting occurrence > for the player’s failures. > > 1st Card EV(%) Adjusted occur. Product > A 50.79 .1000 5.07900 > T 14.34 .3000 4.30200 > 9 - 0.87 .0750 -0.06525 > 8 - 8.31 .0750 -0.62325 > 7 -17.94 .0750 -1.34550 > 6 -20.76 .0750 -1.55700 > 5 -19.66 .0750 -1.47450 > 4 -17.55 .0750 -1.31625 > 3 -15.22 .0750 -1.14150 > 2 -13.13 .0750 -0.98475 > 1.0000 0.87300 > > > Total improvement over random distribution = 0.8730 + > 0.41 = 1.283% > Dealer’s advantage as a function of his first card. > > 1st Card EV( %) Adjusted occur. > Product > A 34.17 .1000 3.41700 > T 17.32 .3000 5.19600 > 9 4.11 .0750 0.30825 > 8 -5.76 .0750 -0.43200 > 7 -14.46 .0750 -1.08450 > 6 -23.58 .0750 -1.76850 > 5 -20.33 .0750 -1.52475 > 4 -16.28 .0750 -1.22100 > 3 -12.63 .0750 -0.94725 > 2 -9.27 .0750 -0.69525 > 1.0000 1.24800 > > > Total improvement over random distribution = 1.248 – > 0.41 = 0.838% > Thus the final EV = 1.283 – 0.838 = 0.445 > EV = 0.45% > Moral? You should avoid the utmost a heads up game > while using these techniques. > Obviously the player’s final expectation as a function > of 1,2,3,4,5,6 or 7 players is: > EV = Sum Ei {for i = 1 to 7}/7 > This is a figure between 1 and 2 percent. An > elementary mathematical interpolation between both > extremes should convince even an obtuse disbeliever. > At least I haven’t see any evidence whatsoever to > support the notion that McDowell’s math is full of > errors and his conclusions are worthless, as by a > carefully reading from the American expert Arnold > Snyder’s review, one would probably infer. > > > > > > With 3 or 4 > predictive bets per hour, don’t quit your daily job > anyway, if you are planning to use this technique as a > solo weapon, I mean. :-) > On the other hand, McDowell’s book looks to me an > innovative and groundbreaking piece of work. His > scholarly approach to the subject is really > fascinating. The dubious inferences of equation 7-3 > should be evaluated with a little more of > benevolence. JMO. > > > > > > Sincerely > Zenfighter >
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