Author Topic: Final Decision (Read 5210 times)

ccvi · « **Reply #30 on:** November 27, 2004, 03:46:32 PM »

Quote

Originally posted by ALF
I refer to the key point :

MANDO: "He was lucky, it was one of the two training bombs. "

Isn't it amazing how just a small little thing can make such a change. A randome act in this case is much diferent than a decision to reveal. It is part of my original point that we must 'eliminate' the possibility of the 1st drop being a live bomb to make it work, thats what Monte did, and thats what a randome event, as described does not do.

253 for (la_index = 0; la_index != 3; la_index++)
254 {
255 if ((la_index != la_realbomb) && (la_index != la_lever))
256 {
257 la_lost = la_index;
258 }
259 }

This doesn't seem to match "he was lucky".

mechanic · « **Reply #31 on:** November 27, 2004, 05:00:07 PM »

very strange indeed. not sure i understnd the purpose of this action. is it in any reference to bombing tactics or merely a 16 year olds math problem?

MANDO · « **Reply #32 on:** November 27, 2004, 07:36:24 PM »

Quote

Originally posted by BlauK
Mando, can you change your program so that the left bomb is always originally selected and a dud is always dropped from middle? Would that make a difference?

Yes, I can, but the difference would be 0%.

Think on the steps:

1 - randomly a bomb is selected as real bomb.
2 - randomly a placement is selected for the lever.
3 - a fake bomb is dropped (BUT BEING SURE THAT THIS TRAINING BOMB IS NOT SELECTED BY THE INITIAL POSITION OF THE LEVER).
4 - Final decision is taken.

ccvi · « **Reply #33 on:** November 27, 2004, 07:46:26 PM »

Quote

Originally posted by MANDO
3 - a fake bomb is dropped (BUT BEING SURE THAT THIS TRAINING BOMB IS NOT SELECTED BY THE INITIAL POSITION OF THE LEVER).

This is not what happens by pure luck, this is wizzards work. A random mechanical failure could also have dropped the real bomb.

You need to drop a random bomb and ignore the cases where the real one drops.

MANDO · « **Reply #34 on:** November 27, 2004, 07:46:54 PM »

Quote

Originally posted by ccvi
The mechanical failure does not know the position of the real bomb, monty and the wizzard do.

Certainly, but the case is that the lost bomb is a training one. If you lost the real bomb from the beginning, this would not increase your chances changing the lever or not. You are against a "secure fact" (not sure about the english term), you will miss for sure.

MANDO · « **Reply #35 on:** November 27, 2004, 07:51:27 PM »

Quote

Originally posted by ccvi
You need to drop a random bomb and ignore the cases where the real one drops.

ccvi, read the initial description. When the pilot noticed the black led, he inverted the pane so see the bomb falling. At this point, the pilot know whether the bomb is red (training) or green (real). Of course, if the pilot sees the green bomb faling, he will abort the mission and return to base.

ccvi · « **Reply #36 on:** November 27, 2004, 08:04:00 PM »

Of course he will, but it could still have happened. Those cases you're not ignoring, but you're adding them to those where he needs to switch.

a) 1/3: real bomb selected, fake dropped -> keep switch where it is
b) 1/3: fake bomb selected, real dropped -> rtb
c) 1/3: fake bomb selected, fake dropped -> switch to other bomb

Your failure-wizzard is manipulating every case of b) to be a case of c), of course you end up with a) vs. b)+c) then.

Dropping 1 random bomb, keeping the real one by pure luck, can and will result in loss of the real one in the case b), which just isn't the case in the scenario. So you just need to compare a) and c).

MANDO · « **Reply #37 on:** November 27, 2004, 08:09:11 PM »

ccvi,

case B is rtb, period. You should not consider it to compute the chances of destroy the target once you are diving ready to press the trigger.

The question was not "what are the chances of hitting the target after takeoff", in any case, "what are the chances of hitting the target when diving over it with a bomb selected". Those cases with 0 chances (green bomb is lost and noticed by the pilot) should not be considered.

ccvi · « **Reply #38 on:** November 27, 2004, 08:17:38 PM »

Quote

Originally posted by MANDO
Those cases with 0 chances (green bomb is lost and noticed by the pilot) should not be considered.

Correct. But you do consider them by manipulating them to match one of the cases that need to be considered. By always dropping the fake, even when in realtiy it would have been a case of early rtb.

Kweassa · « **Reply #39 on:** November 27, 2004, 08:55:46 PM »

It's gonna be whatever is bad for the pilot.

Common wisdom of tendencies suggest that when something goes wrong, things always tend to happen to rush to the worst consequences of them all.

So, usually, a realistic approach is what Dredidock would suggest - the pilot will abort the bomb run altogether and dump whatever is left during the way, with no regards to statistics at all.

It doesn't make any difference whatever he chooses, as it is highly likely that whatever he does is not gonna work, unless he gives the act up altogether.

There is no 'logic' in this matter at all

- only empirical 'tendencies'. Times like these granny's advices work better than mathematics.

hawker238 · « **Reply #40 on:** November 27, 2004, 09:51:56 PM »

MANDO,

How come in the program, the good bomb can be on the middle pylon? I thought it was absolute that the middle bomb was a dud and that it would always be the one being dropped? I don't think I understand the problem.

Also, I ran the sim for 1500 drops, with "Never change the lever", and I got 33% success rate (1501 attacks, 497 hits). How does this figure?

bozon · « **Reply #41 on:** November 27, 2004, 11:48:50 PM »

the difference between the 50% of selecting between the two remaining bombs and the 66% case is whether you "re-shuffle" the deck (take off the 2 bombs and randomly reattach them) after the center one has fallen.

normally we are used to the case in which we shuffle the deck or re-roll the dice before each gamble and therefor all previous information in erased. In this case, the "dice" was rolled only once, before the game started.

Bozon

MANDO · « **Reply #42 on:** November 28, 2004, 03:47:45 AM »

Quote

Originally posted by hawker238
MANDO,

How come in the program, the good bomb can be on the middle pylon? I thought it was absolute that the middle bomb was a dud and that it would always be the one being dropped? I don't think I understand the problem.

Also, I ran the sim for 1500 drops, with "Never change the lever", and I got 33% success rate (1501 attacks, 497 hits). How does this figure?

Hawker, my first post was a single "case" of the problem. The program selects any pilon (centerline included) for the real bomb. The initial placement of the real bomb and the initial placement of the bomb selector lever can be any one, the problem will not change.

The KEY information is that the pilot will always see a training bomb falling and that bomb is placed in a different pilon than the initially selected by the lever.

If you run no more than 150 or 200 attacks with "Always change" you will have a 66% instead of a 33%, If you run no more than 150 or 200 attacks with "Change the lever randomly" you will have a 50% instead of a 33%, this is the beauty of the problem.

RTSigma · « **Reply #43 on:** November 28, 2004, 04:59:37 AM »

I'm waiting to see if this will turn into a "you don't bury survivor's" question/joke

MANDO · « **Reply #44 on:** November 28, 2004, 06:15:48 AM »

Here is a new version of the simulator, now you can also play manually to test your "luck".

If you select "Play manualy" option, you will be able to start manual attacks clicking on "New manual attack" button. The initial bombs will be initially hidden, but you will see the led indicators and the initial lever position and then you need to click one of the buttons to select manually the final position of the lever.

Final Decision Simulator 2