RANDOM thoughts

[Daliman]

Blackjack diety Arnold Snyder wrote a very similar, but much more fleshed-out example for a Blackjack Forum atricle called "Swami Pastrami" or something like that. looking around online for it.

[jcm4ccc]

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Question 1:
Assume we are playing a game where I will roll a pair of normal fair 6-sided dice. If no die shows a 6, then I will reroll both die. When I stop rolling the dice (because one or more die has a 6) I will pay you $X if both dice show 6. If instead there is a 1, 2, 3, 4, or 5 to go with the 6 when I stop rolling the dice you will pay me $1. What is the value of X that makes this a fair game? (If you were to offer X=8 to most people do you think they'd play the game?)


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I believe that x=5 is a fair game (on average both people break even). 6:1-6:5 = 5 ways, 6:6=1 way any other outcome is irrelevent...

maybe I should have finished reading thread before posting, but if it is not 5, then what is the answer? Certainly over the short term you may rarely or frequently see 6:6, but over long term x should = 5, if not please explain why not.

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Nope. It took me a while to figure this out. The fair number is 11.

Here are the 12 different ways the dice can come up:

61
16
62
26
63
36
64
46
65
56
66

1 out of these 12 is 66.

[junkmail3]

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Question 1:
Assume we are playing a game where I will roll a pair of normal fair 6-sided dice. If no die shows a 6, then I will reroll both die. When I stop rolling the dice (because one or more die has a 6) I will pay you $X if both dice show 6. If instead there is a 1, 2, 3, 4, or 5 to go with the 6 when I stop rolling the dice you will pay me $1. What is the value of X that makes this a fair game? (If you were to offer X=8 to most people do you think they'd play the game?)


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I believe that x=5 is a fair game (on average both people break even). 6:1-6:5 = 5 ways, 6:6=1 way any other outcome is irrelevent...

maybe I should have finished reading thread before posting, but if it is not 5, then what is the answer? Certainly over the short term you may rarely or frequently see 6:6, but over long term x should = 5, if not please explain why not.

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Nope. It took me a while to figure this out. The fair number is 11.

Here are the 12 different ways the dice can come up:

61
16
62
26
63
36
64
46
65
56
66

1 out of these 12 is 66.

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There are actually only 11 possiblities (which I'm sure was just an unintentional oversight on your part) . 66 can only occur one way.

So, 10:1.

[jcm4ccc]

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There are actually only 11 possiblities (which I'm sure was just an unintentional oversight on your part) . 66 can only occur one way.

So, 10:1.

[/ QUOTE ] Yeah, didn't think it through. But I was thrilled to come up with the semi-right answer. It's a pretty tricky question, I think.

[freemoney]

i understand and appreciate your post but i think the idea of seeing significant mistakes your opponents make that you do not continually make allows you to gauge your ability to beat/compete at a certain level just as much as playing 124234 SnGs.

[Dr_Jeckyl_00]

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There are actually only 11 possiblities (which I'm sure was just an unintentional oversight on your part) . 66 can only occur one way.

So, 10:1.

[/ QUOTE ] Yeah, didn't think it through. But I was thrilled to come up with the semi-right answer. It's a pretty tricky question, I think.

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Damn it! I thought I was good at this stuff, how could I screw that up... thanks for the answer

[Irieguy]

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So to repharse Irieguy's analogy as it applies to SNG (and this is the important point):

So in SNG land imagine someone has done the heavy lifting of the math and figures out that the chances of a break-even player having a 15% (or better) ROI over 500 SNG is just 20%. Player X just finished 500 SNG and had a 15% ROI. Player X now thinks they are 80% likely to be a winning player. The biggest mistake here is that Player X isn't taking in to account the distribution of the population. The vast majority of SNG players are losing players (for the sake of argument let's say 95%). The average SNG player loses the rake. So player X isn't somehow picked from a uniform distribution that is as likely to be -100% ROI as +100% ROI but rather a distribution centered on -rake ROI that gets drastically less players the further you move from -rake ROI. This is now a conditional probability question just like question 2 above and actually player X is much more likely to be a break-even or losing player currently being misidentified by our "one witness" (the 500 SNG sample) then a true winning player being correctly identified.

Irieguy's secondary point:

"Furthermore, the most successful of the 'skilled professional' group will also be beneficiaries of randomness to a much larger degree than they would like to admit" is worth remembering too (and has Daniel Negreanu's name all over it, for one).

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Thank you, SumZero. This is the hidden nugget for which Benholio was searching. Interestingly, it wasn't hidden... but will remain invisible to most nevertheless.

Irieguy

[jcm4ccc]

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Thank you, SumZero. This is the hidden nugget for which Benholio was searching. Interestingly, it wasn't hidden... but will remain invisible to most nevertheless.

Irieguy

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I think the vast majority of people on this forum are quite intelligent and can understand arguments and analogies when they are presented well. Is your argument "invisible to most" because the message is obscure or the messenger is obscure?

[Dr_Jeckyl_00]

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Thank you, SumZero. This is the hidden nugget for which Benholio was searching. Interestingly, it wasn't hidden... but will remain invisible to most nevertheless.

Irieguy

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I think the vast majority of people on this forum are quite intelligent and can understand arguments and analogies when they are presented well. Is your argument "invisible to most" because the message is obscure or the messenger is obscure?

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I have to admit I am confused by OP's message. Sounds like he is saying if you're profitable, it is most likely due to randomness and nothing to do with skill... I think we all agree that no matter how good your hand is, it can be beaten (except for one hand) but when you play correctly, your hand will be beaten less often then when you play poorly. So randomness affects all of us, but if affects certain people less because they take steps to mitigate the effects of randomness... Is this what OP is saying???

[SumZero]

I think what you want to do is treat it similar to a maximum likelihood calculation. But rather than merely solving for p-hat you solve for what is the probability that p is > 0.

So basically you need to have the distribution of the population (not just the number below 0, although you could guess that it might be scew-normal centered on a -rake ROI and set the sd based on your number below 0 who are losers) and then for every point (say X ROI) on the distribution curve multiply the probability that someone random is this quality by the probability that they could produce the observed behavior given they are of that X ROI [really you want to do this for the continuous population density function, but with computers you can approximate it by testing discrete points, say every 0.1% ROI from say -50% ROI to 40% ROI). Then at the end you will have a new distribution and can see what percentage of the distribution (area under the new curve) is above 0.