vpFREE2 Forums

The Dice Challenge

#1

The challenge in grasping this is that many see the second die as independent of the first one, so that it appears that it really doesn't matter what the first die is, the probability of the second one "must" be 1 in 6, since the second die doesn't "know" anything about the first die and lands independently of the first one. While I can clearly see the correct solution on this one, my own intuition on the "Monty Hall" version of essentially the same problem made it difficult for me to finally give in, and as someone with (I thought) a good instinct of basic probability, I could only take solace in the fact that some leading mathematicians also failed to "get it." Perhaps the many posts similarly reflect this (and, of course, many of the posts are more about the "real" bet than the hypothetical one originally posted).
I think the idea of labeling the two dice is an excellent way to understand this.
If you have "Die A" and "Die B", it's one situation when you say "If Die A is a 1, what are the chances that Die B is a 1", and another situation when you say "If Die A OR Die B is a 1, what are the chances that the other one is also a 1". The way this is presented, the second situation is clearly the one we're talking about.
--BG
1b. Re: The Dice Challenge

I can't believe that there are so many posts on this. It is simple 5th grade probability. Alan can't be that dumb (can he?). I do have an out (forgive my poker terminology): Alan can say he wanted the 2 dice labeled 1 and 2, the dice to be rolled simultaneously and if die 1 showed a 2 the chance that the other die (die 2) would show a 2 would be 1 in 6.

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#2

sometimes the simple things are hard to get, Its like trying to explain that the double up feature thats on on some VP machines is NOT an even odds bet, It subject to the return of the game you are playing since you have to play and win before you can use the feature. IE: In NSUD, 99.73 return is the overall return of the double up feature also. Since you have the disadvantage and no slot points are given why bother.

Took me long time to get into my head though lol. Never did it because of no comp points given.

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#3

mjperr82@yahoo.com wrote:

sometimes the simple things are hard to get, Its like trying to explain that the double up feature thats on on some VP machines is NOT an even odds bet, It subject to the return of the game you are playing since you have to play and win before you can use the feature. IE: In NSUD, 99.73 return is the overall return of the double up feature also.

This is hard for me to get. What does the return of the game matter
when the proposition is whether to double a pay or not?

#4

I think Barry nailed why some folks thing this is a 1 in 6 probability.

Taking Barry's example a little further, let's say you have 2 dice and roll one of the die until you get a 2. Then, you roll the second die. What is the probability that the second die will be a 2? Clearly, 1 in 6 times.

The challenge is to understand that the above situation is way, way different than the rules for the Dice Challenge. In the dice challenge, you roll both dice together and there are 3 different possible outcomes. Outcome 1 is neither die is a 2. Probability is 25/36. Outcome 2 is that both dice are a 2. Probability is 1/36. Outcome 3 is that exactly one die is a 2. Probability is 10/36. For this challenge, Outcome 1 is a don't care. Outcome 2 is the winning roll and Outcome 3 is the losing roll. From the subset of Outcome 2 and Outcome 3, you win 1 time in 11 rolls.

Interesting problem. You could further break down Outcome 3 into the individual cases when die A is the 2 vs when die B is the 2, but that might just confuse the issue.

In probability, when in doubt, enumerate. If Alan lists all the possible combinations ( expanding the Outcome1, 2 and 3 above) and counting winners and losers , he should see what the correct answer will be. If he doesn't want to do that fairly simple exercise, I don't think he will ever get it.

More importantly, how do I get in on this wager :).

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#5

the return of the pay is subject to the return of the game , you are doubling your win , not your bet,

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#6

Respectfully disagree.

The double up is a discrete wager (although, admittedly, engaging in it is dependent upon a prior win). Adding it to play has no impact on the EV of that play.

For example, 10 plays of any vp game with or without double up activity has exactly the same EV. If the double up wager was other than an even bet, then its presence would impact play EV in the prior example.

But, truth is, I'm willing to have someone believe whatever they want on this subject. It's truly one of the most inconsequential debates in vp.

- H.

---In vpFREE@yahoogroups.com, <mjperr82@...> wrote :

sometimes the simple things are hard to get, Its like trying to explain that the double up feature thats on on some VP machines is NOT an even odds bet, It subject to the return of the game you are playing since you have to play and win before you can use the feature. IE: In NSUD, 99.73 return is the overall return of the double up feature also. Since you have the disadvantage and no slot points are given why bother.

Took me long time to get into my head though lol. Never did it because of no comp points given.

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#7

Harry, anything that helps a perosn understand probability in gambling I think is of some use and a worthwhile use of brain power.

The question on Double Up EV is more a question of semantics than probability. It's all in how you define the particular EV in which you are interested. If you are looking at the EV of all your money in play for a given 100 hand sample, adding Double Up will increase the overall percentage EV of the money you have in play for that session. Playing 100 hands at 99.73% return and 46 hands at 100% return will increase your overall average percentage return but since you are putting more money in play, you will win or lose the same amount.

Let's say you play 100 hands of NSUD ( 99.73%), and get the following hand distribution ( quick auto play on Winpoker), 1 SF, 9 quads, 4 full house, 1 flush, 4 Straight, 27 trips and 54 whiffs. You happen to break even on this particular short session.

Regardless of whether you double up or not, your results from the NSUD portion are the same. Unless you are one of those people who believes that when you hit the keys actually changes your expected results. That notion aside, the NSUD portion of the play only determines how often you have an opportunity to double up. The NSUD EV of the game is determined by the pay table. The Double Up EV of the game is determined by its 'paytable'. Regardless of whether you double up 1 time, 10 times or 46 times, the EV of the Double Up Feature is 100%. It is just a question of how often you double up.

In the above example, you have 500 coins wagered at an expected return on 99.73% so your expected coin out is 498.65 coins. You now also bet 500 coins on double up and your expected coin out from that bet is 500 coins.

For the 1000 coins wagered ( Double Up plus NSUD), your expected return is 998.65 coins or 99.865%. Seems like double up is a good idea. Unfortunately, you are risking twice as much money so your expected loss is the same 1.35 coins. All you have done is increase the amount in play and thus the variance.

I think it is a pretty interesting exercise ( my wife thinks I'm weird).

In summary, adding a 100% return play to a given, less than 100% play will increase the percentage return but not the actual coin return, due to increased wager size. It's the same argument as the odds on the pass line in dice.

Now , if the discussion is whether to play 200 hands of NSUD or 100 hands of NSUD with double up ( same expected coin in for both activities), that is a different discussion

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#8

Well do you get comps and or tier for double up play?

#9

greeklandjohnny@aol.com wrote:

In the above example, you have 500 coins wagered at an expected return on 99.73% so your expected coin out is 498.65 coins. You now also bet 500 coins on double up and your expected coin out from that bet is 500 coins.

mjperr82@yahoo.com implied that the expected coin out of the double up
was 498.65 coins.

#10

since it depends on a prior win to engage the bet and the prior bet to get the win is subject to the EV of nsud (99.73) so is the double up bet as you doubling up 99.73 not 100

and you are right it is inconsequential to say the least , lol ,

now trying to explain that a pair of dice has 2 ways to make an 11 , one dice=5, 2nd dice= 6, / one dice=6, 2nd dice=5 , can be frustrating or profitable ; )

MJ

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#11

mjperr82@yahoo.com wrote:

since it depends on a prior win to engage the bet and the prior bet to get the win is subject to the EV of nsud (99.73) so is the double up bet as you doubling up 99.73 not 100

The payback of the game has nothing to do with the payback of the
double up bet.

#12

<<<<since it depends on a prior win to engage the bet and the prior bet to get the win is subject to the EV of nsud (99.73) so is the double up bet as you doubling up 99.73 not 100>>>

That sounds like a really bad way of saying that doubling up has no effect on overall ER.... which means that the ER for double up is 100%... but, in the words of Finn the human, "what evs."

C

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#13

Well do you get comps and or tier for double up play?

Not in my experience. That makes it pretty worthless to me. YMMV.

C

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#14

I was once very tempted to double up when hitting jackpots for more
than $1200 on a machine on which they were frequent in order to save
on the number of hand pays, but I couldn't bring myself to take the
extra fluctuation.

···

Well do you get comps and or tier for double up play?

Not in my experience. That makes it pretty worthless to me. YMMV.

C

#15

I have done this on occasion. It tends to frustrate the slot attendants wondering what to write on their form under "winning combination". It usually requires an explanation and sometimes supervisor examination.

···

Sent from my iPhone

On Jun 5, 2015, at 7:24 AM, 007 007@embarqmail.com [vpFREE] <vpFREE@yahoogroups.com> wrote:

I was once very tempted to double up when hitting jackpots for more
than $1200 on a machine on which they were frequent in order to save
on the number of hand pays, but I couldn't bring myself to take the
extra fluctuation.

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#16

One good thing has come out of this dice question. I googled math forums and found math.stackexchange.com. This is a question and answer forum with multi-degreed math professors answering the questions. Iaaked them about the two dice question. One of them, with the username jiehro, even went on Mendelson's forum and gave then a great clinic on dice combinatorics. Unfortunately, Alan is still stuck on 1 in 6. I just posted a tough math question on math.stackexchange related to a video keno game I'm analyzing and got a speedy respone. Those guys are a great go to if you cant solve a math problem on your own.