Being hot vs being due

[Chris Daddy Cool]

Suppose you and your friend are flipping a quarter for $10 a pop for a day. You win on heads. He wins for tails.

Somewhere in the middle, you find yourself down $160 and tails has landed 7 of the last 8 times and your friend offers you to switch to tails.

Which one of these thoughts are you more inclined to believe in?

[soko]

I may switch, not because of either of the choices you said but maybe the coins weight is not balanced.

[b33nz]

It doesnt matter... unless it is different weight, but realistically speaking if it is a 50/50, then it doesnt matter at all, lol. If i had to choose on a 50/50 I would stick to heads since 'I'd be due'.

[Sephus]

the correct answer (if it's possible that the coin is not fair) is switch to tails, because you have slightly more evidence that the coin is biased toward tails than toward heads.

if you somehow know that the coin is unbiased it obviously doesn't matter.

the only way to justify preferring to stick with heads rather than switch to tails is if you came into the day suspecting that your friend is more likely to bring a coin biased in your favor (heads) than his own (tails).

Tails. It doesn't really matter, but the slight chance of it being favored towards tails would make me lean towards it.

[sfer]

There's an old saying in finance that finding a consistent loser is as good as finding a consistent winner since you can just short the loser's strategy. Basically, do what you want, homiehomie, I'll take the other side.

[Chris Daddy Cool]

If you were the other guy, would you be more or less inclined to switch?

[soko]

[ QUOTE ]
If you were the other guy, would you be more or less inclined to switch?

[/ QUOTE ]

This is the same question as the OP.

I wouldn't believe in either of the thoughts provided, but I would switch to tails. It seems to matter to my friend. If I then go on a rush with tails, I may be able to convince her that it's her fault, put her on tilt, and then cause her to take a -EV gamble. Sort of like Party BJ.

[ QUOTE ]
It doesnt matter... unless it is different weight, but realistically speaking if it is a 50/50, then it doesnt matter at all, lol.

[/ QUOTE ]

did you really laugh out loud at this point?

being "due" is a gamblers fallacy, and it really doesn't make a difference if you switch, assuming the coin is fair.

[ QUOTE ]
[ QUOTE ]
It doesnt matter... unless it is different weight, but realistically speaking if it is a 50/50, then it doesnt matter at all, lol.

[/ QUOTE ]

did you really laugh out loud at this point?

[/ QUOTE ]
lol, I really laughed out loud at that, but as for psychology I think I would be more inclined to get pissed off if I switched and then proceeded to loose, where as if I stayed and lost I could just accuse the mofo of cheating.

But honestly does anyone ever gamble on coin flips, I mean god damn why are there so many of these little scenarios always being posted

[SNOWBALL138]

[ QUOTE ]
But honestly does anyone ever gamble on coin flips, I mean god damn why are there so many of these little scenarios always being posted

[/ QUOTE ]

I came up with a deceptive coin flip prop bet that netted me a whopping $.75 before my friend quit on me. O well.

[Chris Daddy Cool]

[ QUOTE ]
[ QUOTE ]
If you were the other guy, would you be more or less inclined to switch?

[/ QUOTE ]

This is the same question as the OP.

[/ QUOTE ]

not neccessarily because the other guy has been on the winning end.

[AlanBostick]

Terrible poll design. I must vote to see the results, and neither choice represents my belief.

Both positions are fallacies; your poll presumes that polltakers must subscribe to either one or the other, and leaves no room for polltakers who subscribe to neither.

[cold_cash]

Buzzkill.

I'm due baby!

[MTBlue]

I'm still amazed that people are actually are sticking with heads more than switching to tails. The chances that this coin is perfectly fair is growing smaller and smaller and it is much more likely that the coin is biased toward tails.

I switch between heads and tails everytime because due to the coin's physics, its will necessarily show a bias towards landing on one side (even if that bias is an extremely small one). This way I minimize my loss towards its natural bias without knowing which side it is biased towards.

[GuyOnTilt]

[ QUOTE ]

But honestly does anyone ever gamble on coin flips, I mean god damn why are there so many of these little scenarios always being posted

[/ QUOTE ]
Hahahahaha! Man, you really should see some of the [censored] we do.

Edit: Case in point: OP has lost well over $1k in our last two Rock Paper Scissors sessions. /images/graemlins/tongue.gif

GoT

[GuyOnTilt]

In this particular scenario, my first instinct is definitely to stick with what's due for whatever reason. That doesn't go across the board though, again, for whatever reason. Sometimes momentum outweighs being due. Not often, but sometimes.

GoT

[RydenStoompala]

You left out "3. Kill Yourself. You're flipping coins for even money all day so your life is over."

[ThinkQuick]

[ QUOTE ]
Tails. It doesn't really matter, but the slight chance of it being favored towards tails would make me lean towards it.

[/ QUOTE ]

Agreed. There is a nonzero chance that the results are due to the coin being biased to land tails. Let that work with you.

note that this has nothing to do with runnning hot or being due..

[AlanBostick]

[ QUOTE ]
I'm still amazed that people are actually are sticking with heads more than switching to tails. The chances that this coin is perfectly fair is growing smaller and smaller and it is much more likely that the coin is biased toward tails.

[/ QUOTE ]

Go read the problem as posed again:

[ QUOTE ]
Suppose you and your friend are flipping a quarter for $10 a pop for a day. You win on heads. He wins for tails.

Somewhere in the middle, you find yourself down $160 and tails has landed 7 of the last 8 times and your friend offers you to switch to tails.

[/ QUOTE ]

You're tossing coins all day. Let's say you started at 9:00 AM, toss once each minute, and are continuing until 5:00 PM.


"Somewhere in the middle," i.e. around 1:00 or 2:00 PM, i.e. after three hundred tosses or so, you're stuck $160 -- that is, tails have come up 16 more times than heads has, and that the last seven tosses have been tails.

After three hundred tosses, you expect heads to have come up 150 +/- 8.7 times. Being behind by 16 tosses at midday is a two-sigma event. But note that you had just tossed tails seven times in a row. Just before that run, you had only been behind by nine tosses -- just slightly more than a one-sigma event. And a run of seven tails in a row is not terribly unlikely, with odds of just 127:1 against.

The OP doesn't specify how often the coin is tossed. If you tossed every second, rather than every minute, by 1:00 PM you would have tossed the coin 14,400 times, and would expect to see heads 7,200 +/- 60 times. Being sixteen tosses behind is well within expected results and you would also expect to have seen a number of long runs of tails and long runs of heads, and there would be no reason to even begin to suspect that the coin is biased.

[MTBlue]

If this a unbiased random event, then your odds on future tosses are not affected by switching to tails. (Tails=Heads)

If this is a biased event i.e. Tails>Heads or Heads>Tails then switching to tails is the right choice. The chances are greater at this point that the coin is biased toward Tails instead of heads. It is possible that the event is biased toward heads just more unlikely.

There are two scenarios biased and unbiased. Biased P(T)>.5 > P(T)<.5. Unbiased P(T)=.5. Compared to heads where the Biased P(H)<.5 > P(H)>.5. Unbiased P(H)=.5

Unbiased scenarion the switch is inconsequential to the results. In the biased example the switch makes sense.

[ThinkQuick]

I appreciate your analysis demonstrating that there may be no difference between the game coin and a fair coin.

And it isn't even the run of tails which would have me switch, although this event does allow for the possibility that something recently happened to the coin.

Here is what I am saying,

We must assume there is some (albeit small) chance of the coin being weighted
There are 3 possibilities:

a) the coin is weighted towards tails
b) the coin is fair
c) the coin is weighted towards heads

You are offered a one time opportunity to switch mid-day

If the coin is weighted to tails and you switch to tails, you gain expectation
If the coin is fair and you switch, nothing changes
if the coin is weighted to heads and you switch to tails, you lose


You are down 16 flips after 14k flips. We cannot prove that the coin is weighted but this insignificant but nonzero tails-favoring demonstrates that if it is weighted, it is more likely weighted to tails. If you were down 1 flip after 14k flips then the odds of a being true would still be greater than the odds of c being true. Therefore switch.

I can see no argument for staying. By the law of large numbers (law of averages), if the coin is fair you will still be down about 16 flips at the end of the day. But if it isn't fair... take advantage of that small possibility by switching.

[AKQJ10]

[ QUOTE ]
the correct answer (if it's possible that the coin is not fair) is switch to tails, because you have slightly more evidence that the coin is biased toward tails than toward heads.

[/ QUOTE ]

True, unless you suspect your friend of selectively unbalancing the coin. Then you'd be foolish to switch, because he offered you the switch, which must mean he's confident he can switch it back.

Other than subtleties of cheating at coin-flipping, this topic is a waste of disk space.

[NLSoldier]

[ QUOTE ]
In this particular scenario, my first instinct is definitely to stick with what's due for whatever reason. That doesn't go across the board though, again, for whatever reason. Sometimes momentum outweighs being due. Not often, but sometimes.

GoT

[/ QUOTE ]

[NLSoldier]

GOT and HomieHomie,

obviously these guys arent asian and will never understand.

gamb000000l,
nl

What the hell is "momentum" in coin tossing. Please. I'm asian by the way, and I still know that on a fair coin, staying or switching still gives you the same odds :P

[uncleshady]

This question is why that "history board" is up next to most Bacarrat tables in Vegas.

[raze]

I'd stay on heads, cuz if I switched and then heads started evening out, I'd be really pissed

[GuyOnTilt]

[ QUOTE ]
What the hell is "momentum" in coin tossing.

[/ QUOTE ]
Good lord, let me explain it to you. Having the momentum is the opposite of being due. Depending on the game in question, one can be better than the other and visa versa. In coin tossing or red/black flop betting, for example, momentum works against you and being due is king, whereas in Chinese RPS (http://forumserver.twoplustwo.com/showflat.php?Cat=0&Number=4171873&an=0&page=0#Post 4171873) or craps, momentum is everything and being due has very little relevance, other than to decrease the chances of you winning.

GoT

[Mempho]

[ QUOTE ]
[ QUOTE ]

But honestly does anyone ever gamble on coin flips, I mean god damn why are there so many of these little scenarios always being posted

[/ QUOTE ]
Hahahahaha! Man, you really should see some of the [censored] we do.

Edit: Case in point: OP has lost well over $1k in our last two Rock Paper Scissors sessions. /images/graemlins/tongue.gif

GoT

[/ QUOTE ]

Rock, paper, scissors is beatable depending upon the opponent, however.

[ThinkQuick]

[ QUOTE ]
[ QUOTE ]
[ QUOTE ]

But honestly does anyone ever gamble on coin flips, I mean god damn why are there so many of these little scenarios always being posted

[/ QUOTE ]
Hahahahaha! Man, you really should see some of the [censored] we do.

Edit: Case in point: OP has lost well over $1k in our last two Rock Paper Scissors sessions. /images/graemlins/tongue.gif

GoT

[/ QUOTE ]

Rock, paper, scissors is beatable depending upon the opponent, however.

[/ QUOTE ]

Yes of course, and this has been discussed.

At the least it probably isn't 50/50 between two human opponents without randomizing strategies.

[tonypaladino]

Anyone see Rosencrantz and Guildenstern Are Dead?

I hate you.

independant trials