2UP coin toss question
For those that dont know the game, 2UP is a game where 2 or 3 coins are tossed and people bet on either heads or tails, in the case of 2 coins where one of each lands it is thrown again until resolved.
My question is does 2 coins or 3 coins being thrown have a lower variance within resolved outcomes?
Or are they both the same??
Quote: StatsTomorrow in Australia is ANZAC day, part of the tradition on ANZAC day is to play 2UP at the pubs and clubs.
For those that dont know the game, 2UP is a game where 2 or 3 coins are tossed and people bet on either heads or tails, in the case of 2 coins where one of each lands it is thrown again until resolved.
My question is does 2 coins or 3 coins being thrown have a lower variance within resolved outcomes?
Or are they both the same??
They are the same.
Then consider the probabilities. Every process described gives an equiprobable situation, i.e. 50% either way.
So the games are identical, not only in terms of variance but any other prob. parameter.
Differences are in time / number of throws needed, of course. And maybe in terms of enjoyment or suspense.
making 100 bets on each game lowers the probability of a net win for the 2 coin game verses the 3 coin game.Quote: kubikulannDifferences are in time / number of throws needed, of course. And maybe in terms of enjoyment or suspense.
The 2 coin game will have a probability of showing a net loss of about 47.18%
where the chance of a loss with the 3 coin game is about 46.02%
Some can feel that difference
was this not what started probability study over 300 years ago, a small difference like this over some length of play
rolling a pair of 6s in 24 rolls
that was between 49.140388% and 50.553155%
we can see what a larger variance looks like over another smaller one when considering all possible game outcomes, because they are there.
N=100
3 coin game = green
Sally
Do we speak of the same game?
Betting heads or Tail should bring the same "net" result, whether once or a hundred times. So I don't see how this could produce anything other than 50%?
My understanding:
2UP - heads wins if two heads, (resp. tails) and there is a tie if the coins land heads and tails.
3UP - heads wins if there are two or three heads. (resp. tails)
Quote: mustangsallymaking 100 bets on each game lowers the probability of a net win for the 2 coin game verses the 3 coin game.
The 2 coin game will have a probability of showing a net loss of about 47.18%
where the chance of a loss with the 3 coin game is about 46.02%
Some can feel that difference
was this not what started probability study over 300 years ago, a small difference like this over some length of play
rolling a pair of 6s in 24 rolls
that was between 49.140388% and 50.553155%
we can see what a larger variance looks like over another smaller one when considering all possible game outcomes, because they are there.
N=100
3 coin game = green
Sally
No, I think you are misunderstanding the game as stated. There are no pushes. If it's a tie, they re-flip. Both are 50/50 games; the only difference is the procedure that they use to choose the outcome.
yes, the ev = 0 and that can be seen in the chartQuote: kubikulannSally,
Do we speak of the same game?
Betting heads or Tail should bring the same "net" result, whether once or a hundred times. So I don't see how this could produce anything other than 50%?
sounds good to meQuote: kubikulannMy understanding:
2UP - heads wins if two heads, (resp. tails) and there is a tie if the coins land heads and tails.
3UP - heads wins if there are two or three heads. (resp. tails)
How about just 2 games played for each.
Let us see the chnace of a net loss
3UP we can lose 2 units with p=.25
even = .50
+2 units = .25
so a 25% chance of a net loss after two games played
The 2UP
net: prob
-2: 6.250000
-1: 25.000000
0: 37.500000
1: 25.000000
2: 6.250000
Looks like a 31.25% chance of a losing session for just 2 games played with Ties included as they are a possible outcome.
Of course the average loss and win will be different too because of variance.
Sally
I see one game can end in a tie.Quote: AxiomOfChoiceNo, I think you are misunderstanding the game as stated. There are no pushes. If it's a tie, they re-flip. Both are 50/50 games; the only difference is the procedure that they use to choose the outcome.
But if the rules state the game MUST end and it could take 30 years to end the game???
I was just comparing 100 games played including ties and 100 games for the 3UP
So, it would then take more than 100 games for 2UP to have 100 resolved games.
Like the dont pass and pass line bets at Craps
Each player makes 1000 bets but only the pass line player has a probability of 1 of seeing 1000 resolved wagers
Sally
Quote: mustangsallyI see one game can end in a tie.
No, it can't. If there is one head and one tail it is not a tie; they re-flip.
Quote:But if the rules state the game MUST end and it could take 30 years to end the game???
Yup. That is the way that the question was phrased. It's totally reasonable, too -- lots of games work like that. In baseball (not to mention the playoffs of just about every other sport) they play until someone wins.
Quote:I was just comparing 100 games played including ties and 100 games for the 3UP
Yes, but the question specifically asked not to include ties.
Quote:So, it would then take more than 100 games for 2UP to have 100 resolved games.
Depends on your definition of "game". Over here, it is being used to mean "resolution".
The OP specifically states "thrown again until resolved". A bet never ends in a tie.Quote: StatsFor those that dont know the game, 2UP is a game where 2 or 3 coins are tossed and people bet on either heads or tails, in the case of 2 coins where one of each lands it is thrown again until resolved.
And, frankly, the 30 years hypothesis is more than far-fetched. In practice, all games will be resolved in less than two minutes.
Quote: kubikulannThe OP specifically states "thrown again until resolved". A bet never ends in a tie.
And, frankly, the 30 years hypothesis is more than far-fetched. In practice, all games will be resolved in less than two minutes.
I don't know; I have to assume that there is a lot of drinking involved here. 2 minutes might be less than the median time to find the coins...
Especially each time they roll off the table...
