Author Topic: Unequal Payoff Paradox  (Read 276 times)

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Kynge_Rycharde

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Unequal Payoff Paradox
« on: April 21, 2017, 04:27:21 PM »
Is anyone aware of, or has noticed the following.

Let's say there are two players. Let's call them Smith and Jones. Both will bet the same amount ( two chips), and both will bet on the same numbers (1-6 double street).

Smith chooses to place his two chips as a line bet. Jones chooses to place one chip on the 1-3 street, and one chip on the 4-6 street.

Number 4 appears, so both players win. Smith gets back (5 * 2) + 2 or twelve chips. Jones gets back (11*1)+1 or twelve chips, but loses the one chip wagered on the 1-3 street for a total of eleven chips returned.

Another way to look at it is that both players start off with ten chips; both make a two chip wager, so now both have eight chips left. Smith receives twelve chips, and now has twenty (8+12). Jones receives eleven chips and now has nineteen (8+11).

I'm sure that somehow I'm missing something here, because from what I have read, no matter what variation of a bet that you make, the payoff is supposed to be the same. And yet, from the above example, it would appear that it is better to make one two-chip wager, rather than two one-chip wagers.

Comments and guidance would be appreciated.

Regards,

Kynge


 
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scepticus

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Re: Unequal Payoff Paradox
« Reply #1 on: April 21, 2017, 05:38:22 PM »

You have misunderstood the payouts, KR
Both bet 2 chips and both receive 12 chips  on a win . Both have a profit of 10 chips on their bets.
 
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thomasleor

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Re: Unequal Payoff Paradox
« Reply #2 on: April 21, 2017, 05:44:42 PM »
The statistical chance of both men winning their bet on 6 numbers is 0.1621%,  or 1 in 6.167 attempts. The casino has to match this with equal payouts.

Consequently both receive 12 units back from the casino standing on a BR of 20 units, each of them having doubled their original BR with this single bet.
« Last Edit: April 21, 2017, 06:01:34 PM by thomasleor »
 
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kav

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Re: Unequal Payoff Paradox
« Reply #3 on: April 21, 2017, 06:13:50 PM »
Jones gets back (11*1)+1 or twelve chips, but loses the one chip wagered on the 1-3 street for a total of eleven chips returned.
The fact that he loses the one bet doesn't change the fact that he gets (11*1)+1 = 12 chips. So both get 12 chips back.
 
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Reyth

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Re: Unequal Payoff Paradox
« Reply #4 on: April 21, 2017, 08:00:23 PM »
I think the problem is you have counted a winning chip as a loss and with that corrected, both players get 12 chips. ;)

HTH! :D

In all seriousness though, its an easy mistake to make; I have made it many times among other such mistakes and so just like with programming, I have learned to "check everything" because I am bound to make a mistake.
« Last Edit: April 21, 2017, 08:03:03 PM by Reyth »
 
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