Give me some good paradoxes

[atrifix]

This depends on the rest of the play, or there are certain other conditions present.

E.g.: Player always moves all-in preflop with AA. In such a situation 22 cannot do better than AA.

[davebwell]

I saw this one in a book called Keys to Infinity.

the probability that an integer with n-digits contains a 3 is 1 - (9/10)^n, therefore as n tends to infinity the probability that an integer contains a 3 is 1, yet there will be infinitely many integers containing no 3.

[LuckOfTheDraw]

Existence. Either something has been here forever, or everything came crom nothing.

a) Forever effects the notion of infinity, and this makes no sense.
b) Something outta nothing? This makes no sense.

[vhawk01]

Basically, because of how vastly superior your play is to theirs, all hands have a positive EV, 22 vs. AA being no exception. The probability tables you memorize only judge the chance of each hand winning with 5 cards on the board, not how much money will be won in any case.

[FortunaMaximus]

[ QUOTE ]
[ QUOTE ]
The most common example of the paradox in America involves batting averages in baseball. It is possible — and in rare occasions it has actually happened — for one player to hit for a higher batting average than another player during the first half of the year, and to do so again during the second half, but to have a lower batting average for the entire year, as shown in this example:

First Half Second Half Total season
Player A 4/10 (.400) 25/100 (.250) 29/110 (.264)
Player B 35/100 (.350) 2/10 (.200) 37/110 (.336)


[/ QUOTE ]

How is that a paradox? Player A played less ball in the first half, hit well, but hit a lower percentage during the second half when he played a lot, so what?

Maybe I'm improperly relating "paradox" with "logically unexplainable."

[/ QUOTE ]

It is neither a paradox nor logically unexplainable. Dividing the season into half is the yardstick flaw.

If you look at the sample size in units of 10 (at-bats, which is the sample base here) instead, it should disappear in this example. Are such paradoxes possible in other examples?

[TimWillTell]

There a quite a few religions that have a Mozes getting ten commandments.
Jews have it, christians have it, rastafari's have it, maybe muslims to, I don't know. But they all say, their God exists and the other doesn't.

[HLMencken]

[ QUOTE ]
Pocket-pair-paradox.

In Deepstack No-Limit Holdem there are quite a few players who are not capable of folding aces.
Against such players even a low pocketpair becomes a winner.
So every time in such a situation A,A go against 2,2... on average 2,2 wil do better than A,A.

[/ QUOTE ]

How is that a paradox?

Good players will beat horrible players. Wow, who knew?

[morphball]

[ QUOTE ]
E.g.: Player always moves all-in preflop with AA. In such a situation 22 cannot do better than AA.

[/ QUOTE ]

The player need not even go all-in preflop, now I may be rusty due to playing Omaha, but I am pretty sure if AA just bets more than 1/6 of his stack (assuming no menaingful pot here) 22 is a net loser.

[atrifix]

[ QUOTE ]
The player need not even go all-in preflop, now I may be rusty due to playing Omaha, but I am pretty sure if AA just bets more than 1/6 of his stack (assuming no menaingful pot here) 22 is a net loser.

[/ QUOTE ]

I didn't bother to figure out the break-even point, but suffice it to say that going all-in preflop is not a necessary condition, just a sufficient one. There are a lot of necessary conditions in order to make 22 vs. AA a winner, however.

[MatthewRyan]

[ QUOTE ]
[ QUOTE ]
E.g.: Player always moves all-in preflop with AA. In such a situation 22 cannot do better than AA.

[/ QUOTE ]

The player need not even go all-in preflop, now I may be rusty due to playing Omaha, but I am pretty sure if AA just bets more than 1/6 of his stack (assuming no menaingful pot here) 22 is a net loser.

[/ QUOTE ]

that doesnt work because if you're playing 600nl and you open for $100, you only win the blinds; thus 22 is still more profitable.