DutchDave
DutchDave
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November 17th, 2010 at 6:55:15 PM permalink
Say your are playing in a Texas Hold'em tournament and you start in the big blind. Before the first deal the player to your left says that they are going all in without looking at his cards. Cards are dealt and everyone else folds to you. What is the minimum hand you should have to have at least a 50% chance of winning? 75% chance? 90% chance?
teddys
teddys
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November 17th, 2010 at 7:00:34 PM permalink
You need a hand that has a >50% chance of winning against a random hand. I would call him with two high cards or a mid-to-high pair. J-10 off suit or a pair of threes or fours would probably be the threshold.
"Dice, verily, are armed with goads and driving-hooks, deceiving and tormenting, causing grievous woe." -Rig Veda 10.34.4
rdw4potus
rdw4potus
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November 17th, 2010 at 7:03:35 PM permalink
The first column of the table on the Wiz's other site shows a nice ranking of hands. Based on that table, it looks like your answers are:
50% chance of winning = J7 suited
75% chance of winning = JJ
90% chance of winning = does not exist. AA is about 84%

Note: these answers would be different if you descriped "winning" as surviving and counted ties as "wins."
"So as the clock ticked and the day passed, opportunity met preparation, and luck happened." - Maurice Clarett
mkl654321
mkl654321
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November 17th, 2010 at 8:20:11 PM permalink
Quote: teddys

You need a hand that has a >50% chance of winning against a random hand. I would call him with two high cards or a mid-to-high pair. J-10 off suit or a pair of threes or fours would probably be the threshold.



You aren't exactly addressing the OP's question here--he wants to know what hands have x% probability of winning. What you "should" call with depends on the amount of the all-in player's bet. For instance, if his bet was exactly twice the big blind, you should call with the top 75% of hands. Interestingly, there is no situation where it would be correct to call with EXACTLY the top 50% of hands, because no matter what the size of the all-in was, you would be getting better than even money on your call.
The fact that a believer is happier than a skeptic is no more to the point than the fact that a drunken man is happier than a sober one. The happiness of credulity is a cheap and dangerous quality.---George Bernard Shaw
DJTeddyBear
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November 18th, 2010 at 5:19:32 AM permalink
MKL -

You've missed an important point.

The OP said FIRST HAND. Therefore, his stack is the same as everyone else's.
I invented a few casino games. Info: http://www.DaveMillerGaming.com/ ————————————————————————————————————— Superstitions are silly, childish, irrational rituals, born out of fear of the unknown. But how much does it cost to knock on wood? 😁
DJTeddyBear
DJTeddyBear
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November 18th, 2010 at 5:43:24 AM permalink
I know this doesn't address the original question, but I was in a tournament at Taj Mahal with a similar situation.


The first hand, I was Big Blind. There were a couple limpers. A guy in late position goes all-in. Everybody folds.

Next hand, I'm Small Blind. Nobody before him calls. Again he's all-in. Everybody folds. People are commenting that this feels like an on-line tournament.

Next hand, I'm the Button. Again, nobody calls before him. This time he limps. Another guy limps. I look and see an Ace, so I limp. The Small Blind calls, and Big Blind checks.

The flop is A-9-4 rainbow. I double check. My kicker is a 4. Two pair. Early positions check. That guy make a normal sized bet. One guy and I call.

The turn was low rank (I forget what) and put the fourth suit on board. That guy makes another normal sized bet, but for more than the flop bet. I'm the only caller.

The river is an Ace. Full house baby! He's first and again makes a normal increased bet. I raise it to about triple his bet. This means, in total, I put about 30% of my chips into this hand. He goes all-in. I'm thinking that he COULD have a better full house, but how do I fold a full house? Particularly to this guy? I call. He has an Ace with a high kicker for trips. My full house was good.


And THEN the guy makes his speech: He has a bet with his buddy to see which one would bust out first.
I invented a few casino games. Info: http://www.DaveMillerGaming.com/ ————————————————————————————————————— Superstitions are silly, childish, irrational rituals, born out of fear of the unknown. But how much does it cost to knock on wood? 😁
mkl654321
mkl654321
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November 18th, 2010 at 9:21:25 AM permalink
Quote: DJTeddyBear

MKL -

You've missed an important point.

The OP said FIRST HAND. Therefore, his stack is the same as everyone else's.



Yes, but we still don't know how big those stacks were. If it truly is the very first hand, the BB would probably only be getting something like 1.03 to 1 for his call, which for all intents and purposes, means call with the top 50%.
The fact that a believer is happier than a skeptic is no more to the point than the fact that a drunken man is happier than a sober one. The happiness of credulity is a cheap and dangerous quality.---George Bernard Shaw
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