With pressure from the rising blinds and players fighting for a finite number of chips, it's not possible - or rather it's completely improbable - you'll make it through any poker tournament without ever being in a coin-flip situation.
For clarity: Naturally, we're not talking about the actual act of flipping a coin here (although many poker players have won and lost large amounts of money doing just that).
The poker equivalent of the coin flip is getting it all in against one opponent with your probability of winning approximately 50%.
Classic examples: A-K vs. JJ; A-T vs. K-Q.
Anytime you flip, you're risking your tournament life (or a portion of your very valuable chips) with a 50% chance at missing.
NOTE: SARS masks are not proven effective against coin flips.
In case you're unsure about investment odds and probabilities, those are not good odds. If the odds are poor, any decent investor would tell you simply not to invest. Wait until an opportunity arises in which you have more favorable odds.
This is sound advice, and is exactly what you should be doing (for the most part) in cash-game Hold'em.
Unfortunately, in a poker tournament, the increasing blind pressure adds other factors into play. These factors force you to flip simply to stay alive in the tournament. You're forced to play the situation, regardless of the actual hands in play.
To sum up: You don't want to be taking coin flips, but there will come a point where taking a flip becomes your best chance at staying alive or making it deep.
Make Your Opponents Make the Choice
While you can't choose not to take coin flips, you can choose when to take them.
In the majority of all coin flip situations, one player moves all-in and the other player calls.
(Note: there are times when both players have a pocket pair, or some other combination of hands that give one player an edge over the other. Since these situations will go both ways (between the pusher and the caller) we'll exclude those situations from this conversation.)
After removing those situations, the player calling is calling for a 50% shot at taking the pot, but the player pushing actually has a better opportunity at making money.
It's not possible to put an exact number to it, but the concept is simply known as fold equity.
Just by being the player to have pushed, you have the chance that your opponent will fold. When this happens, you win the pot 100% of the time. If the opponent calls, then you're a 50% shot.
As you can see, the caller never has any fold equity while the pusher always does.
In other words, you want to be the aggressor, the pusher. If you're never making any moves, it's going to be terribly difficult to force your opponent into making a mistake.
Force your opponents to have to choose to flip with you or fold. If you're always making that choice as the caller, you're reducing your edge and counting on luck to bail you out.
30% is not 50%
If you're at the point where your best chance at progressing in the tournament is by taking a coin flip, you need to think in terms of this: 30% is not 50%.
Ziigmund has flipped for literally hundreds of thousands of dollars.
Basically, you need to avoid calling all-in bets with easily dominated hands.
Players will often call with hands such as A♠ 2♠ looking for a flip, knowing this hand is better than even money against K♥ Q♥ or any other non-paired, non-ace hand.
Unfortunately, matching up with any other hand with an ace in it has you at a little less than 30% to win - same as being up against a pair.
So a hand like this is a very poor choice when hoping for a coin flip. First, you have to get lucky to even be in a coin flip before you can have the chance at winning the flip itself.
This goes for hands such as 3♥ 3♦ as well. This is not a bad hand, and is ahead of anything other than a higher pair.
But if you're up against a higher pair, you're in a really tight spot. You need to know the range of hands your opponents will be willing to push or call an all-in with before you can choose your own range.
In many tournament situations, pocket threes might be a great candidate for a hand to take a flip with.
But if your opponent has a large stack, and is the kind of player only to raise hands with legitimate strength, you're putting it all on the line on the hope they have a something like A♥ K♥.
The first step in being successful in tournaments is to make sure that the coin flips you take actually are coin flips. If you get it all in with a dominated hand, you're simply giving your money away.
Bottom line: You're going to have to take coin flips in tournament poker; it's up to you to make sure you take them when it's best for you.
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