It's a pattern you often see while playing the smaller stakes tables: somebody goes unprovoked all in pre-flop. You're forced to toss your otherwise playable hand and watch as everybody else does the same. Occasionally somebody gets fed up with it and calls. Usually to watch their money lost to a pair of aces or kings.

So why do people go all-in? And more importantly, is it a winning strategy? The answer is essentially no, though it can be employed as a profitable tactic.

Strategy

The strategy is to go all-in when you hold a premium hand, typically an ultra premium hand like an high pair or ace-king.

Only one consideration seems to apply: do it only if the betting thus far is low. That is the unprovoked aspect. If somebody does a 10-20xBB you shouldn't do it, rather just call normally (though even here you could still do it and it wouldn't alter the results much).

There are two outcomes to this move:

• Everybody folds and you take the blinds, or in some cases some small bets
• Somebody calls and you go to a showdown

Obviously should everybody fold all the time the strategy is a long-term win, albeit the rewards aren't so high. If somebody calls then it becomes a game of chance.

The Odds

We have to make some assumptions before we calculate the odds. Let's first assume that you perform this manoeuvre only when holding one of the top 5% of pockets. Then we'll assume you're playing at a table with some crazies who are willing to call with any of the top 10% of pockets. We'll also say you are at a nine player table.

The Cost of Blinds

Each round at a table costs you 1.5BB (for simplicity assume SB = 0.5BB). Since you only play the top 5% of hands you will go 20 rounds before playing one. For simplicity again we'll ignore those times you limp in or otherwise play a hand normally. This means for each time you go all in it costs 3.33BB (20 / 9 * 1.5).

Revenue from blinds

So how often does everybody fold? Well, we said that people will only call with a top 10% hand. This works out to at least one person calling 57% of the time. That seems too frequent, so let's reconsider and say half the people would only call with a 5% hand, and the others with a 10% (so four people each). This lowers the value to a call 47% of the time.

Thus 53% of the time you'll take what blinds and calls have been posted so far without contest. Assuming an average 30% call rate, plus BB, plus SB the table on average would have 3.9BB. Though due to your variable position those extra calls may not come, but then sometimes people will also raise one or two BB. So let's just assume an average pot of 5BB.

Each time you do this manoeuvre you'll earn 5BB * 53% = 2.5BB from the blinds.

Revenue from calls

We'll again consider the two groups of people, the 5% and 10% callers.

If you get a 5% call you have a 50% chance of winning -- since you are both playing the same set of pockets.

If you get a 10% call your odds a bit better. Calculating this exactly is quite difficult so we'll use some sample points. A♠ A♦, the top hand has an 83% chance of winning. Let's use then A♠ T♠ as the bottom 5% hand. This has only a 35% chance of winning. Right in the middle would be 9♠ 9♣ with a 47% chance.

Being very rough you have on average a 53% chance of winning. Now, your returns depend on what the other person, and you, have for a stack. Let's assume you tend to have 50xBB on average. That works out to 53% x 100BB = 53BB, or a 3BB gain each time you use this tactic.

Combined with the 5% callers that's actually only a 1.5BB gain though -- as half the time you'll break even.

Your stack size must remain on average the same. If you just let it build over the long-term you're guaranteed to lose everything. This is because each time you lose your entire stack disappears. So essentially each win will require you to leave the table and go to a new one.

Summing up

So on average each time you go all-in costs you 3.33BB and wins you 2.5BB + 1.5BB. That works out to only about a SB gain each time. This hardly seems worth it.

Yet people do it often. So let's restrict this nonsense to the absolute top hands like A♠ A♣, K♠ K♦ and A♠ K♠. This will give you a 69% win rate on the 10%, 64% on the 5% callers, leaving you a gain of about 16BB each time.

You'll of course only be playing 1 in 100 hands, which costs you 16BB. That eats up all your revenues.

Partial Strategy

Employed on its own this strategy doesn't appear to make a lot of sense -- the risk reward ratio is quite small. Perhaps you hit some tables with extreme crazies that will call anything, but that won't happen so often.

Though as part of a normal strategy it would likely work out okay. This would mean the blinds you'd normally just be losing can now be used towards regular play. You don't even have to play to win, you just need to break even until your hit your ultra-premium hand.

Be careful though, the moment two people call it falls apart. Only a pair of aces retains a decent chance at 59%.