Thursday, May 17, 2012

How Big is Big? Short Answer: Big. Long Answer: BIG!


Recently, there’s been a small thread churning on 2+2 in the Poker Theory section on hand combinations. Specifically, someone commented on PokerStars latest promotion, in which they were centering the festivities around their upcoming 80-billionth hand dealt. Yes, you read that right: 'Stars is going to pass their 80,000,000,000th hand within a week or so.

Anyway, the question posed was whether 'Stars had dealt/played every possibly hand of hold’em yet in that 80 billion hands. That's a lot of cards and combos, so surely they must have dealt out every possible combination of cards at a theoretical 9-handed table by now, right?

The short answer is: No they haven’t, and it’s not even close.

The longer answer is that the math geeks on 2+2 worked out that there is a mind-blowingly huge  2,969,534,343,999,738,737,074,447,813,120,000 possible combinations of ways the cards can be dealt out at a 9-handed Texas hold'em table. This can be rewritten/approximated in scientific notation as ~ 3x10^33 poker hands.

How big is this number?

Short answer: big.

Longer answer: really freaking big. A trillion is 1x10^12, so this number is larger than a trillion trillion. Or think of it this way: considering that there have only been 4.3x10^17 seconds since the Big Bang; if you had been dealing unique nine handed holdem games since the beginning of the universe at one hand per second, you've seen less than a teeny tiny itty bitty fraction of less than 1% of possible hands. The number of possible hand combinations is so large that it is actually unlikely that there has ever been a duplicate hand dealt since the invention of Texas Hold'em. Seriously.

Now that's a big number. And it's also why poker has yet failed to bore me. Every hand dealt out at a table offers countless possibilities and ways to think about it.

In a related subject, Mr. Multi was in my office yesterday talking about Gus Hansen and hand ranges, pointing out that before analytical math guys like The Great Dane came along, most players were taught to put their opponents on specific hands, not ranges. In light of today's big number, we see just how foolish that is. Yes, sometimes you can put an opponent on a specific hand, but the vast, vast, vast majority of times it's basically impossible to narrow someone's hand down to two specific cards. In other words, hand ranges are the key to the "R" in REDi. Why? Because there are a freaking huge number of hand combinations that can be dealt, that's why.

All-in for now...
-Bug

No comments:

Post a Comment