The relevance of variance

• Bronze
Joined: 08.10.2008
I have been discussing with Bliausmas today the relevance of a rare occurance such as being dealt jack five offsuit (of the same suit) 8 times in a row in another thread created by lfcday.

Original Thread: So much for variance!

I had originally made the comment that being dealt jack five offsuit is merely being dealt trash 8 times in a row. Sure, it is a statistical rarity, but is it really relevant to the game? Further discussion led me to consider how relevant other statistical rarities are to our game, for example a streak of being dealt pocket aces 8 times in a row.

The reason why I consider being dealt jack five offsuit 8 times in a row as being the same as being dealt any random combination of trash 8 times in a row is because it always ends in the same outcome. I fold. Folding 8 hands in a row is not uncommon for me, so why should it affect the game? I don't expect the actions of my opponents to differ significantly from my actions due to such a streak. Therefore my general strategy and expected outcome shouldn't change either. In short, the event 'being dealt jack five offsuit 8 times in a row' is, for practical purposes, just one of many outcomes of the more relevant event 'being dealt trash 8 times in a row'. Which is itself a fairly common occurance.

A streak of 8 back to back pocket aces however, is a different story. If I were to raise 8 times in a row, I would expect my opponents to alter their actions against me, and so they should. It is a far more likely scenario that I am getting a bit over confident and attempting to bully the table than recieving a rare streak of pre flop monsters. It would cause more action as they try to make moves against me with more marginal hands expecting to have a higher expected value against me. Such a streak is more relevant to the game as it would change the way our opponents react to our strategy even though our strategy hasn't changed at all.

So based on this theory, it could be expected that the amount of action you would recieve for the nth raise in a row will rise with some relation to n. And from this it could also be expected that for two identical sessions differeing only in the distribuiton of your pre flop hole cards, that you would expect a higher profit from a session in which all your monsters were clumped together in a streak rather than being more evenly distributed.

This is all theoretical. I haven't had the good luck to see pocket aces 8 times in arow. However, I have had smaller streaks of big hands (not monsters) which did see increased resistance after several raises in a row.

What are your thoughts on this theory?
What are other situations in which variance should affect how we play? e.g. Do we have more success at pure bluffs when we are card dead.
Has anyone experienced any good streaks where such results have emerged?

Of course 8 time back to back pocket aces is an extreme example. It was just the example that came up in the other thread. This discussion of course applies to any and all streaks of good or bad (or average) cards.
• 4 replies
• Bronze
Joined: 11.03.2010
You see, we are viewing the same thing from different sides. You told it yourself very clearly - "Sure, it is a statistical rarity, but is it really relevant to the game?". Nope, it's not relevant at all, but those statistical rarities are the things I referred as cool. You don't care about it as it doesn't influence your game, but I do, since I liked math and statistics from my childhood, and I was stupid enough to study math in university But anyways, being dealt AA 8 times in a row would be very profitable for you, and you would definitely think it's cool, wouldn't you? But for me it's the same thing no matter if I see J5o or AA that many times in a row - that's mathematically/statistically cool.
• Bronze
Joined: 08.10.2008
I think its fair to say that the quote 'beauty is in the eye of the beholder' applies here. But the point I was moving towards here (hence the new thread), is that some of these statistical rarities (either rare or just uncommon) can be more than just a thing of 'beauty' (if you think they are). As we plan strategy for when we play we should consider how they affect what we should do in the game and how to milk them for all they are worth.
• Bronze
Joined: 24.04.2009
summary so far of the two threads: it doesn't fucking matter what trash cards you get dealt 8 times in a row since you fold anyway.
• Bronze
Joined: 11.03.2010
Well yes, if we talk about how these "beauties" affects our game and stuff, there's not much we can say more than has been said in the last post.