# The Butterfly Effect

The Butterfly Effect, a phrase coined by American mathematician Edward Lorenz (an early pioneer in the field of chaos theory) is a concept that states that “small causes can have larger effects.”

From Wikipedia:  “The phrase refers to the idea that a butterfly’s wings might create tiny changes in the atmosphere that may ultimately alter the path of a tornado or delay, accelerate or even prevent the occurrence of a tornado in another location. The butterfly does not power or directly create the tornado, but the term is intended to imply that the flap of the butterfly’s wings can cause the tornado: in the sense that the flap of the wings is a part of the initial conditions; one set of conditions leads to a tornado while the other set of conditions doesn’t. The flapping wing represents a small change in the initial condition of the system, which cascades to large-scale alterations of events (compare: domino effect). Had the butterfly not flapped its wings, the trajectory of the system might have been vastly different—but it’s also equally possible that the set of conditions without the butterfly flapping its wings is the set that leads to a tornado.”

It is a popular metaphor in science writing, in describing how sensitivity to some set of initial conditions can have a very large impact on some later state of things.

Last night a butterfly flapped its dainty wings at the poker table, and the resulting tornado cost me some money.

We were at a private house game.  It’s late.  The host has announced that at the end of the current orbit, he is breaking up the game and sending us all home.  Consequently, the play has loosened up in an already loose poker game, as some of the players want to be sure not to miss out on one last opportunity to smash the flop and recoup some losses or add to their gains.

I’m in the small blind, when the player on the button posts a live straddle of 4 BBs.  For purposes of this blog, I’ll refer to him as “Chris.”  Chris is not one of those players who always straddles every time he has the button, but this time he does.  I don’t really care whether other players straddle or not; it requires some adjustments and I generally feel confident that I can make these adjustments better than most players.  (Then again, maybe not.)

Anyway, I look down at pocket kings.  There were eight players at the table and I briefly considered just calling the straddle in hopes that one of the seven players to act after me would raise.  If Chris were known to frequently make big raises from the straddle position even with random card strength, as a stealing strategy, I might have done that.  But it seems unwise to risk a cascade of callers, so I raise to 11 BBs.  In hindsight, I could and should make a larger raise and still expect a caller or two.  I don’t want to run off all of my customers with such a strong hand.  Despite Chris’ straddle, 11 BBs is a large opening raise for this game, but I’ll be first to act on all subsequent betting rounds so a multi-way field is not very desirable.

The next player, in the big blind, very quickly calls.  Given the size of my raise and the speed of his call, this indicates strength.  For purposes of this blog, I’ll call him “Jeff.”

One other player calls, and Chris also calls, which given his positional advantage post-flop and the great pot odds he is getting (7 BBs to call with 37 BBs already in the pot gives him approx. 5.3-to-1 pot odds), he can call with a very wide range.

The flop is 887.  “Danger Will Robinson, Danger!” goes the voice in the back of my head, and I check.  Jeff bets 20 BBs, and consistent with my earlier thoughts when he called my pre-flop bet so quickly, I think his range is dominated by pocket pairs 99-QQ.  One player folds, but Chris calls on the button.  I call as well.  I’m not ready to put all of my chips at risk, but folding at this point would be way too nitty.  For perspective, Chris started the hand with about 95 BBs, Jeff started with around 175 BBs, and I have both of them well covered.

The turn is a 4.  I check again, hoping to keep the pot small.  Jeff bets again, this time 45 BBs.  So much for pot control. Chris pauses briefly, then takes a deep breath and goes all-in for his last 63 BBs.  I would have called Jeff’s bet, and still feel good about my read on him.  Chris, on the other hand, isn’t risking his entire stack with a drawing hand like T9, nor a middling strength hand like A7 or even 99 on this board.  He doesn’t seem afraid of either of us and has no real fold equity here.  Does he think Jeff might fold for 18 more BBs, with 212 BBs now in the pot?  Hardly.  I fold my kings, and Jeff makes a crying call, declaring that he knows he’s never good here unless he hits a 2-outer.

The minor surprise is that Chris doesn’t have an 8 in his hand, but 65, for a turned straight.  This actually gives Jeff 4 outs, as he flips over pocket queens.  Another queen or 8 would make him a full house.  The river misses, however, and Chris scoops up a nice pot.  I silently congratulate myself on sensing danger and releasing my hand, and tell Jeff and Chris what I was holding as I’m pondering the dynamic of what just happened and wondering how I might have played this differently or whether I simply lost the minimum.

After the hand is over, Chris comments about the impact of his straddle, saying that if he had not straddled, the entire hand would have gone down differently.  He might have called whatever action occurred prior to him on the button, but surely with pocket kings in the small blind I would raise enough to make it impossible for him to continue.  Not only that, but with pocket queens in the big blind, Jeff might put in a big re-raise over the top of my bet, especially if he thinks I’m just trying to steal the dead money in the pot.

Not only all of that, but Chris also notes that the only reason he straddled is because the game is about to break up, so this would be his final hand on the button and he straddled just in case he might get a good situation for leveraging his positional advantage.  15 or 30 minutes earlier he would not have straddled.

As played, I was first to act, so my raise communicated enough strength to make Jeff cautious about re-raising with six more players yet to act pre-flop.

It is tempting to describe Chris’ straddle as the flap of the butterfly’s wings that altered this hand.  But it is more subtle than that.  The initial small change in conditions that led to other changes ultimately shifting chips from Jeff’s and my stacks to Chris was the clock, and our host’s need for sleep.  Our host was the butterfly, fluttering his wings by announcing the game would end soon.

Imagine this hand without a button straddle.  There might be multiple limpers or a raise to around 6-8 BBs.  Chris would over-limp, and may or may not call a modest raise.  From the small blind with pocket kings, I’m definitely going to re-raise.  I cannot say for sure how much, as it would depend on the action in front, but it would likely be more than Chris would call with 65.

With Jeff being the big blind, last to act with pocket queens, he and I could have ended up in a pre-flop raising and re-raising war.  That would have turned out good for me.  If we didn’t get all-in pre-flop but were heads up, I would have been more likely to take a bet/bet/bet line post flop.

Alternatively, what if I had just called Chris’ straddle, as I briefly considered, hoping to trap a raiser and subsequent callers?  Another flap of the butterfly’s wings.  Then Jeff likely raises with pocket queens.  I’m not sure how much, but likely more than 11 BBs given that there would already be one caller of the straddle.  When it got back around to me, I would still re-pop it, having the effect of driving Chris out of the pot if Jeff’s raise didn’t already do that.  Again, this scenario is probably very good for me.

Damn butterfly!

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1. Great post, David.

But you left out one alternate scenario.

What if your home game did the button straddle “the right way”?

What’s the “right way”? Well not the way you do it.

If there’s a button straddle, the action should start on the UTG player, like it always does. Apparently in your home game it starts on the small blind, which is to my mind horrible. Now, in Vegas rooms that offer the button straddle, about half of them do it your way (the wrong way) and half do it the right way (my way). So you’re not alone out there; you’re just wrong.

But regardless, whether you agree with me or you are simple wrong, you could still examine how the hand would have played out if you handled the button straddle the way half the rooms in Vegas do. My guess is that after a bunch of limps, you would have made a big raise, and perhaps Jeff would have re-raised thinking you might be trying to steal all the limps. Chris goes away, you re-raise and you win a huge pot from Jeff.

But perhaps you have a different scenario that can imagine.

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1. Good point Rob, there is another scenario.
In this game, I’m just a player, not the organizer so the betting protocol for button straddles isn’t under my control. Most of the house games at which I play allow button straddles, and all of them start the action on the SB.
I’ve played in Vegas rooms that do it the other way, with action starting UTG and proceeding to the cutoff, then skipping the button to the blinds, then back to the button to act last.
In that case, it’s hard to speculate how many players would call the straddle before it becomes my turn to act, but I’m very likely to put in a larger raise and Jeff is more likely to re-raise than as played. Interestingly, as the hand actually went down, Jeff lost considerably more than I did… maybe my absolute worst position post-flop helped make it easier for me to be able to get away from the hand after the turn came.

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