but the thing is, there’s an entire different layer to it. no longer handiest do you’ve got uncertainty about what your opponent may additionally have since the playing cards are dealt face down, however you even have uncertainty about what your opponent’s method is. when we go during the hand analyzing method, we tend to make assumptions about how opponents would play palms. “smartly, if he had A-okay, he’d doubtless have raised there or bet there, and if he had A-J, he would have called there or checked there.”
These are the types of assumptions you ought to make in case you are looking to damage the mathematics of poker down into something that’s truly approachable.
but there’s an error in this procedure—an inescapable error. You have no idea for certain how your opponent would play any of those palms. basically, with most opponents you have got appreciable uncertainty about how they would play any hand. Even probably the most predictable opponents will shock you occasionally, and the unpredictable ones—well I don’t need to let you know how inscrutable they may also be.
There’s a suit, un-detachable hunk of uncertainty constructed into all this good judgment. And the aspect is, this type of uncertainty does some unintuitive issues to percentages.
To remember how this works, let’s analyze a less complicated difficulty than poker. Let’s say we’re making a bet on how tall the subsequent man to walk through a door can be. For the sake of argument, say you recognize that the common median man to your metropolis is 5 foot 10 inches tall, and that 20 p.c of all men are between 5 foot 9 inches and 5 foot eleven inches. i will be able to guess you $2 against your $3 that the subsequent man to stroll through the door is beneath 5 foot 11 inches. poker domino
the way we’ve defined this issue so far, that might be a fair guess. Half the guys are shorter than 5 foot 10 and a further approximately 10 percent are between 5 foot 10 and 5 foot 11, so about 60 p.c of guys are shorter than 5 foot eleven. If I make you lay 3:2 odds, it’s a fair wager.
however now let’s say we go to a metropolis elsewhere in the country. You comprehend the heights will work roughly the identical method in this new area, but you aren’t as certain about what the standard is. You believe it’s roughly equally seemingly during this new region that the commonplace is anyplace from 5 foot 8 inches via 6 foot tall.
Is it nonetheless a fair guess to ask you to lay three:2 that the next man throughout the door is shorter than 5 foot 11?
You might feel so. Your estimate of the average top hasn’t modified—5 foot 10 is still your standard estimate of the average. So if the typical hasn’t modified, and also you’re simply rather less definite, the wager hasn’t changed either, appropriate?