so why give your opponent two chances to suck out on you?
I can see the positives for when you get it all in with a good draw, to give yourself two chances to hit it
I think the aspect of Run It Twice you're kind of forgetting to account for (and this sounds really obvious but it's very common) is that the pot is split into two. So in your first example, as much as you are giving your opponent 2 chances to suck out of you...you're at the same time FORCING him to suck out on you twice if he wants the whole pot.
In the second example, it's the reverse, you're giving yourself 2 chances to hit it...but again if you want the whole pot you gotta hit it twice.
So actually the two examples seem massively different...but in reality they are identical. The maths is like this
Lets take a standard 70/30 Spot (you have AK vs 56 on A47 something like that)
You're 70%, you run it twice. 70% of the time you win the whole thing....30% of the time you lose the whole thing. Simples.
Run it twice. You're now only 49% to win the whole thing (70%*70% - yuo have to win both boards twice) so that sounds bad. HOWEVER, as a result you're now only 9% (30% * 30%) to lose the whole thing.
If the pot = £1000, run it once your equity is worth £700.
Run it twice 49% of the time you get it all (£490) 9% of the time you get none (£0) and 42% of the time you get half (£210 (£1000/2 * 42%) £490+ £210 +£0 =
£700Do it from the reverse, you have the 56 vs AK on A47...
Run it once, 30% of the time you win it all, 70% of the time you lose it all = £1000 pot = £300 equity.
Run it twice, you only win it all 9% of the time, but now you only lose it all 49% of the time.
9% win (£90) 49% lose (£0) and 42% chop (£210) = Equity when running it once
£300You can run it 1 time, 2 times, 5 times, 100 times. The win% and lose % changes but the bottom line EV remains identical.
Problem with all this though is we're humans, it doesn't matter how sensible and level headed you are, everytime you run it twice win the first and lose the second you're always going think "Dammit should have run it once" and you'll be told be everyone at the table too.
Everytime you run it twice, lose the first and win the second you'll think "Thank god i ran it twice" and no doubt someone else will say it to you too
Everytime you run it twice and lose both you'll feel hideously unlucky and every time you run it twice and win both you probably couldn't care less about why you ran it twice