Calculating the odds of completing a hand

[TAAZ]

Hello everyone!

Does anyone happen to know how to calculate the odds of completing a hand on the turn and on the river ? Flush and straight draws ?

I watched the video of Jonathan Little and Alex Fitzgerald "Neutralize their position" and I remember them talking about the x4, and x2 rule, and they do not seem to approve of it.

This is what I remember from the video:

HU, we have a flush draw
our hand : Kd3d

the flop: Jd6d5c

there are still 9 outs in the deck out of 52 (deck) - 2 (our hand) - 2 (villain's hand) - 3 (flop) = 45

9/45= 0.2

I do not really know how to interpret this number.

Could anyone please help me through this ?

Thanks in advance!

Taaz

[Dilly]

I would stick to the x4 and x2 rule.

You have a flush draw, so 9 outs, of the remaining 45 cards in the deck which means .2=20% chance you make your flush on the turn. If you wanted to know chances of making it if you get to see a river you do that formula+9/(45-1)=.4045454545...so 40% you make it by the river....rule of x2 and x4 would have gotten you 18% or 36%....you generally add a little to the rule.

The bigger thing to keep in mind beyond the simple math are the other data points of the situation. Does villain likely block some of our outs? Do we always win when we get there, does villain have counter outs, etc. Also remember the implied odds, we can often continue getting less than the correct odds if we're getting good implied odds

[LondonImp]

A great way to succeed in poker is by simplifying the spots you play.

If a solver wants us to bet 2/3 pot 95% of the time and 1/3 pot 5% of the time, we simplify this strategy and just bet 2/3 pot 100% of the time.

It's the same with the x4 and x2 rule. Is it perfect? No. Is it close enough to be very useful for quick calculations in game? Yes.

Unless you're a maths whizz just stick to this.

[MOUSE85]

Multiply every out by two, then by the number of cards to come. For every out above NINE, subtract the difference from your answer.

[LondonImp]

Multiply every out by two, then by the number of cards to come. For every out above NINE, subtract the difference from your answer.

This is only true if we are on the flop expecting to see the turn and river.

If we are on the turn we can be more accurate by doing: (Outs * 2) + 1% if more than 5 outs, or +2% if more than 13 outs.

I'm lifting this from Modern Poker Theory, not from memory. I should remember this to be honest, thanks for reminding me.