How accurate is Clonie Gowen's estimate?

[LetYouDown]

Typically for questions like the hand above, it's much easier to calculate the probability of missing and then subtract from 1. There are 21 cards that will improve you to a pair of Q's or better. There are 47 cards left in the deck.

So basically, to miss entirely, the turn/river need to be 2 of the remaining 26 cards that don't improve your hand. There's C(26,2) ways for this to happen. There's C(47,2) possible ways for the turn/river to come.

So, in English it's:

1 minus the probability that I'll get 2 cards from the 26 cards that don't help me divided by the total number of ways the remaining cards can come.

[Bulldog]

You need a heart for a flush, but your opponent needs two hearts for a higher flush, correct?

You have 9 outs twice, or a 36% chance (estimate based on this method) to get there. Odds of runner runner flush are about 4%*. So 36% - 4% equals 32%.

*Actually 4.16% when you know five cards (the three on the flop and the two in your hand) and three of the suit are accounted for in those five. In this specific scenario, where we know seven cards and five of that suit are accounted for, it's 2.83%.

[Absolution]

Pretty sure this is right, but I plotted this very quickly:



i.e. With 2 cards to come you start really overvaluing your hand after about 8 outs. With 1 card to come you're always undervaluing your hand.

[ismisus]

Very accurate. The figures will be correct if you count your outs right. If you have a flush draw, you have 9 outs, 9*2*2 = 36%. If the board is paired, I give myself 5-8 outs depending on the amount of people/betting patterns.

If you have a straight draw, you have 8 outs, 8*2*2 = 32% after the flop. After the turn you have 8*2*1 = 16% chance of hitting your straight.

If you have a pair, you have 5 outs of improving to a 3 of a kind or two-pair. 5*2*2 = 20% after the flop.