Math on redraw

[MJJ]

My friend and I have been argueing about how the math works for this hand...
(home game)
I have ~8000
He has ~12000
(starting stacks were 12000, we have 12 people left of 20, top 4 pay)
I am in BB w/ 3 4 , one limper to me (bad player who I have played with quite a few times) I call (500 each)
flop: 2 5 10x
I bet 500, he pushes
I know this guy's play well enough to be 95% sure he has a set
I lay down the big draw, he shows the set

Here was my math-
I have 13 outs (9 spades and 2 other A's/6's) to make a str8 or fl (2 that make str8fl)
Problem is he has redraws even if I hit- If I hit on turn (and he has set) he can pair 3 of the board cards for boat (9 outs) plus the case card for 4 of a kind (10 total) so he will beat anything but the str8fl if he hits his redraw..
I said that I am ~52% to hit* but he is ~20% to hit* his redraw- so 52% of the time I will hit but he will still beat me 20% of the time that I do hit my draw; so I am only ~41% to hit and have him not outdraw me
The problem is accounting for the times i would hit the str8fl- do I add add 8% to the 41% (2 outs x 2 cards) or is there another factor here?

* I used rule of 2+4 for math: 13 outs w/ 2 to come ~52%, 10 outs w/ 1 to come ~20% (because I only care about the hands I made and that means 1 of his cards is not pairing board)

** We ran the cards- I would have made fl on turn, he would have made boat on river

Thanks, MJ

[MJJ]

Yes, the 'correct' play would be to bet more on the flop- This play was based on the guy I was playing

Yes, I probably have the pot odds to call here after his AI- I didn't want to put tourney at risk on coinflip

[Dave B]

I was next to you when this happened and I couldnt believe that you laid it down, but is was so early, that I dont think it was a bad play.


He was 58% to 42% on the flop unless one of his 10s was a spade.


If you know you are against a set, you need to let it go. But that is so rare that it is hard to let it go. Lucky for you, you were absolutely right on your read and the results.


If you flop a set, you have a good shot at the boat.

[MJJ]

Thanks Dave, I think it was the 'right' play too, especially since it was a live tourney and I had to put some value in staying alive (maybe I'll call that added social odds... )

My big question is how to account for my 2 'pure' outs in the math. I know I can put the hands in a calculator and get the %'s; I want to know how to do the math (As in quick math sitting at the table...)

[Dave B]

It isnt easy.


IF, you put him on a set:

He has 7 outs on the turn for his boat or 14%
IF he misses the turn, he gets 3 more outs w/ the turn card or 20%

so, 86% times 80% is about 70%-set will hit boat 30%

You have 15 outs, so your odds of hitting are 70% times 70% or about 50%. Odds are usually a bit better w/ a str8 flush, because 2 running cards will help-worthless against a set that will get to a boat beating your trips.

Finally-you have 2 outs where he will be drawing dead. So 8% for you


Table math:

50% - (50%x30%) + 8% = 43% This is 1% off from the real odds.

[MJJ]

I came up with a different method after thinking about it awhile- same result though...

I have 13 outs- 2 pure outs and 11 that can be beat w/ redraw
So 11 outs: 11x4=44% I hit str8 or fl, less 20%* he redraws= 35% I win
Plus 2 outs: 2x4=8%, his redraw won't matter (Str8fl,) 8% I win
Equals 43% total (35%+8%)

* I have him with 10 outs, I only use times 2 because I am only concerned with the hands i hit (which means the card that hit me will miss him) leaving him only one additional card to hit his redraw... He has 4 cards he can pair- 3 of them have 3 more in deck, other one has 1 (for 4 of a kind)

I don't know about doing this on the fly at the table; but I believe the math is correct