Chasing the Backdoor Draws, Pot Odds Theory

[Josh Chud]

Yo,

So i've been playing limit for about 6 months now, i also am really into the numbers of the game, so a couple calculations i did (and am sure you can find on the web) result in this:

Odds of getting a flush by the river pre-flop holding 2 suited cards: 5.8%
Odds of flopping a flush: .8%
Odds of flopping a flush draw: 16.666% (1 in 6) (it might be 1 in 7, as of this posting im away from my odds log book)
Odds of hitting your flush after flopping your draw: ~35% (everyone knows that one)
Odds of hitting your backdoor flush draw: 3.33% (72/2162)
Odds that next card gives you flush draw if you are on backdoor flush draw: 21.2% (10/47)
hitting flush on river: 19.565% (9/46)
Preflop Odds board pairs by the river: 54%

So here's the question then:

you hold A [img]/images/graemlins/spade.gif[/img] 9 [img]/images/graemlins/spade.gif[/img] on the button in a 10-20 game. 3 limpers, seat 8 raises, cutoff reraises, you call, knowing you are on a loose table and you're call will inspire the SB or BB to call, and the rest of the limpers will definately call. This will bring about 6 people into the pot and there should be approximately 180$ preflop.

We must also assume the following things about your hand:
1) Your hand is no good except for 2 possible final holdings, a set of 9's or the nut flush w/ no paired board.

Flop comes K [img]/images/graemlins/club.gif[/img]8 [img]/images/graemlins/diamond.gif[/img]2 [img]/images/graemlins/spade.gif[/img] giving you 1 over w/ a backdoor flush draw.

Now, normally i think the book answer here is to fold, but i have a theory that basically states this:

you have slightly greater than 1 in 5 of hitting your backdoor flush DRAW on the turn. So if you are getting better than 5:1 to call then you should see the turn. in the previous example, even against a raise you are getting 10:1.

Here is the result of you seeing the turn and river (assume no raise here):

47 times you will pay to see the turn for average (50% raised) 15$: 705$
10 times you will hit your draw and pay to see the river, even against a raise, lets say its raised 50% of the time on the turn.
so, 46 times you pay average of 30$ to see the river: 1380$
why 46 here? because assuming you hit your draw, you will over the long run hit your flush 9 out of 46 times, so we will calculate the number of times you will hit vs. not hit on the river, not just one isolated incident.

Assuming multiway pot by the river (3 way or more) the pot going to the river before final round of betting will be ~330$ then you can win some additonal bets w/ the nuts so your final takedown when you win is around 370$.

OKAY so: 9 times you win 370$ - thats 3330$
and you spent: 705$+1380$ = 2385$

Is my theory at all feasible? or am i crazy for chasing backdoor flush draws in large pots?

also there are other scenarios not present here, you could hold JTs, or 9Ts, and hit gut shot along w/ backdoor flush draw, there are alot of scenarios obviously in the game that would allow us to continue w/ a stronger holding... the flop previously mentioned could've come w/ a 9, this would give us 2 more outs, etc. But for arguments sake, lets assume the flush is your only out.

[kenberman]

Ed Millers book "Small Stakes Hold Em" has a section dedicated to questions like these. You should pick it up.

Basically, he says a backdoor flush draw is worth about 1.5 outs (he derives this from the frequency the draw will come in by the river). This is the figure I use to total up my outs, and weigh against the pot odds.

[elysium]

hi josh

most of these backdoor situations are disqualified before the bet reaches you. the number of opponents in the hand pre-flop, and whether or not the pre-flop was raised are a couple criteria you use to eject; the top card on board can crinkle, not having the correct 3 card straight is lethal, and on and on.

soon enough, the numbers and strategy will blend in for you. right now you need to think in terms of mucking that trash. instead, try to look at the strategics involved in a hand, and what the minimum requirements are for staying in the battle, then check to see if you've got them.

look at the battle, and then check to see if you have the weapons. don't check your weapons and look for a battle. the battle is in constant motion, and as you follow its ebb and flow, you risk being drawn in by the tide. you want a weapon for the battle, not a battle for the weapon.

you do not yet know what you need for the fight josh. next semester will find you posting a hand's action and field conditions, running the numbers if you will, and then asking what is needed to win. only then will you look at your cards. the pull of the sea of numbers can be very alluring once in the water, josh. if your boat is full of holes you want much more that a little backdoor to an oar.

i'm glad i reached you in time. nice chatting.