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# very elementary math question re. bluffing in 5CD

• Bronze
Joined: 14.01.2013
this question pertains to following up postdraw on a semi-bluff predraw: assume 30% of the time we have a hand to value-bet ; assume by betting we are offering our one opponent 3:1 pot odds ; if we want to bluff sometimes to get value from our value hands, and want to break even on our bluffs, then, following Sklansky, 25% of the hands we bet should be bluffs ; if, out of 10 hands, we bet 4, then we have the correct percentages ie. 3,or 30% of the 10, are for value and 1,or 25% of the 4 we bet, is for bluff. I see all this as correct, but I dont know how to generalize it to all potential bluffing situations of this kind. Possibly there are others like myself on this site who are mathematically challenged but still wish to play poker as correctly as possible. If someone knowledgable in very simple math could tell me in general how to, properly, get to this answer, it would be much appreciated.
• 3 replies
• Super Moderator
Super Moderator
Joined: 02.09.2010
Isn't it better to think in terms of ranges?

If 25% of the hands we play are "bluffs" then do we arbitrarily pick some time to just raise w/ absolute air?

If however we pick a range for a position, so that 3/4 of that range are > 50% equity, then the remainder (the 25% that are bluffs) have less than 50% equity, but will still win some of the time.

This doesn't consider that from time to time you will raise with a flush draw, for example.

Bluffing also works in reverse. For example, if you NEVER limp, you can't limp to induce a raise when you have a monster -- a pat flush eg.

So every so often I'll limp QQ from EP "just because". Even if I fold it w/o showing it, it tells other players I'll limp/fold.

I've been trying to construct such a range for the Button in 5-Card Draw.

If you raise a hand from the button, you have two players behind you.

The SB is getting 5:1, the BB is getting 2.5: 1 to call.

I read in an article that you can raise 99 from the BTN if you also hold AK

The lowest hand that fits this description is 99AK2.
There are 624036 hands that already have this beat.
-- approx 24%
Therefore, the chances that one or the other of them has us beat ALREADY is 48%, and about 6% of the time, they both do.

Not only that, but there is the draw to consider, and our chances of improving on the draw.
If we stick with the pair of 9s example,
We will improve 29% of the time, since we hold a pair.
We can guess what hands they hold by what they draw:
Assuming they both call
I break it down like so:
Draw 3: Pair, thus same chance to improve
Draw 2: Pair with kicker -- better chance to hit two pair (and likely a better one) but slightly worse chance to improve over all
Draw 2: Already has trips -- much less chance to improve, but we're already beat
Draw 2: Cathop flush draw -- don't worry, be happy
Draw 1: Two pair, we're already beat, but only 9% they'll improve
Draw 1: Flush or straight draw -- roughly 18% chance they'll improve.

Now let's say we DO improve...
Lots more decisions.

That's a pile of stuff to consider without even taking into account the tendencies of the people in the blinds -- do the fold a lot?
Call? 3Bet?

BTW, from the above, I concluded that I don't like opening 99AKx from the BTN unless the blinds fold a awful lot <== I consider it a bluff.

I know I didn't answer the question "how do I calculate a mathematically formula for how often to bluff?", but it's the best I can do.

Also, I'm pretty sure it isn't "very simple math" -- It took me over a week of putzing about with Excel and reference tables even to get the stuff above.

Finally, in limit games, the big blind is getting 2.5 : 1 to call ALWAYS, and the odds of improving a pair drawing 3 are 2.48:1

Fold equity is consequently quite low. You might think that they will fold any hand w/ no pair, but in that category are a whole mess of hands that will rise up and eat you for lunch -- flush draw, straight draw and so on.
If there is a raise and two callers ahead of the BB, he now has correct pot odds to call with those.

All the best,
--VS
• Bronze
Joined: 14.01.2013
Thank you for the response. All I was reallty asking was how to calculate what % (x) of your hands to play in total if you are going to play 30% of hands dealt (in this specific circumstance) plus 10% of the tolal ( 10% of x ). This must be simple, but being mathematically illiterate I cant figure it out. My question was posed in the context of bluffing postdraw optimally. And I do realize that trying to actually play 5cd "optimally", at least at the lower limits, is very much a money losing strategy. But, there is no money to be made in lmit 5cd anyways, and,this game being exponentially simpler than limit holdem, and the essential math required to play "optimally" much much simpler, so I have been trying to learn how to play poker through 5cd. I know for sure, after trying for a while, that learning to play holdem is plain silly (cost in time and effort ,given limit capacity, vs reward possible , given the expertise out there). But 5cd is perhaps the easiest poker game to learn learn how to play correctly. And,dispite what I said before and dispite your well-reasoned misgivings, I have found that trying to play "by the book" as best I can is in fact + ev at least in limit on stars .25-.50 and .50-1.00 . In the real world I have found opening on the btn with 88A and another paint to be profitable. And, by the way, in regard constructing opening ranges for the button, there is a lengthy post on another thread on this site with a weath of good information on this subject. Perhaps it was compiled and posted, but the value of the analyses is obvious .
• Super Moderator
Super Moderator
Joined: 02.09.2010
Can you provide a link to the other thread?
I'd love to read it.

In reply to your question:
In order to break even, your success rate must be:
The bet size divided by the pot + the bet.

Example:
PreDraw, you raise and one other player calls
We'll assume you have a flush draw, and we'll also assume that you will always lose if called.

The pot is 2.75 Big Bets (BB)
You bet 1 BB

If villain folds, you win 2.75
If he calls you lose 1

1/3.75 = .2666
To check:
If you win the pot 26.66 times out of 100 you won 73.333 -- Wooo Hooo
But you lost 1 BB 73.333 times, so you're dead even <sigh>

Anything better than that -- or if you hit your flush occasionally -- and it is all gravy.

All you need to remember is:
S = B/(P+B)
S is success rate to break even
P is Pot
B is Bet

Cheers,
--VS

***Disclaimer
I'm a maths fish, so if I screwed this up, we'll both learn something
(I think I've got it this time though, 'cuz I used Excel to check my calcs)