odds of flopping a set 3 straight hands in omaha h/l and not winning any of them?

I don't really keep track, but it's fairly common for me to fold 3 orbits, and I estimate my stats as being 17/13 or so.

I'd day I fold 3 orbits at least once or twice a week.

Thread will now officially live forever; I just added it to the best of LLSNL sticky.

Well done throughout, sir.

If you voluntarily put money in the pot 17% of the time, then folding 3 straight orbits is folding 27 straight hands (assuming 9 handed), odds of which would be (.83)^27, which comes out to .0065, or .65%. So 0.65% of the time you fold 27 hands in a row. Maybe bip could explain what that means more since I'm having a tough time deciding if you have to look at sets of 27 hands that do not overlap each other, or if the count simply starts over every time you play a hand.

24-27 folds, actually.

and I would think it is any 27 hand streak of folds

I'll try.

We have to make assumptions to simplify and get an approximation (at least I do).

Assume:
-We only are dealt 1 pair
-Assume the random pair on average is 77 (mid way between 22 ad AA)
-Assume we are playing any hand with a pair and other cards are irrelevant.
-Playing with random playable ranges of villains 3 handed I get approximate winning percentage (hi) for a set of 7s in the neighborhood of 50% (obv this varies some depending on ranges but this will do) so the losing percentage is 50%.
-we are ignoring holding our own blockers which obv is a possibility that would make the hand unplayable

Odds of being dealt some pair in your 4 cards:
3/51+6/50+9/47=.35 or 35%

Odds of flopping a set
2/48+2/47+2/46= .13 or 13%

Odds of losing = 50%

So odds of being dealt a pair then flopping a set and losing are:
.35*.13*.50 = .0227 or 2.2%

Odds of this happening 3 times in succession:
.0227*.0227*.0227= .00000027 or .000027%

In theory... in practice it's probably 50% or so.

cAm teh close enough for government work

Sounds like a rough session

Chip - I would love to answer precisely, but this question is not specific enough and it would heavily depend on opponent behavior (folding, betting, etc.).

However, qualitatively - the odds are probably not that tremendously long... losing with the set is relatively easy in this case, it would be the flopping three in a row which would be the longer odds.


-------

To flop 3 sets in a row in Omaha (if you played just 3 hands for the session & assuming saw flop with every hand)

52*51*50*49/4! hand combos = 270,725

Double paired hands = XXYY
13 ranks XX * 12 ranks YY / 2 orders * 4*3/2 X combos * 4*3/2 Y combos =
78*6*6 = 2,808 double paired hands

To hit a set with a double pair hand:
48*47*46/3! flops = 17,296 flops
Flops that contain one X and no Y(and no pair for flopped FH)
= 2 Xs left * (44 * 40 / 2 orders) = 1,760

(same number for "include one Y and no X")
= 1,760
Flops that contain X and Y (and no quads)
= 2 * 2 * 44 = 176

Odds to flop set with double paired hand
(note: this may also include boards where you also flop a flush)
= (1760 + 1760 + 176) / 17,296 = 21.37%

Odds to get a double paired hand and to flop a set =
2,808 / 270,725 * 3,696 / 17,296 = 0.2216% ~= 1 in 451

Single paired hands = XXYZ
13 ranks for XX * (12 ranks Y* 11 ranksZ / 2 orders * 4 suits Y * 4 suits Z) * 4*3/2 combos XX =
13*6*48*44/2 = 82,368 single paired hands


To hit a set with a single pair hand:
48*47*46/3! flops = 17,296 flops
(without pairing the board)

This is a little tricky because of your YZ cards in XXYZ hand:

Flop can be XYZ, XYA, XZA, XAB

XYZ = 2 * 3 * 3 = 18
XYA or XZA = 2 * 6 * 40 = 480
XAB = 2 * 40 * 36 / 2 = 1440

(1440 + 480 + 18) / 17,296 = 11.2% ~= 1 in 8.92

Odds to get a single paired hand and to flop a set =
82,368 / 270,725 * 1938/17,926 = 3.41% ~= 1 in 29.3

So overall odds of being dealt a paired hand in Omaha followed by flopping a set in given hand =
(3.41% + 0.2216%)^3 = 1 in 20,893


.. and to address "losing with a set in Omaha" - I almost feel it would be more amazing to win with a flopped set in an Omaha H/L game

We could get an approximation by making this assumption that any improvement on the hand (a FH or quads) will win you the pot, while any non-improvement will result in a loss. While clearly not perfect (sometimes the set wins, sometimes the FH loses, etc)- I will call it good enough...

(I am also going to pretend your other two cards do not exist and ignore the double paired situations..etc.. at this point we are approximating very inaccurately anyways)

You must miss 7 turn "outs" and then 10 river "outs" to lose =
40/47 * 36/46 = 66.6% unimproved

So you lose 66.6% of the time and win 33.4% of the time in my simplified scenario. Compound the odds above (about flopping set) with the odds to lose that hand @ 66.6% =

(66.6%) ^ 3 * 1/20,893 = 1 in 70,726

wow - that sucks Chip.

(last note: again this is as if you only played 3 hands and the result was as noted... if you played 150 hands that session you would have ~150X the odds of this happening, so you get into the 1 in several hundred range)

^^^^
dude is wicked smart

yeah happened to a friend sunday night. gets up from the table, takes like a 20-minute break. rebuys and goes broke within 3 hands, flopping sets on all 3. she runs worse than anyone i've ever seen.

My casino has a high hand jackpot, and everyone always thinks they are going to get beat by a better hand, and therefore is willing to sell the action on the high hand. (Essentially insurance.) How would I go about figuring out how likely a hand is to be beat based on hand strength, time left in the promotional period, and number of tables running?

Do you have to use both cards?

Yes.
But quads dont have to be PP's, your kicker has to tie or play.

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Ok - those details do make a difference - thanks. I will give you a table of what each hand is worth per time*players left.

Rule of thumb when laying odds to general people is to offer them 1/2 what it is worth. You might be able to stretch that even more (~1/3). Too much and it becomes obvious and people will refuse your offers (even if fair) just because they believe you are ripping them. 1/2 seems to balance pretty well for them not noticing the advantage.

One more question - does the hand have to reach showdown?

i.e. - opponent folds on turn where you made a royal flush... can you still show the hand to collect?

No, it does not have to go to showdown.
But it has to go to atleast the flop.
So in the unlikely chance that no one has declared a high hand at 5:59, AA preflop does not count.
Also there is a minimal pot size.
$20, doubt that has much affect overall.

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Bip

While doing this could you do it with the rule that quads must use both hole cards also?

Our casino does this also quads minimum board kicker plays. Periods are 4 hrs long.

Can do cAmm.

Two more assumptions:
-If you tie a hand, too bad - first to get the hand wins 100%
-Kickers count for topping a hand (AAAA9 will take the lead from AAAA8)

In our casino ties chop at the end of the 4 hour high hand period but it's pretty rare. And yes kickers play (they are always board cards obv.)

Alright I've got a good one for you

Last night I'm playing and I have JsTs. I call a raise out of the blinds and the flop comes gin, KcQs9s. Go back and forth against a guy and we get all-in. He has KdKh. I jokingly say, just don't hit your quads. Sure enough, the turn is Ks. And of course, the river spikes me a royal with As. Pretty -EV of me to be playing in a room that doesn't have a BBJ btw.

Anywho, about 2 hours later, I raise with KcTc and get two calls. Flop comes QcJcXs. I bet and get called. Turn comes Ad giving me nut straight. End up getting all-in against a guy who, wouldn't you know it, has AsAh. So the Ace of clubs to give me the royal is still in the deck. This time, I'm not so lucky and it comes out a blank. At least the guy didn't boat up though.

So my question is, what would be the odds of hitting two royal flush over quads hands within, let's say, a span of 100 hands?

My open questions:
1) Omaha vs holdem - still working on this
2) High Hand values per rank and time left
3) peck's question above.

1 - is still a while off (I need time at home to program, has not happened in a while)
2 - I will try to answer this weekend (also writing a program, but it is much simpler)
3 - I have answered a very similar question ITT before (when I did the BBJ hand equities) - if I get a chance, I will re-apply that data to answer

What are the odds of not getting AA, KK or QQ over four straight sessions - total of about 20 hours?

Bip, I don't get odds for the life of me.

1. What direct odds am I getting on a call if $200 is in the pot and villain bets $100.
What if villain bets $150. What if villain bets.$200


If the pot is $160 on the river and villain bets $50 how often do I have to be good

If there is $100 in the pot on the flop and I have a flush draw (20% chance to hit on the turn) and villain bets $80, how much do I need to make after I make my flush to make this profitable?


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edit: i thought i found some outs. nvm

five straight sessions - 23 hours.

24:1...ldo should have played one more hour and asked "what are the odds of waiting 24 hours for KK and running into AA"?