Probability of losing these hands - Gambling and Probability

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Probability of losing these hands

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07-03-2022 , 11:18 PM

DumbosTrunk

Verified Coach PLO5

Join Date: Apr 2017 Posts: 7,320

Hi all,

What is the aggregate probability of losing a 55/45, a 70/30, an 85/15, a 60/40, and a 40/60 (the last one on both runouts) in one session?

Thanks,
DT

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07-04-2022 , 03:26 PM

Didace

Carpal \'Tunnel

Join Date: Nov 2009 Posts: 19,879

Since it's all one session, 100%. If you mean something less than your lifetime, then we need to know how many hands in the session. But, at any future session, then it's 100% again.

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07-04-2022 , 05:04 PM

statmanhal

Pooh-Bah

Join Date: Jan 2009 Posts: 4,987

I think OP is asking for the probability of losing all 5 hands when you have the showdown odds for each.

Assuming the hands all go to showdown with the stated favorite odds, the probability you will lose all 5 hands is simply the product of all the lose probabilities, in this case,1.215%.

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07-04-2022 , 05:22 PM

DumbosTrunk

Verified Coach PLO5

Join Date: Apr 2017 Posts: 7,320

Quote:

Originally Posted by statmanhal

Thanks, you got it right - I was wondering how likely it was to lose as a favorite or slight dog in all these hands. I played these five hands over a 6-hour session and we were dealt maybe 200 hands.

But wait, if it's the product of the loss probabilities why would it be only 1.215%? Wouldn't it be lower?

Also, would you draw any conclusions about a game's integrity based on these results?

Last edited by DumbosTrunk; 07-04-2022 at 05:30 PM.

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07-04-2022 , 06:57 PM

statmanhal

Pooh-Bah

Join Date: Jan 2009 Posts: 4,987

Your right, it is lower as I left out one case. The chance of losing all 5 hands is 0.5%.
Sure, that's a low occurrence probability but that doesn't mean it will never happen.

Also, in some postings like this, the poster may have misremembered or didn't give all the facts. Note how I underlined the assumption of showdown for all five hands. If you lost any of the hands because you folded them, then all bets are off.

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07-04-2022 , 08:28 PM

heehaww

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Join Date: Aug 2011 Posts: 5,081

The chance of losing all 5 of those particular hands, factoring in the double-runout for the last one, is about 0.3%

But that's not the same as the chance of losing "a 55/45, a 70/30, an 85/15, a 60/40, and a 40/60...in one session"

The literal meaning of the question can't be answered because it depends on how people play, which affects the chance of even getting those matchups to begin with.

If OP only cares about the chance of losing them given that they occurred, we still need more info: in the rest of the session, was Hero involved in any similar matchups?

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07-04-2022 , 11:19 PM

DumbosTrunk

Verified Coach PLO5

Join Date: Apr 2017 Posts: 7,320

Quote:

Originally Posted by heehaww

I left out that I was also involved in one hand I won all in as a 60/40 favorite and the 55/45 was in fact a chop not a loss. Otherwise these are all the hands I played all in to showdown. I have given the postflop equities involved accurately. I appreciate the feedback. Given that the probability was quite remote, should I wonder whether I was being cheated? I am ordinarily a good winner in this game.

Last edited by DumbosTrunk; 07-04-2022 at 11:25 PM.

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07-05-2022 , 08:53 AM

Didace

Carpal \'Tunnel

Join Date: Nov 2009 Posts: 19,879

Quote:

Originally Posted by DumbosTrunk

Given that the probability was quite remote, should I wonder whether I was being cheated?

No. Like I said, it happens to everybody eventually. It would be stranger if you never had a day like that. Is there anything more that adds to your belief something might be going on?

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07-05-2022 , 02:35 PM

DumbosTrunk

Verified Coach PLO5

Join Date: Apr 2017 Posts: 7,320

Quote:

Originally Posted by Didace

No. Like I said, it happens to everybody eventually. It would be stranger if you never had a day like that. Is there anything more that adds to your belief something might be going on?

It’s a semi-private casino game and I lost most of these to the same player as a favorite pre and postflop. Thanks for everyone’s feedback. This was my single worst session so it got me thinking. Sounds like it was most likely just variance.

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07-05-2022 , 03:34 PM

#10

heehaww

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Join Date: Aug 2011 Posts: 5,081

Quote:

Originally Posted by DumbosTrunk

I left out that I was also involved in one hand I won all in as a 60/40 favorite and the 55/45 was in fact a chop not a loss.

The chance of losing a 70%, an 85%, at least one out of two 60%'s, and a double-run 40% is .3 * .15 * (1-.6^2) * .6^2 = 1%

More relevant is that you had a total of six pre-river all-ins and lost four. Ignoring chops, the chance of losing at least four with those equities is:

.45(.4*.4*.3 + .4*.4*.7*.15 + .4*.4*.7*.85*.36 + 2(.4*.6*.3*.15 + .4*.6*.3*.85*.36 + .4*.6*.7*.15*.36) + .6*.6*.3*.15*.36) +
.55(.4*.4*.3*.15 + .4*.4*.3*.85*.36 + .4*.4*.7*.15*.36 + 2*.4*.6*.3*.15*.36)

≈ 10.5%

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07-05-2022 , 06:49 PM

#11

DumbosTrunk

Verified Coach PLO5

Join Date: Apr 2017 Posts: 7,320

Quote:

Originally Posted by heehaww

Thank you! Brutal.

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