View Full Version : What are odds of this kind of Bad Beat Streak?

11-08-2002, 06:24 PM
Without going into specifics (although I know you all are dying to read a post full of 20 bad beat stories), I'm curious how to solve this simple problem:

Last night I endured a nightmarish streak of bad beats. I lost 22 out of 24 hands in which I was a 3-1 favortie or better on the flop (HEADS-UP EVERTYTIME!!!!). Now, I think I know how to figure out what the odds are of losing 22 of 22 hands in this situation, but I forget how to calculate losing 22 of 24. Let's say, for simplicity's sake, that I was a 3-1 favorite on all the hands--the truth is I was closer to 80%, even up to 86% after the flop in a few of these hands--argh, talk about tilt, I vaguely remember telling one player how much I'd love to shove my AQ up his *** /forums/images/icons/mad.gif . But, again, to simplify things, let's just say I was a 3-1 favorite. What are the odds that a 3-1 favorite will lose 22 of 24 times? Thanks in advance.

11-08-2002, 07:54 PM
I believe you want to know the probability that you lose 22 or more times given 24 plays where you were a 3-1 favorite.

I believe this will equal:

Summation i = 0 to i = 2 for the following:

.75^i * .25^(24-i)

Which is an extremely small number which leads me to believe one of the following:

1) You were not a 3-1 favorite (perhaps you calculated your odds incorrectly).
2) You are not being completely honest.
3) I am simply wrong in my above calculation, thereby making whatever I said to be invalid.

Blasting off,

11-08-2002, 08:21 PM
1) Plugged in ALL the hands into twodimes, so I assume the odds are calculated correctly. A handful of 60-65%, majority between 75-80%, and a couple over 86%. So I just kind of figuring 75 for a roundabout average.

2) After 12 or so of these beats, my buddy, who was at the table with me, and I started writing them down in order to run them at twodimes. So, I feel I'm being fairly honest. Although 4 or 5 hands may have been 3 handed. And perhaps 2 were 4 handed? Not sure. But huge majority were heads up after flop.

3) It ain't my place to question your numbers. Thanks.

11-08-2002, 10:55 PM
You also need to incorporate the "choose function", i.e. the number of different orderings of the i wins and 24-i losses. Then you end up with the binomial formula. This would give an approximation to the probability, but since the probability of winning changes on each hand, it wouldn't be exact. Also, you have to be pretty careful with these calculations for many reasons. For example, they weren't all heads up, it was probably more than 24 hands, etc. Especially if it "feels like 22/24". Also, it's very, very, very, unlikely that anonymous averaged an 80% favourite in those 24 hands. Very, very, very unlikely.

11-09-2002, 01:32 AM
No, of course it wasn't 24 hands in a row. This was over the course of maybe 3 hrs. I was getting incredible starting hands for this period of time, hitting the flop hard, and getting sucked out on on the river. Now, of course there were a few hands during this time in which I wasn't a 75% favorite (hands in which i was a dog, hands in which I mucked on the flop, on the turn, on the river). But I'm only interested in the number of hands in which I saw the flop, was a huge favorite (average 75%), and got sucked out on in inhumane ways. There were 22 of these, and 2 in which I saw the showdown and won--the only 2 pots I won during this 3 hr period. The hands that began multi-way all became heads-up after the flop. Anyway, to answer the previous posters concerns, this is not 24 hands in a row. That would be impossible. I find it hard to believe I even saw the flop 24 times in 3 hrs. But, as I say, it seemed as though I was getting one monster starting hand after another. Had pocket Aces 5 times. Pocket Queens twice, Kings Once, Jacks twice, Tens 3 times. AQ 3 times. AK 3 times. Lost flopped sets to flushes and runner runner flushes w/o filling up/ Lost flopped top-2 pair to runner-runner str8s, etc. You know, imagine your last 2 months worht of bad beats, occuring in one 3 hr period. Anyway, I'm just concerned with the probability of losing 22 hands (or more) out of 24, in which the player is a 75% favorite. I appreciate the help.

11-09-2002, 01:39 AM
Right, the odds of 22 or more losses out of 24 is the sum of exactly 22,23, and 24 losses, which is the same as the sum of exactly 0, 1 and 2 wins. This is:

sum[i=0 to 2]C(24,i)*.75^i*.25^(24-i) =

.25^24 + 24(.75)(.25)^23 + (24*23/2)(.75)^2(.25)^22

= 9.0878x10^-12 = 1 in 110 BILLION

BTW, I think the Brits call a billion a trillion, right Lori?

11-09-2002, 06:19 AM
Doh! I actually knew that. I rushed, but it was my fault. I take the blame.

Thanks for the correction!

Crash Landed,

11-09-2002, 07:10 AM
You wrote:
"Anyway, I'm just concerned with the probability of losing 22 hands (or more) out of 24, in which the player is a 75% favorite."
Okay, whatever gets you through the night. Just know that this probability is WAY WAY WAY WAY WAY WAY smaller than the probability of whatever bad run happened to you happening.

11-09-2002, 05:53 PM
yes, 110 trillion i got as well.

So i guess i don't believe the exact information behind it.

but if you were allin or played full way through 24 hands, the chance of winning between 0 and 2 is 1 in 110 trillion.

Hopefully your luck will turn.

11-09-2002, 11:35 PM

11-09-2002, 11:51 PM
chance that in 24 trials exactly 22 times an event of prob .25 will occur is 8.82494E-12 (using the excel COMBIN function)

I hope you believe that this happened to you and then i hope u come play in my game -- this is about the chance that u r not deluding urself.


11-10-2002, 02:26 AM
No offense, but what exactly are you looking to gain out of learning this number? If you write down the probability of getting that whooped like this by Lady Luck, will your local card room give you a partial refund?

And by the way, the number is a very small one. Can you now sleep better at night?