My Allin Prelop Results - Statistically Relevant?

[C M Burns]

Now that i've played with this idea some, i've found that you do not really nee that many hands to have a strong degree of statistical relevance. You should be able to anylise such a problem using the binomial distrobution. (I found a good site to do clacs http://ic.net/~jnbohr/java/CdfDemoMain.html) What you are basically doing is a series of "experiments" with a known expected outcome. The only problem is that your expected result changes with each trial, I don't know enough to figure how much of an effect this has.

But your problem is basically the same as the standard biased coin example, e.g how do u tell if it is biased. So lets say you toss it 100 times and get 75 heads is it biased. you can't really "prove" it only give a degree of likeyhood of the result and say any thing below a cirtain value is "proof". What we can calculate using the binomial distrobution is over and infinite set of 100 flips, what % would have 75 or more heads. you get a probability of far less than 1% (.99999 reversed). Generally in "science" anytime you get a result that is likley to have occured by chance less than 5% of the time it is reamed "significant" so this would be a very biased coin.

Now for the poker hands (you lost 38/78) if you were a 60% favorite on average you would expect this about 5% of the time, unlikley but considering how often these hands come up something you will see from time to time.

What if out of 100 hands where you were a .6 favorite, but only won .5, now you are out around 2% (out of all the sets of 100 of these hands)I'd say you would have to get bellow 1% to be suspicious. you could get this if you only won 50/100 hands where you were a .67 favorite, so not outside the realm of testing.

But again I am not quite sure how the fact that you are averaging over different expected probabilities factors in, and also you are selecting specific hands non randomly.

You could cirtatinly do this where you had the same expected win rate like a coin flip hand where you were the pair, with about a .52 chance to win. if out of 100 hands you are losing more than 60 you might want to be suspicious. for example you would expect to lose 65/100 1 out of 5000 sets of 100 of these hands, or at least 500000 hands of small pair head up vs. 2 overs.

well that enough thinking anyone who knows more feel free to correct me.

[Utah]

Cool. Thanks for the site. If I am using this correctly, it tells me that my results have a huge statistical relevance as the results fall well below 1 percent.

Results for favorable Allins: .009
Results for Unfavorable Allins: .15
Overall: 4.99E-4

My guess is that the actual probability of each bet would only sku the results slightly.

Also, I started tracking these results after a long series of improbable losses, so the real results of the last couple of hundred allins could even be worse.

[DaffyDuck]

Should you be concerned that you're a dog 1/3 of the time when you're all-in? I'd like to know if this is normal for a good player. I haven't tracked it so I don't know but this seems like too high of a percentage to be all-in when you're not favored.

Thanks.

[FloppedFlush]

Exactly. It not only depends whether you have an advantage or not, but also how big your advantage is.

If most of these hands in your sample were middle pocket pairs, then the numbers are pretty much exactly what you would expect. You're either a small favorite (against two overcards, winning about 54% of the time) or a big underdog (against a bigger pocket pair, winning about 19% of the time).

[Utah]

That is a good question. However, my results could be skewed by a lot of things - e.g. The number of times I am forced in with a small stack.

That being said, it would be important to add in the number of times I push in and dont get called. I will push in a lot to take the pot.