WARNING: this is going to be an extremely long post, and it will deal entirely with poker and statistics. If these don’t interest you, I suggest going HERE to read a blog I posted earlier today with some mini-updates about my son. He’s the real reason most of your read this blog. Don’t read the whole thing and then complain that I wasted your time – I warned you.
So some of you may remember I tried a smaller version of this back in January of 2008. Basically, in a discussion with some buddies online, I made the hypothesis that Full Tilt Poker favors the bigstack in poker (while on FT, most people say it always favors the weak hand, but I disagree, saying it will only favor the weak hand if they are also the bigstack.) So I set out to test this by playing 100 tournaments (I ended up with 120 as my sample.) That produced almost 400 all-ins. I figure that’s a pretty good cross-section to test a theory. First off, some notes about the experiment:
- I tracked every all-in on a Word Document which can be downloaded here: www.esoderek.com/data/File/Poker Stats.doc. I’ve tried linking it three times and it’s not working for whatever reason. It should be pretty self-explanatory. Each tick is one all-in. If it is green, that means I was dominant. If it was red, then that means I was dominated. More on domination in a minute.
- I only tracked all-ins. I did not track severely crippling hands. Unless one (or more) people’s chips were all in the pot, I didn’t take note of it. Also, I didn’t take note of times when the chipstacks were exactly even (which was rare) and I didn’t keep track of hands that resulted in a split pot, even if it was a very lucky/unlucky series of cards that produced that split pot. Finally, I didn’t include pots where the chips were put all-in AFTER the river card was already out as there would be no chance for the computer to change the outcome.
- These numbers indicate when I was actually all-in, not intent. What I mean is this: if I had very few chips and got pocket Aces, I might slow-play them by only doing a small raise in order to get the most chips out of the hand. I may know FULL WELL that I will push all in no matter what the flop is, but I do not consider it an all-in until I actually commit the chips. Even if this means that after the flop I might be behind – if that’s the case, it went down on my sheet as a behind hand, even if I was mentally committed while I was ahead.
- Domination – There is no numerical definition of “domination” that I could find online other than ‘being well ahead/behind on a hand’, so I quantify it as 75% ahead or behind. This is a pretty significant number. For instance, AK is NOT dominating AJ. It’s 70%/30% or so. So the hands that are colored are pretty significant favorites. Also, this number is at the time of the all in. So if I don’t go all-in until the turn, the chances of it being a hand with some type of domination are much higher than pre-flop, as there’s only one card left to come out.
- As far as the terms “ahead” and “behind”, I used the statistical likelihood of winning, not actual. The website that I used was this one: http://www.cardplayer.com/poker_odds/texas_holdem. After each all in, I’d plug the exact cards of the participants in at the time of the all-in. If I had a greater percentage to win than the opponent, I was ahead. If that percentage was greater than 75%, I was dominating. If I had a smaller percentage than my opponent, I was behind, and if my opponent had a great than 75% of winning, I was dominated. (NOTE: I realize that this doesn’t take into account other people’s cards, as that could easily affect the numbers. I figured I had to do it this way since I can’t see mucked cards. The way I saw it – I’ll probably get hurt by others’ cards as often as I’d get helped, so it would even out.)
- I also tried to do this with multiple-people as well, not just heads up. Pretty much, if more than two people are in the hand, it’s almost impossible to be dominant, as there are usually too many outs to keep you over 75%. It got confusing once you had to deal with two other people, who was ahead in chips, and how their percentage was in comparison to yours. Suffice to say, I did my best and these did not account for many of the all-ins. I guess my point is – there is an possibility of error of + or – a couple of percent.
Anyway, onto the results:
While this doesn’t get to my theory yet, I figure it was important to know how I did during my overall 120 tournaments. If it was a particularly bad stretch, for instance, the numbers could be chalked off to a bad streak. The first half of the tournament, I had a very bad slide, but made up nearly all of it during the second half. Overall, I was about even financially, having lost maybe $10 or $15.
In terms of overall all-ins, I was actually ahead. I won more than I lost. I had 213 wins vs. 184 losses (53.7% winning percentage). This accounts for ALL all-ins, including mine or if I was calling someone else’s. That’s not bad. I just think that’s important to know going on.
Bigstack vs. Smallstack
I’ll start off with the whole ball of wax here. Here is the stat that tests my theory. And here are the numbers. When I was a bigstack (whether it was my all-in or someone else’s), my record was 112 wins and 66 losses (a 62.9% winning percentage.) That’s pretty impressive, to be sure. When I was the smallstack, my record was a less impressive 92 wins and 116 losses (44.2% winning percentage.)
So that’s it, right? My point is proved? Well, yes, but I wasn’t satisfied with that. I demonstrated that as a bigstack, I won considerably more than I lost, which is what I set out to do. But why? And where did it happen? I broke it down even further.
First, I tested out how often I was ahead vs. behind for each circumstance (bigstack and smallstack). Here’s what shook out.
When I was the bigstack and ahead (better percentage than my opponent): 93 wins, 30 losses (75.6%)
Bigstack but behind: 19 wins 36 losses (34.5%)
This makes sense. I will win more when I’m ahead than when I’m behind, no matter how many chips I have. But look at how much those winning percentages drop when I’m the smallstack.
Smallstack and ahead: 63 wins 44 losses (58.9%)
Smallstack but behind: 28 wins 73 losses (26.7%)
When I was the smallstack, BOTH percentages were almost exactly a quarter worse. That, in my mind, is significant. So I was trying to figure out possible causes for this. Sure, when you don’t have many chips, you will push with weaker hands (maybe a K10 or something like that) than when you’re calling as a bigstack. But that couldn’t really account for everything. Personally, I try never to go below 5 big blinds without pushing all in, so I usually have some ammunition when I do push. Therefore, it gives me a little extra time to find a much better hand (a pocket pair or at least KQ suited) However, I was noticing that many times I would be the smallstack and pair the top card on the flop. I’d push only to be against a slow-played pair of Ks or a miracle set. It was uncanny how many times I had a GOOD hand as a smallstack and would be dominated. So I decided to run the #s to see if I was more dominant as a bigstack than a smallstack.
Domination – Frequency
First off, to see how often I was either dominant or dominated based on my chipstacks. The results were slightly different than I expected.
As the bigstack, I was dominating 48 of my 119 calls (40.3%). As a smallstack, I was dominating 38 of my 100 (38%).
As a bigstack, I was dominated 27 of my 53 all-ins (50.9%). As a smallstack, I was dominated 36 of my 94 (38.3%).
I had expected no real difference here, as in theory you should have a dominant position based on your play and your read, not your chips. (By this I mean that I find it easier to read another player having a MONSTER hand vs. having a pretty good hand based solely on his betting.) This mostly held true except for one thing. I realized when I am calling an all-in, it is much more likely that I am either WAY ahead or WAY behind. Perhaps I am too loose a player when I have chips. But aside from that one stat, it goes to show that there isn’t a great disparity between the frequency of domination, regardless of chipstack. So how did those dominating/dominated hands hold out?
Domination Win Percentage
One expects that if you are more than a 75% favorite to win a hand, you should almost always (but not always) win. Well, that’s true.
As bigstack when I was dominating, I won 43 and lost only 9 (82.7%)
As smallstack when I was dominating, I won 31 and lost 9 (77.5%)
As bigstack when I was dominated, I won 6 and lost 21 (22.2%)
As smallstack when I was dominated, I won 7 but lost 31 (18.4%)
Again, it shows pretty conclusively that regardless of the overall strength of my hand, I tended to do a little better when I was bigstack than when I was the smallstack. So far, I was yet to receive a single stat that disproved my theory. My point in being this thorough was to eliminate a simple factor, such as I tended to push too easily when I was low on chips… etc.
I think it should be noted that I may not be the luckiest person at online poker. As you know, I won more all-ins than I lost – how could I then possibly be down money, although not much? Well, simple – the timing of my won hands wasn’t as good as the timing of my losses (or possibly I would get worse beats on bigger-money tournaments.) Also, it should be noted that I should have won more than I did. Note:
I was strong (having the better hand) 230 times out of the 386 all-ins (59.6%). So I should have won around 3/5s of the pots I was in, right? No. Remember in the beginning my actual winning percentage was only 53.7%. Six percent doesn’t sound like alot, but it is when it’s in the negatives.
This whole experiment came about because a friend of mine has done VERY well on the site. So it made me wonder – I bet he’s a bigstack more than I was, so he wouldn’t notice these bad beats as much. After all, every poker player remembers those hands where his pocket Qs lose to 5 6 offsuit, but how many poker players remember when their much stronger hand goes on to win? Not many. So I compiled one last stat:
I was the bigstack in 178 all-hands. (Of those, I was strong 69.1% of the time)
I pushed all-in in 208 hands. (Of those, I was strong 51.4% of the time – still more than half!!!)
I’d be curious to see if my friend who has done well on Full-Tilt was bigstack more than smallstack during an all-in. It might account for his contentedness with the site.
The results were pretty much exactly what I’d hoped for. They’re not astronomically biased, which is what some naysayers would want to see (where the bigstack wins 80% of the time), but if that were the case, people would catch on and nobody would put money into the site. In fact, if I add my 120 tournament numbers to the numbers when I first kept track, the results are the even more indicative of my point while still not being obvious: 165 wins and 98 losses as the bigstack (62.7%) vs 109 wins and 164 losses as smallstack (40%). I further think they do this for two reasons:
1) Online, people can sign up for a tournament and not actually play in it. Even though they get chipped off, they could still catch lucky cards on their eventual all-ins and sneak into the cash. By tweaking the numbers a bit, the site all but assures that no vacant player will cash, because they will always be the smallstack at the time of their all-in.
2) This speeds the game up and allows more games to be played, making more money for the site.
An interesting side-effect of this experiment was that I saw how my actual play changed. This happened in two major ways.
> I would use my chipstack as the final decision-maker on a hand I was unsure about. If I had a large chip lead and had just a drawing hand (A10) and someone made a sizeable all-in, even if I pegged myself as an underdog (thinking they had Js or something) I would call, assuming I would suck them out. Conversely, if I didn’t have many chips and I had 7s and a bigstack raised heavily before me, I’d fold, thinking he had 8s or 9s which would crush me. This worked to my advantage quite a bit.
> What actually might have hurt my game was I would tend to overplay hands when I had a hunch I was strong but they had many outs. If I suspected someone to have a flush draw on the flop and I had top pair, I’d push MUCH harder than I normally would, especially if I was down in chips. This way, if they called (which people always do on flush draws – it boggles my mind), I could say I was strong when I went all-in, even if I suspected I would lose. That’s probably not a good strategy to have in poker. That’s not playing smart poker, that’s giving yourself a reason to complain when you lose. Thankfully, it doesn’t seem to have carried over in my real game poker.
Anyway, if you read all of this, you’re a very silly person. Anyway, I stick by my assertion that Full Tilt Poker slightly favors bigstacks. And once I start playing again, hopefully it will be to break that streak of 5 straight suckouts that I am currently riding (and the reason for my poker haitus).