Poker: they always get there on the river
I was playing a game of online poker recently with friends, for low stakes. A few of the players were strongly of the view that the online app is biased in favour of the player on a draw. The draw always seemed to hit its magic card on the river. While this is just a riff on the ‘this app is rigged’ school of thought, I will try to explain why this perception feels true. I’ll also pull some stats from that night to confirm whether it was true that one evening.
I’ve blogged about this before — see ‘fooled by randomness, are online poker sites rigged?’, mainly because I know quite a bit more about probability than poker! I’m sticking to my knitting, as they say. I won’t rehash all the arguments made there. A key one is that online is poker is played faster than live poker, so unlikely outcomes occur more frequently. In the course of a 100–150 hand evening someone is bound to get very lucky (and someone else will get unlucky, naturally).
Another key point for me is that I can’t see what incentive a site like pokerrrr has to bias its random number generator. Does the happiness of the player who makes their straight really exceed the unhappiness of the player who just had their 2 pairs overtaken, for a net utility gain to the table? I’m not convinced.
My new thought on the topic, rather obvious in retrospect, is that we will indeed see a disproportion number of flushes and straights at showdown on the river. Let’s say we have 10 situations in the course of a night where there are two players who have made it to the turn, one with a made hand and the other with a flush draw. Bet. Call. We go to the river.
The player with the draw has 9 outs to make their flush, which has a probability of approximately 9 * 2% = 18% of occurring. So on average in 2 of those 10 situations the flush gets there on the river. Now the point is we are almost guaranteed to see those 2 hands at showdown. Both players have good hands.
In the other 8 situations, however, we won’t see the busted flush draw - apart from the occasional failed bluff. So it does indeed appear like ‘they always get there on the river’. This is also why some players can simultaneously complain that their draws never come home and that they also keep getting sucked out on. The app is both rigged and is out to get them!
To see how this actually panned out in my recent online session, I laboriously looked through the 106 hands played that night. 106 hands. 71 rivers. 41 showdowns. 10 draws that hit on the river.
71 hands (67%) going all the way to the river is an absurdly high percentage: my poker group are the loose and splashy ‘take it to the river’ types. But that’s an aside. Of these 71 hands, in 41 hands there was a showdown while in the other 30 hands it went bet/fold and we did not get to see the players’ cards.
In 10 hands the player who was behind at the turn went on to win at showdown. Is this a lot or a little? It certainly feels like a lot, especially if you’re a player who got sucked out on 6 or 7 times in the course of the night! Often they held the stronger hand from the flop. The app (not to mention the World) is self-evidently against them.
As a percentage of the 41 showdown hands, 10 is also a lot. Only the best combo draws have odds of coming home of 25% with just 1 card to come. Note I am including hands that made 2 pair, trips and full houses, which only have 3–4 outs. That said, we are talking only 1 session of poker. Play 41 draws repeatedly twice a week for a year, and you would expect to see 10 of them come home relatively often.
But remember that we actually had 71 hands that went to the river. If every hand had someone on a flush draw at the turn, we would expect to see 14 (~20%) of those draws come home on the river. Now 10 suck outs actually looks like reasonable, a modest number even.
106 hands. 71 rivers. 41 showdowns. 10 draws that hit. We need to compare the 10 successful draws with the 71 rivers, not the 41 showdowns.
Looking back at the number of numbers in this blog, I will quote a good friend of mine, “To be honest, I’m not a statistics player really, I’ve learned a fair bit over the years but still play badly”. Fair enough, and he’s being modest. I’m not sure he will read this far. I predict this topic will come up again.
If you did read this far, thank you and good luck at the tables.