Ice Cold Decks
5 Oct 2009
Any idiot can stack a cold deck to trick an opponent in Texas Hold'em Poker into losing all his chips. However usually the player on the right of the dealer cuts the deck, which means the cheater must swap the deck after this point, which makes it much harder to do subtly.
I do not condone cheating in poker, it is immoral, dangerous and often illegal, but out of curiosity I was wondering if it is possible to stack a deck so that no matter which way it is cut, the winning hand is always dealt to the dealer. This would be fun to use as a magic trick, to be able to consistently predict the winning hand. I was skeptical at first, but after running a hastily written script for about half an hour I found such a deck for 2 player heads up:
Give it a go: stack a deck like this (so the 10 of diamonds is on the top of the deck), cut it in any way, deal cards to two players in the usual fashion, deal the community cards (don't forget the burned cards), and you will find that the dealer always wins.
After this, I got wondering, is it possible to do this with 3 players? A few speed improvements to the script and I got just that:
And 4 players! Though this one took the computer about 6 hours to find:
I've tried searching for a 5 player deck, but at the moment the heuristic has only
found one where the dealer wins 50/52 of the possible cuts. My belief is that this
should be possible even up to 9 players, the reason being there are 52! = 8.1*10^67
different possible decks, and assuming the winning hand for any cut is random
then the probability that any given permutation has all 52 different cuts giving the
dealer the winning hand is 1/9^52 = 2.4^-50. This means there
should be a vast number of such decks, of course this overlooks the fact that the
winners from different cuts are highly dependent on each other, but I'm not sure
that is enough of a restraint to make such decks non-existent.
Can anybody out there find decks such as these for 5 or more players? Send me a message on the contact page if you do, and I'll update this page with full credit to the discoverer. The simulation I wrote can be run in a web page here, it's a chaotic mess (why not if it ain't ever gonna be production code?), it might help with ideas.
Some more decks where a player other than the dealer wins for all cuts are below.
2 players, small blind always wins:
3 players, small blind always wins:
3 players, big blind always wins:
4 players, small blind always wins:
Update 28/12/09 - 4 players, big blind always wins:
4 players, "under the gun" always wins:
This "magic trick" has been featured on Scam School.