How to get Lucky

Have you ever noticed how some people just seem to be lucky? The reason for this is twofold, firstly the Barnum Effect (people tend to remember positive results) and secondly these 'lucky' people set them selves up to win against the odds. What I mean by this second point is that some people are good at recognising when they are no longer able to win in the conventional way and so adapt their play style to favour a much less common victory condition.

In Magic: TheGathering (yes another Magic example) we often refer to someone getting lucky and drawing the card they need as 'top decking'. People who are considered good at top decking are actually good at adapting their play style to maximise the number of cards in their deck that can win them the game. Here's an example from a game I played, I was loosing and my opponent had just declared all his creatures as attackers and while the damage that they would deal to me wouldn't make me lose it would mean that I would lose on their next turn, I had one card in hand which was a removal spell. Now you might think that I should destroy the largest of the attacking creatures, but in my view that would only mean I die in two turns instead of one, also I know that there is a creature in my deck that if drawn when they have no blocker will win me the game, so I decide to take the damage. In their second main phase my opponent casts a blocker and goes to end the turn, at this point I use my removal spell to get rid of the blocker. Now because I believe in top decking with style, I untapped my land drew the top card of my library and placed it face down on the table without looking at it, I then announced the creature that would win me the game, tapped the appropriate amount of mana and turned the card over revealing the named creature. While I didn't do very well in that tournament, my game was the only one people still remembered a month later.

So did I get lucky? Well yes and no, while the chance of me drawing the required creature was about one in twenty had I not saved the kill spell for the blocker my chance of winning was zero. It was this recognising a way to win and adapting my play style to it that actually won me the game. Let's have another example this time for Cribbage.

It is your opponents crib, they are 4 points from the end and you are 15 points away. You are dealt a hand of A, 4, 6, 6, 10, 10 (the ace and 4 are not suited) and now have to decide which two cards to discard to the crib. Because maths is fun, I can tell that the average points value for the possible hands are:

A, 4, 10, 10: 7.913

6, 6, 10, 10: 5.217

A, 4, 6, 6: 4.696

A, 4, 6, 10: 4.261

4, 6, 6, 10: 4.087

4, 6, 10, 10: 3.347

So if all we want to do is maximise the number of points we get we should keep the A, 4, 10, 10 hand. However, the most this hand could score is 12 (an A, 4, or 10 as the starter) meaning that we would have to score three points during the play to have any chance of winning, which is not very likely as we have to lead. On the other hand the 4, 6, 6, 10 has a two in twenty three chance of being worth 14 points (a five being revealed as the starter) and in this case we would only need to get one point during the pay to win. So the way I view the situation is do you want to definitely lose but keep the margin as small as possible, or take the gamble and either lose by a larger margin or win? So once again we will have had to 'get lucky', but before we can do that we have to identify that our path to victory involves keeping the hand with the second worst average return, and not the one that you would normally want to keep.