Every experienced bridge player I know – every experienced player, myself included – has had the same reaction when first encountering computer-generated deals: “What the **** is it with all these wild distributions and bizarre splits? This can’t be for real!”
The bad news: it is for real. They are actually truly random. All those hand-shuffled deals all those years, alas, were not.
The good news: it is for real. They are actually truly random. There are plenty of good statistical analyses to back that up.
Bridge differs from some other card games because the entire deck is dealt out, and the play of the hand tends to re-concentrate suit holdings. In rubber bridge for example, three spade tricks in a row to declarer generates a chunk of ten to twelve spade cards in the shuffle stack. Those spades are more likely to be evenly – rather than randomly – distributed in the next hand. Playing duplicate bridge, the chunks are smaller but they still exist; those spade cards are now in chunks of three in each hand. Or consider, for example, the KQJ-fifth of your trump suit that you play in sequence at duplicate. These create structured chunks of cards in the shuffle stack that don’t occur in, say, poker or cribbage.
Manual shuffling does not completely break up those chunks and sequences; they then are distributed evenly (not randomly) by dealing one card at a time to each hand in order. The resulting manually-shuffled hands thus have flatter distributions than statistically random deals.
Here’s a simple test you can do: How many times do you normally shuffle the cards before dealing? Okay… Take a fully-sorted deck – AKQJ… AKQJ… and so on – and shuffle it that many times. Now turn the deck face up and examine it.
Every time two cards appear still in their original sequence – the 6-5 of diamonds, say, or the K-Q of spades – is a flaw in your shuffle. Given the six of diamonds, the five should have a 1-in-4 chance (okay, 12-in-51 to be exact) of being in the same hand. Due to the flaws in your shuffle, they have a zero chance of being in the same hand on the next deal. Likewise for those sequenced cards that are now separated by only one or two positions in the stack. And if your shuffles are typical, you’ll also see some sequences of three-out-of-four (or worse!) in the same suit; these get distributed evenly rather than randomly.
For comparison, I am a truly horrible card shuffler. After my usual three shuffles, my deck contains anywhere from 10 to 15 flaws! My wife has an excellent riffle shuffle, learned from a professional dealer; she averages 1-2 obvious flaws after five shuffles. Five good shuffles, and still not a random deck! There is sound mathematical analysis that suggests it takes at least seven good shuffles to get a fully random deck, and that’s for casino-professional-grade riffle shuffles; shlubs like me need far far more. (If you try the test, feel free to reply to me with your results; discretion and anonymity assured).
So are you lamenting that those 3-3 splits aren’t coming in 40% of the time like they used to? Yeah, it’s a drag. But 36% is the probability for statistically random deals; 40% was an artifact of incomplete manual shuffling.
And finesses that now only work 50% of the time, instead of 51 or 52%? Yep, I’ve been through that. And the queen does not lie ahead of the king 53% of the time like it used to? Argh!
So... if you are appalled by these computer hand distributions: me too. I’ve been there. I feel your pain. But I will take truly random deals, hands down, every day of the week. Manually-shuffled hands don’t meet that standard. They sure were fun, but they sure weren’t random.
-- Ray
Better Bridge in 5 Minutes. Guaranteed! (or the next one is free)
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