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Statistics on trumps splits in BBO

Hello all,

Since the bridge clubs have closed due to the pandemic, I've played about 1000 hands on BBO. On each hand, I noted the trumps split on BBO, assuming the side declaring is the one having the most HCP or, if both sides have 20 points, the side that holds the biggest fit, or the most spades if both sides have equivalent fits. Fellow bridge players tell me they have the "feeling" that, for example, 4-1 splits are more frequent than they should be, and indeed, my manual compilation gave the following results:

For 8-cards fits, occurrence of splits in BBO is (with mathematical probability in parenthesis):

3-2: 63.9% (67.8%), 4-1: 32.7% (28.3%), 5-0: 3.5% (3.9%)

For 9-cards fits, occurrence of splits in BBO is (with mathematical probability in parenthesis):

2-2: 45.0% (40.7%), 3-1: 47.5% (49.7%), 4-0: 7.5% (9.6%)

BBO's bias in favor of 4-1 splits is overwhelming (+4.4% compared to probability); curiously, so is the bias in favor of 2-2 splits (+4.3% compare to probability).

I wrote a program to deal hands, using a simple algorithm: I use a standard Random Number Generator function found in any software development environment, I have an array with numbers from 1 to 52 corresponding to the deuce of clubs up to the ace of spades, I generate a random number between 1 and 52 (first card dealt), I remove it from the array, then random number between 1 and 51 to select the second card dealt, etc. I dealt 1000 hands using this program and obtained the following results:

For 8-cards fits, occurrence of splits in my hands dealer program is (with mathematical probability in parenthesis):

3-2: 68.4% (67.8%), 4-1: 27.9% (28.3%), 5-0: 3.6% (3.9%)

For 9-cards fits, occurrence of splits in my hands dealer program is (with mathematical probability in parenthesis):

2-2: 39.1% (40.7%), 3-1: 51.0% (49.7%), 4-0: 9.9% (9.6%)

I don't know how BBO generates hands, but the above statistics prove that it can't be in random fashion.

 

André Blanchet

 

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