Wednesday, March 8, 2017

Betting the numbers graph, how it works

We consider the scenario where an aggregate of agents bet a particular random number, say the first revision quarterly GDP. Her is how to configure the pit boss.  Tell all players that bets will be compressed to a 6 bit rank betting tree, which is a minimal spanning tree organizing all the bets by 'bin'.  The bin size for a bet is the path length down the bet compression graph.  The bets have been binned such that a random generator of six bit number entering the tree will generate the typical sequence of bets, at proper frequency.  This is an intelligent rounding process.

So, the bets are halted at midnight, the tree is visible (the tree is always visible even during betting).  The GDP number comes in and it has to traverse the tree. The first node separates half the significant bets, the wrong path pays the right path.  This is without replacement, so winning the first node lets you keep one digits worth of winnings, and only risk N-1 digits worth of winnings on down the path.

Then the residual path is further subdivided, until at the end a small group get the payoff, and the losses spread according to the path deviation of the missed estimates.  The most likely bet has the shortest path and the smallest total payout.  There will be many common betss that fit the likely result, say trend yearly growth. This is one color compression.

If the graph were fully populated and binary (not the case generally) then we can see the payouts.  Half the people wing half the bets, a quarter of them wen a quart of the bets, and so on. This is the result when BtitCoin Casino just rolls a 256 bit number, say, from a uniform distribution with replacement. Bettors spread their bets, to even he odds knowing the outcome is uniform random. The odds board prints current bet distribution.

The most common outcome, as in this chart, most of the people mostly break even on most of the path, then they all split the lower residual which is small.  We get this because we are dealing with a semi-predictable outcome. Bets tend to converge as the arrival moment nears, the hidden information is less hidden. We end up with a converging market if insider information.

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