Humans vs bots in the game of SP500

The problem with out betting the bots is that bots are probability neutral. They are exposed and the players are betting bot currency, which has almost zero transaction costs. The game rules are seven banker bots vs any and all humans.

Now the banker bots will chains, and break up the SP numbers so as to conserve bot currency. The price is bot dollars/SP index.

The bot strategy is tangent bets from price close to one. They pass bets out of range down to where they are taken. Prices go from 0 to 1, but not including. The bot near integer 0 does a cotangent bet back up the line, the old reverse,repurchase, lend-klease triple play, the one the fed invented. Call it the cotangent bet, the encoded SP price sent reverse, the constrained flow  condition. Thus SP to digits is almost a reversible ratio everywhere.

Wit, the human will compute the most likely price, ans bet there, as will the bot. Hence, relative to bot coins, all players are no arbitraged, even the bot.  Only the SP numbers can introduce arbitrage points.  The bot always wins because it can never go broke because it is always more accurate than the electricity it costs.
So, at the short end, the peak of the encoding tree, the farthest bot from  the SP numbers., the price never goes to zero.  instead, the last bot will decode a higher price for the SP, a price necessary to keep it one error band away from zero.

You end up with the optimum six bit counter, and it counts the SP numbers, and adapts over 30 odd SP numbers in a row. The bots make as accurate integer map of groups in the SP 500, a polynomial describing the most likely numbers on a finite number line, if they were bets from SP numbers.

Now my readers know me, and they know this will be exactly imprecise. Who is going to want this? How about a WalMart points to SP account for its favorite customers, to go along with its Walmart yield curve, and its Walmart dollar converter. But the points also usable as supplemental currencies in all Walmart. So Walmart is going to jump all over this, they are the WalMart currency bot.