Quote from: ndnhc on February 03, 2016, 06:18:15 PM

Can someone summarize why the bet went through? Was the bet supposed to go through?

The bet went through because the site was using the Kelly criterion to decide how much of its bankroll to risk. The Kelly criterion tells it to risk 35.3% of its bankroll when playing the 'red' line (with 121x max payout).

Quote from: ndnhc on February 03, 2016, 06:18:15 PM

https://www.moneypot.com/bets/18530298 shows <1% house edge. But risking tens of bitcoins at 1% edge is crazy, so I assumed it shouldn't have gone through Huh

People are familiar with dice site style betting, where there are only two outcomes (win/lose). In that case Kelly tells us that the percentage of the bankroll to risk is the same as the percentage house edge.

It's quite different for plinko games where there are a range of outcomes. In that case Kelly tells us to risk more than (house edge)% of the bankroll. See my most recent two charts. Risking 35% hits the peak of those charts. Risking only 1% gets you far lower expected log growth.

Quote from: elm on February 03, 2016, 06:23:57 PM

you are saying that risking 40% of the BR would be optimal but half = 20% would also be acceptable? did I get this right?

It appears that 35.3% is optimal (for the 121x red line - it differs vastly depending on the line we're talking about). And looking at the chart, it looks like risking half that doesn't reduce the expected log growth by a whole lot.

Quote from: elm on February 03, 2016, 06:23:57 PM

what about those 83% or 99% KC risk for the plinko game?

Those were for different payout lines. The 83% was for the 'orange' line, and the 99% was a silly extreme example where all the payouts were very close to 1x and the true house edge was much higher than 1% (since the player isn't really risking most of his stake at all when there's no chance of losing most of it).

The orange line pays out like this:

Quote

   if r >= 26333 and r < 39203: p = 0.4
   elif r >= 14893 and r < 50643: p = 1
   elif r >= 6885 and r < 58651: p = 1.1
   elif r >= 2517 and r < 63019: p = 1.2
   elif r >= 697 and r < 64839: p = 1.5
   elif r >= 137 and r < 65399: p = 2
   elif r >= 17 and r < 65519: p = 3
   elif r >= 1 and r < 65535: p = 9
   else: p = 23

and when I ran a simulation I got a plot of return against risk like this:

It peaks around 83% as expected. Risking half that looks like it gets you around 60-70% of the expected growth.