Quote from: Quickseller on January 31, 2016, 03:30:14 AM

(AFAIK) dooglus, nor RHaver are the ones who own MoneyPot

Your grammar is weird, but to be clear I do not and never have owned any part of moneypot.

Quote from: ranlo on January 31, 2016, 05:31:32 AM

I just want to say that... I'm impressed. Even when two of the more mathematically-inclined people on the forums didn't fully understand the repercussions of the Kelly algorithm, you do. From now on, I will be sure to bring any math-based questions I have directly to you, since you're obviously now the most knowledgeable person on the forums.

Don't feed the troll.

It's clear nobody understood the risks, not even the guy who coded moneypot...

Quote from: RHavar on January 31, 2016, 06:34:36 AM

@Dooglus an interesting note:

Taking the payout line that was used:

[ 121, 47, 13, 5, 3, 1.4, 1, 0.5, 0.3, 0.5, 1, 1.4, 3, 5, 13, 47, 121 ]

We naively assumed the house had a 1% edge, but actually it's an illusion.

We can actually normalize this payout line to:

Code:

[ 172.42857142857144, 66.71428571428572, 18.142857142857142, 6.714285714285714, 3.857142857142857, 1.5714285714285712, 1, 0.2857142857142857, 0, 0.2857142857142857, 1, 1.5714285714285712, 3.857142857142857,66.714285714285714, 18.142857142857142, 66.71428571428572, 172.42857142857144 ]

That is interesting. It took me a while to understand your point, so I guess others may not understand it too.

You noticed than none of the payouts in the array are zero, so if you bet 1 BTC you can't lose the whole 1 BTC no matter which payout you get. And so in a sense you aren't really risking 1 BTC. The losest payout is 0.3x, so the worst that can happen is that you lose 0.7 BTC. So you recalculated the multipliers such that you get the same result from betting 0.7 BTC with your new payouts as you would have got betting 1 BTC with the original payouts. Then there's a zero in the array, and you're truly risking the whole amount you bet.

Calculate the new multipliers as (oldMult - minOldMult) / (1 - minOldMult)
So the 121 jackpot becomes (121 - 0.3) / (1 - 0.3) = 172.4285

Quote from: RHavar on January 31, 2016, 06:34:36 AM

So when betting 0.7 BTC, it's an identical bet! The EV stays the same (-0.01 BTC or what ever), but now we calculate the house edge, we'll figure it out as 0.01 / 0.7 ... or 40% higher.

Right. The house edge of the original row of payouts is 0.9195%, and after 'normalizing' it, it goes up to 1.3136%. You're losing the same, but betting smaller, and so are losing a bigger percentage of your stake.

Quote from: RHavar on January 31, 2016, 06:34:36 AM

The "super payout" line you had, just exacerbates the problem. The most you could lose was ~4% of your bet, so with a 1% house edge, the *real* house edge, after you normalize the payouts would be 25%!

So while crazy, it's not as crazy as you'd first think!

Yes. Before normalization the house edge of this line:
[1.0656, 1.0585, 1.0368, 1.0155, 0.9616, 0.9841, 0.9895, 0.9918, 0.9962,
0.9918, 0.9895, 0.9841, 0.9616, 1.0155, 1.0368, 1.0585, 1.0656];
is 0.9997%.

After normalization:
[2.7083, 2.5234, 1.9583, 1.4036, 0.0, 0.5859, 0.7265, 0.7864, 0.9010,
0.7864, 0.7265, 0.5859, 0.0, 1.4036, 1.9583, 2.5234, 2.7083]
it is 26.0342%.

'Kelly' tells us the same before and after normalization: risk 99.97% of the bankroll. This doesn't seem overly unreasonable. Who is going to play a 26% house edge game at large enough stakes to stand a chance of winning the whole bankroll?

To gain an intuitive understanding of why Kelly tells us to risk more than 26% of our bankroll on a 26% house edge bet, it helps to see the plinko bet as 17 separate bets. For the low payout bets where the ball lands towards the middle we would want to set quite a high max bet, since the payout is a small multiplier of the stake, but for the high payout bets on the outside edges we would want to set a low max bet. We can only set a single max bet, and so we need to find some way of balancing the competing forces. It turns out we maximise the log of the bankroll by giving more weight to the max bet implied by the more common (inner, low payout) outcomes.

As the wikipedia page says:

Quote

Even Kelly supporters usually argue for fractional Kelly (betting a fixed fraction of the amount recommended by Kelly) for a variety of practical reasons, such as wishing to reduce volatility, [...]

Quote from: RHavar on January 31, 2016, 06:34:36 AM

One take away for plinko players would be that the house edge is rather misleading. You actually pay the house edge on the entire bet, rather than just what you're risking.

And so you should never play a plinko game that doesn't have a 0x somewhere on it?