For optimal Kelly betting, note that your CEV is pretty much half your EV. Hence, if you can make twice the hourly rate you could earn elsewhere, you can start to consider playing. Everything else is a waste of time.
Hey I know this feeling. It helps to think in terms of "who's paying the bill". There is simply no way you can gain EV by making (or not making) a zero-EV bet. If you still do, either the bet is not zero-EV - or you won't gain that advantage :laugh:
A related question would be, if you cannot...
With that, I fully agree. If you play insurance/surrender, your EV before peeking for BJ is -2/3.
Are we talking about late surrender ? Because then you cannot surrender before the dealer peeks for BJ. If you don't plan to play insurance, your EV before peek is still the same
1/3 * (-1) + 2/3 *...
I cannot follow you here. The break-even point for insurance is 1/3, not 1/2. Unless your intention is risk-averse play (which is a legit question in this situation), the pure EV-best play is to insure whenever insurance is favourable, and to surrender whenever surrender is favourable. If both...
I think Eric talks about standard input and standard output, which you can easily pipe through other programs. Of course you can provide a scripting interface to your GUI program which will run custom scripts, but stdout / stdin is much more versatile (i.e. you could make provide a web interface...
Ok, let's do a (ridiculous wrong ^^) model of a fictitious soccer team. My model prediction is, that my team will score 0/1/2 goals with probabilities 20%/30%/50% if they are the Home team, and with probabilities 60%/20%/20% if they are the Away team.
In such a simple scenario I would sample...
The Kolmogorov–Smirnov test looks promising on reading, but I'm not sure I understand the test well enough. As I read it, one can test (independent and identical distributed) samples against a given probability distribution. Then there will be a coefficient tabulated somewhere, telling how...
I'm not confident enough with statistical tools, but I'm looking for suitable statistical test. As there are many profound people here, I ask for advice.
My original problem is different from the one below, but I will use the game of roulette to give an accurate example of what test I'm looking...
All cards are either in the shoe, in the discard, or in play.
If you know the number of cards in the discard, and the number of cards in play, you know the number of cards in the shoe.
Then tell me, who will win on a table full of professional poker players ?
The higher the stakes, the higher your skill you need to beat the rake (and the other players).
So you don't agree to "At the end, the packets on the shelves are unloaded into a final deck of n. This may be done in order or at random; it turns out not to matter." (Section 3.1, p.4) ? The proof for that is quite simple.
You're right, I missed the part you were talking about how the shelves where combined into the final stage.
Actually the details of that combination process doesn't matter, because each shelve is chosen at random in the first stage. They could even combine the shelves in a fixed order, it won't...
Thats not the way the shuffler works. The shuffle algorithm is well-explained in the paper: For each card, the algorithm picks 1 of the 10 shelves at random, and then places the cards in the shelf on top or at the bottom - also at random. None of the shelfes are excluded in any process (well...
The difference between your money and this coupon is: You lose the coupon on a win and a push. So simply avoid games where you often win or push.
Look for a high payout game without pushes. House edge is not that important. I would put it on a number bet on roulette.