gronbog said:
Yes, the formula is general, not just for blackjack and yes, the specification of hourly rates is arbitrary.
Thanks for confirming that. I thought it was probably the case. The one thing that was giving me pause was that I'm looking at games where the advantage can get a lot bigger than in blackjack, which might have caused the formula to break down if it relied on some unspoken assumptions.
gronbog said:
You enumerate 3 possible scenarios.
- The first is like wonging out in blackjack. Treat it like a bet of zero with EV=0 and SD=0. This will allow you to get overall results for "rounds observed", which should be used calculate results over various time periods (hourly, weekly, monthly, etc.). Ignoring this scenario gives you results for "rounds played" which can also be useful.
Yeah, I was already thinking along those lines, though getting a bit confused in the process, considering whether rounds observed, rounds played, or both would be the desired/most meaningful input into calculations such as risk of ruin. As with the choice of hourly rates or other periods, I guess the important thing is merely to be consistent.
The raw data that I am currently collecting is essentially -
- Num rounds observed.
- Num rounds played (i.e. one or more bets made on the round)
- For each separate bet type and in total -
- Num bets made.
- Total amount bet.
- Sum of results.
- Sum of squared results. (where each result is the net profit on a round)
- which should be enough to let me extract lots of useful information.
Since a simulation will involve varying bet size with advantage, presumably I can only get figures for basic, 1-unit std deviations if I either set up special flat-betting runs for that specific purpose, or alternatively add some additional counters to keep track of how many of each possible payoff there have been.
It's not really relevant to this discussion, but I am also logging the above data by card penetration, as well as in total, so that I should be able to run a simulation once, configured for the maximum possible pen., then query the results for shallower penetrations by simply excluding the unwanted data, rather than having to run the sim again.
gronbog said:
- For the second, use the initial compulsory bet as the unit. You want your results in terms of that initial wager. We do the same in blackjack where your initial bet advantage (or IBA or EV) are expressed in terms of your initial wager, even thought you may wager more in order to double, split and/or take insurance.
It's not quite the same thing, as the bet is only compulsory in the sense that it has to be made alongside the side bet(s) that we really want to make (because they have gone +EV). It's the normal situation with side bets; it just so happens that in some games one is allowed to make 'side' bets without being required to make the main bet at all.
I'm still not sure if thinking in terms of units is really necessary at all, compared to just dollars or pounds.
gronbog said:
- For the third scenario your unit can bet anything you like. Treat each +EV bet like a separate game.
Once you have the results for each scenario, you can combine them based on the frequencies of each scenario. Be careful here, you can multiply EV by frequency, but not so with SD. You need to multiply that by the square root of the frequency.
Have fun!
I've noticed you've commented further while I've been typing!
I'll save any further thoughts I was going to add here until I've digested everything.
Thanks a lot.
