You make some very good points. We all would like to play with an edge, and of course, when you have the edge you should bet as much as possible. I would add the corollary you should bet as much as possible _that you are comfortable with_. Obviously, TomSki got very angry when he lost his bet, and he was betting $2 a hand to begin with, it probably wasn't an amount he was comfortable with. (Only he knows that, of course; I'm just speculating).*
The fact that he was annoyed about losing $200 doesn't equate with him not being comfortable betting $200 on 64 vs 5. I routinely bet up to $400 on blackjack hands when I have as little as a 2% edge from card counting. Yet I have gotten very annoyed at losing $100 on an accidental "double-up" on a video bj game, even though the bet was a coin flip.
TomSki was annoyed that he accidentally bet $100 on a hand that he meant to bet $2 on. If given the option, he would not have bet $100 on that unknown hand of blackjack. But having been dealt 64 vs 5, he HAD to double down.
Let's say you are faced with a decision of whether to bet $200 on 64 vs 5 or bet $0. (This was not exactly TomSki's decision, but it's similar and it's easier to think about.) How much bankroll do you need?
A Kelly bet is roughly EV * Bankroll/variance. So the minimum bankroll for a $200 bet would be Variance * $200/EV. The variance of the outcome of 65 vs 5 is roughly 1 bet*. The EV is 27%. So, if betting Kelly, you should have about 1 * $200/27% = $750 of bankroll. Betting 1/3 Kelly, you should have about $2250 of bankroll. I'm pretty sure TomSki meets those criteria!
This raises certain interesting questions of optimal bet sizing when you have the edge, Kelly criterion, etc. For example, say you have a free ace coupon--a 47.8% edge on the hand--and you bet whatever the max is, $500 perhaps. Then you get an A-6 versus a dealer 3. Basic strategy says to hit in that situation, but would would you have the guts to do it?
It's not just a matter of guts. The idea of risk averse strategy changes has been around for a long time. Your decision should depend on whether the doubled bet would force you to bet over the Kelly amount. The index number for making the double down decision will be larger if your bet size is not an insignificant fraction of your bankroll.
*(Maybe the fact that he was playing with free play was a factor in the decision, but it sounds like he was using real credits at this point. In the end, of course, video blackjack is not the primary choice for churning free play, since the returns are usually in the 96-97% range).
You are probably referrring to games that pay 1-1 on a natural. I doubt that TomSki was playing a game that bad. Many video blackjack games have decent rules with returns of 99% or better.
--Dunbar
*the variance would actually be a little less than 1 because of the chance of ties; that would reduce the bankroll requirement slightly.
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--- In vpFREE@yahoogroups.com, "shloemoejs99" <shloemoejs99@...> wrote:
--- In vpFREE@yahoogroups.com, "dunbar_dra" <h_dunbar@> wrote:
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> As a serious player, TomSki DID have to double down.
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> I'm sure TomSki (or any serious player) would love a coupon that allowed him to walk up to a blackjack table and bet $200 on a 64 vs 5 from a fresh deck. Or, if presented with a coupon choice to bet either $100 or $200 on 64 v 5, would always bet $200. The EV of the 64 vs 5 bet is 27% no matter how much you bet. Betting $200 is $27 better than betting $100. You don't need much bankroll to justify a $200 bet with a 27% edge.
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> --Dunbar
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> --- In vpFREE@yahoogroups.com, "shloemoejs99" <shloemoejs99@> wrote:
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> > Umm ... hate to break it to you, but you didn't _have_ to double down there. Why not just hit 10 if the bet was something above what you were comfortable with?
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> > --- In vpFREE@yahoogroups.com, "ThomasS" <tomskilv@> wrote:
> >
> > > I was dealt 64 vs dealer 5. Oh no, I have to double down now, so I have to feed in another $100. I get a 2. dealer turns over a 4 and hits a 10 to win and I lose $200 on the hand. ARRRRRGHHHHH!!!!!!!!
> >
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