Question about strategy table...

[London Colin]

Thanks

I wasn't hoping for more accurate results, but instant and more flexible ones. (Although, how long does it take to run 10M hands these days? Probably not that long.)

I was thinking that you could then apply the formula using different values for the single-player figures (based on deck composition and/or differing rules) and see what effect this has.

Also a simulation that shows not just win, lose or push , but also win 2, win 1.5, win 1, push, lose 1, lose 2 to account for double downs, splits, and blackjacks.

If I'm understanding Wong correctly, his table assumes no doubling/splitting and so his figures will be slightly different to those for basic strategy.

I was thinking also about incorporating a strategy of 'DD on any 2 cards (unless it's a pair for which splitting is better)' to put a figure on the chances of successfully doubling past an opponent who only (at most) wins a single bet.

Having given a little more thought to all this, I think the only way a formula could work would be to separately calculate the probability of an outcome(e.g. prob. A wins and B loses) for each possible dealer total, and produce a weighted sum incorporating the dealer probabilities.

These are all just my poorly-informed musings really. I'm looking for ways to combine my day job (software development) with blackjack.

 

[Reachy]

I had asked this before

It's funny but a couple of months ago I asked whether someone had expanded on Table 4 to include DD, split and surrender options. Frankly it would amaze me if someone hasn't. Come on Ken, spill the beans, are we going to be refering to "Smith, Table 4" in the future?

Cheers

Reachy

 

[rounder21]

Double on anything...

I was thinking also about incorporating a strategy of 'DD on any 2 cards (unless it's a pair for which splitting is better)' to put a figure on the chances of successfully doubling past an opponent who only (at most) wins a single bet.

On p. 132, Wong states the probabilities of doubling on anything (or splitting the pair when it is your better option). This strategy is used when winning one bet will definately not be enough to make you advance. He says with this strategy your probability of winning is .33, pushing is .08, and losing is .59

On the "double anything" strategy you should split aces, 2s, 3s, 8s, 9s, and 10s always. Split 6s and 7s against 2-6, and split 7s against 10. Double down everything else.

Actually a .33 probability of winning isnt all that bad if its enough to get you over the top and advance. The problem is if you arent last to play, your opponent could double also if you catch a good card and he/she thinks he/she is not going to advance. The .33 probability is just the probability of winning the hand I guess.

Rounder21

 

[London Colin]

Thanks Rounder. I'd seen that, but forgot it was there.

Actually a .33 probability of winning isnt all that bad if its enough to get you over the top and advance. The problem is if you arent last to play, your opponent could double also if you catch a good card and he/she thinks he/she is not going to advance. The .33 probability is just the probability of winning the hand I guess.

Indeed. It's a tricky business to work out how to combine the probabilities of a group of players who may or may not decide to DD, surrender, etc. You may need to account for who is going first and strategy modifications that might take place.

I guess we are then getting into the realms of Artificial Intelligence, rather than just arithmetic.