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When pushes are excluded, it depends on the rules as to what the win rate is. But 21forme is obviously right. I'd make the ultimate win rate for this problem a bit higher, because we can improve the outright rate for winning according to the discussions above. You never double except when you'd never hit more than once, and you never split when playing the hand out improves your outright win percentage, irrespective of e.v.
You can find all these numbers in the appendices of BJA3. So, if you make the win rate, say, 0.48, then 20 hands in a row is 1 in 2.37 million.
Don
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