Ask The Wizard #205

Arnold Snyder's book, which I highly recommend, contains a brief section on defeating a similar type of side bet. In this context, with only four suits to track, the side bet becomes susceptible to the strategies outlined in that book when played in a single-deck scenario. Big Book of Blackjack You’re participating in a game involving three players: (a) you, (b) your competitor, and (c) an impartial judge. Each participant secretly selects a real number between 0 and 1. Once all selections are made, the numbers are disclosed. The player whose number is nearest to the judge's chosen number, without exceeding it, is declared the winner. If you're closer, you earn $1; if your rival is closer, you lose $1. If both exceed the judge's number or if there’s a tie, the game results in a stalemate. Royal Match Is there an optimal number you could choose to achieve the highest potential gain, assuming your opponent chooses randomly? Additionally, how would the game change if your opponent had their own strategy?

0.75.

If you aren't employing a card counting method, then it won’t make a difference. However, if you are counting cards, any burned cards should be accounted for in the total deck or shoe remaining when you convert to the true count. mathproblems.info , problems 196 and 197.

The odds of being on the losing side of KK against AA can be calculated as (4,2)/combin(52,2) × (combin(4,2)/combin(50,2)) = 0.000022162 for each rival at the table. This translates to a frequency of once every 45,121 hands, so your calculations are indeed accurate. For the 400 hands you played, the expected occurrence would be 400 × 0.000022162 = 0.008865084 per opponent. The following table illustrates the probability of seeing KK against AA three or more times over the course of 400 hands, depending on the number of opponents.

Oh my goodness! This is an extraordinary website, and it’s hard to believe I’ve only just discovered it. I've spent several days diving into your data, analyses, and commentary. Your insights are so convincing that I can't find any grounds to challenge them. combin Since I can't manipulate the statistics, my inquiry revolves around something I can control, which is the duration of my playing sessions and my bankroll. Given that a million or a billion hands is made up of numerous 'sessions'—let’s say between 300 to 1,000 hands—doesn’t it make logical sense to either a) play until you hit a predetermined winning target, or b) continue playing until you bounce back from a losing streak and end that session at a break-even point?

I have one more question: could you suggest a software simulation system that accommodates all variations of rules, implements stop/loss measures, allows for different lengths of 'sessions', and adjusts hit/stand strategies based on bet sizes? I would really like to put my approach through its paces on the computer.

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