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I have some questions regarding this casino Texas Poker game. You can wikipedia the rules but basically the game goes as following:

  1. You make a blind bet first .
  2. The dealer deals three cards, and deals two cards to you and the dealer himself. Dealer does not look at his hand, but you can look at your hand.
  3. If you decide to play, the you must make another bet worth twice your blind bet, oterwise you lose your blind bet and game ends.
  4. If you decide to play, then the dealer deals anoter two cards before opening your hand.
  5. If dealer beats you then you lose all your bet, if you beat dealer then you get paid the sum of your blind and subsequent bet.

However, there are two exceptions regarding the payout for (5):

  • If dealer has a weaker hand than a pair of 4, then this is a "no gae" and he pays you only the blind bet regardless of if you win or not.
  • If you have straight, full house or better then you are usually paid more than 1:1 of your bets.

My question is, call me naive, but I feel this game seriously favours the player? Thinking in a simple way -- lets say the blind bet is 5 usd. As if the player plays every hand, then he and dealer has equal chance of winning 15 usd. Now the player even has an option to pay only a third of the total bet(i.e. pass at (3)) to stop the game -- and I think it is reasonable to assume the player makes correct decision 50% of the time at least. (i.e. namely that if the player decides to pass 10 games then he would lose more than 5 if he did not stop) it just makes me think I would much rather be the player than the dealer. The only thing I am not sure about this analysis is the how the 'no game" rule affects the probability.Would be grateful if someone could point out

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The Wikipedia entry for the game you are referring to has the answer to your question: the house edge (i.e. the average win percentage for the casino assuming perfect play from the player) is between 2.0 and 2.5%.

Note that perfect play does not have the exact same meaning you provide. Perfect play means calling (paying the extra \$10 in your example) whenever he has more than 50% chance of winning given the information available.

The casino's advantage comes from the risking \$15 only after he has seen all the cards, unlike the player that must decide whether to risk \$15 knowing only 5 cards.

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  • $\begingroup$ Um the casino cannot really decide to play or not... He will play only if the player plays. $\endgroup$
    – nobody
    Commented Aug 13, 2015 at 7:27
  • $\begingroup$ Um think in this way. The casino and the player all play unset the same rules, if it was not the "no game" rule. Thus the chance of winning is same for both dealer and player. Now the player can pass very bad cards with less than half of the total bid. $\endgroup$
    – nobody
    Commented Aug 13, 2015 at 7:30
  • $\begingroup$ He "decides" whether to play for \$15 (if he has a pair of 4 or better). Otherwise he just lost \$5. $\endgroup$
    – twalbaum
    Commented Aug 13, 2015 at 7:32
  • $\begingroup$ Remember the casino also has a "no game" option, which costs him the same as the player's, and he can take it when all the cards are known. $\endgroup$
    – twalbaum
    Commented Aug 13, 2015 at 7:39
  • $\begingroup$ I see what you mean now. It is indeed the ' no game ' thing that is doing the trick. I ws bit confused because the no game thing means casino has to pay the player even if he bests the player bit worth hand weaker than a pair of four, but I guess most player would give up if he had such a weak hand anyway $\endgroup$
    – nobody
    Commented Aug 13, 2015 at 8:12

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