Discount Gambling

Session Outcome Distributions for UTH w/ Trips Bet

Posted in ultimate texas hold'em by stephenhow on March 28, 2010

Last night while playing Ultimate Texas Hold’Em, I finally decided to play the Trips bet every hand, just for the fun of it. I played for a few hours, and left while I was winning about $20. (Most of that was due to two dealer mistakes, where I pushed against the dealer hand, but they paid my Blind bet anyways.) Anyways, if I only play a few hours, its worth it to play the Trips bet, since it adds to the camaraderie of the table. The dealer also seems to care more about you when you bet the Trips (probably because that’s when they get toked). I figured the Trips bet adds to the variance of the game, but I calculated the session outcome distribution for 100 hands just to make sure:

Session outcome distributions with and without the Trips bet.

Yep, more variance, more cost, and more fun.

Online Ultimate Texas Hold’Em Practice Game

Posted in ultimate texas hold'em by stephenhow on March 19, 2010

Finally, you can now play Ultimate Texas Hold’Em online with my new practice game. The main purpose of this game is to allow people to practice different betting strategies, and to learn for free. Learning UTH in the casino can be very costly, since most people don’t bet their hands like they should. I put in basic strategy hints in the game which gently suggests when to bet.

Click on the screenshot below to play the game:

Or you can still play the older but simpler and faster Java game (check that you have Java 1.6):

Ultimate Texas Hold'Em Practice Game (Screenshot)

Bet The Set @ Barona i-Table

Posted in blackjack sidebets by stephenhow on March 6, 2010

Another bonus side bet offered on the i-Table at Barona is a version of Bet The Set that pays for various types of pairs made on the player’s first two cards. For an n-deck shoe, the probability of being dealt a pair is 13*C(n*4,2)/C(n*52,2), and the probability of a suited pair is 4*13*C(n,2)/C(n*52,2).

Bet The Set bonus, 6-deck @ Barona
Hand Frequency Payout Return
Suited Pair 1.6077% 20:1 +.321543
Offsuit Pair 5.7878% 10:1 +.578778
nothing 92.6045% -1:1 -.926045
Total -.025724

The pit boss told me they increased the suited payout yesterday from 15:1 to 20:1, which would be an improvement of 8%, changing it from a sucker bet to a fun bet. They’re probably trying to promote the new i-Table games, and it’s an easy thing to change the payouts, since they’re not printed on the mat, but instead displayed on the player touch screens. At only a 2.5% house edge, this is very cheap as bonus bets go.

Royal Match @ Barona i-Table

Posted in blackjack sidebets by stephenhow on March 6, 2010

One of the nice features of the Shuffle Master i-Table is that they can change the odds of the bonus side-bets at any time. Yesterday, they increased the payout on the Royal from 50:1 to 75:1. The change showed up on the display, so I calculated the improvement.

For an n-deck shoe, the probability of hitting a Royal (KQs) is (4)(n^2)/C(52*n,2) and the probability of getting dealt suited cards is 4*C(n*13,2)/C(n*52,2).

Royal Match Bonus for 6-deck shoe @ Barona
Hand Frequency Payout Return
Royal Match (KQs) 0.29680935% 75:1 +0.222607
Suited 24.462033% 2:1 +0.489241
nothing 75.241158% -1:1 -0.752412
Total 100% -0.040564

The change from the 50:1 to the 75:1 payout on the Royal improved the return from -10.2% to -4.1%. So, it went from a sucker bet to a fun $1 bet you can place every hand.

Blackjack Odds Side Bet @ Barona Casino, CA

Posted in blackjack sidebets by stephenhow on March 4, 2010

At Barona Casino near San Diego, they’re spreading a new blackjack table game with an electronic twist. The game uses a human dealer, regular cards, and a modified blackjack table (Shuffle Master i-Table). However, players don’t use chips to bet, but instead use a drag & drop touch-screen. There’s no printing on the mat, and the table has a clean look, uncluttered by chips. This game is offered in a separate “Chipless Blackjack” pit of 4-5 tables.

The decks are shuffled by hand, and loaded into the shoe normally. The shoe reads the cards as they’re dealt, so it knows what everyone’s totals are. Your display prompts you for your actions. The game is a little faster than normal blackjack, since the dealer doesn’t have to mess with any chips, except during buy-ins and cash-outs.

This electronic format offers an interesting odds side bet on your starting two-card hand. The computer offers you particular odds for winning, based on your total vs. the dealer up card, as an optional side bet. For example, say you’re dealt 6,4 (=10), and the dealer is showing a 4. It offers you something like $2.69 on an additional $5 side bet (equal to the original bet) to win the hand. If you lose the hand, you lose the side bet. If your hand pushes, the side bet also pushes. Note that the true odds for winning this double should pay about $2.95, so the vig here is about $.25 😦

I worked out the true odds for a $5 bet, a six deck shoe, and dealer hit on soft-17. (The offer is made after the dealer peeks for blackjack.) The table is presented below.

I played for a few hours, and checked how close the offered side bet was to the true odds. For a $5 bet, the payouts were almost always lower than true odds by about $.25 -$.50 (no surprise here). For the payouts above $10, this might be acceptable. However, this vig really hurts the low payouts. For example, a player 20 against a dealer 10 should win about $.32 for a $5 bet. Their offered odds on this hand were often lower than $.10. That’s really bad, since you’re not even getting 1/2 the fair odds. The only odds that seemed to be true odds were for 14 vs. a dealer 6 and 7. The worst odds seemed to occur for double and split opportunities, and anything against a dealer 10 or A. (I think this is because in some situations, like 7,7 vs. an 8 upcard, the odds are quite different for splitting vs. hitting; to avoid any player edge, they offer you the lower of the two.)

In my session, almost no one took odds. Most people correctly assume the house isn’t offering true odds, and they don’t have a chart for comparison. True odds aren’t very intuitive, since people don’t think of blackjack hands in these terms.

So, as usual, you have to pay some vig to get odds in a blackjack side bet. The vig for $5 bets seems to average between $.25 and $.50 for all payouts. I’m not sure, but I think the vig scales up with the bet size, so its no better for $10, $25, or $100 bets.

Positive Count Shoe

I tried a simple experiment to see if a positive count shoe would swing the odds enough to make the side bet +EV. I removed a 2, 3, 4, 5, and 6 from the deck (+5), then re-calculated the odds. Overall, this made the basic blackjack game +EV, swinging it from about -0.5% to +0.5%. Then I checked a few odds points that would benefit the most from this positive count. I saw that a (T,4) vs. a dealer 6 moved from $6.37 down to $6.20. This doesn’t overcome the vig, and the offered odds are still probably below this. Similarly, for the same +5 shoe, a (5,6) vs. a dealer 6 improves only from $2.34 to $2.25. So, a negative shoe count doesn’t help the odds bet much, and will never overcome the vig.

Negative Count Shoe

Experiments with a -5 count shoe (five Tens removed) show that the higher odds bets improve more in absolute payouts than for improvements from positive count shoes. For example, a 14 vs. a dealer 10 upcard improves from $14.78 down to $14.36. Intuitively, the odds improve because fewer Tens in the shoe mean a higher chance of the dealer not having 20, and a better chance for the player to draw to a hand. Similarly, a 16 vs. a dealer 9 improves from $16.59 down to $16.18. These are significant improvements, but I believe that the vig on the higher odds bet are steeper for a reason: to account for this variation. So overall, it looks like counting isn’t going to ever make the odds bets +EV 😦

True odds for winning a hand, H17, 6-deck shoe ($5 side bet).
upcard 2 3 4 5 6 7 8 9 T A
soft totals
A,2 $4.53 $4.27 $4.01(H) $4.31(D)
$3.84 $4.45 $5.40 $6.29 $6.26
A,3 $4.76 $4.48 $4.19(H) $4.32(D)
$4.23 $4.82 $5.89 $6.80 $6.77
A,4 $5.00 $4.69 $4.66(D)
$4.33(D) $4.05(D) $4.63 $5.33 $6.43 $7.37 $7.36
A,5 $5.23 $4.91 $4.68(D) $4.35(D) $4.04(D) $5.09 $5.84 $7.02 $7.94 $8.00
A,6 $5.00 $4.70(D) $4.37(D) $4.03(D) $3.80(D) $4.38 $5.89 $7.00 $7.83 $8.25
A,7 $4.41(D) $4.13(D) $3.83(D) $3.60(D) $3.39(D) $1.83 $3.55 $6.26 $6.93 $7.26
A,8 $1.95 $1.86 $1.79 $1.67 $1.62 $0.99 $0.95 $1.92 $4.33 $3.08
A,9 $0.78 $0.76 $0.74 $0.70 $0.68 $0.44 $0.41 $0.37 $0.32 $0.68
2,2 $5.84(S) $5.55(S) $5.19(S) $4.84(S) $4.51(S) $5.37(S) $7.09(H)
$8.56 $9.61 $9.77
3,3 $6.11(S) $5.75(S) $5.30(S) $4.94(S) $4.60(S) $5.70(S) $8.16(H) $9.78 $10.85 $11.05
4,4 $5.25(H) $4.90(H) $4.53(H) $5.14(S)
$4.79(S) $4.10 $5.77 $8.13 $8.79 $9.36
6,6 $6.47(S) $6.04(S) $5.58(S) $5.16(S) $4.86(S) $8.14(H)
$9.34 $11.05 $12.07 $12.25
7,7 $6.16(S) $5.77(S) $5.32(S) $4.97(S) $4.63 $5.76(S) $11.82(H)
8,8 $5.01(S) $4.69(S) $4.41(S) $4.10(S) $4.01(S) $3.86(S) $5.50(S) $7.85(S) $8.38(S) $12.28(S)
9,9 $4.29(S) $4.08(S) $3.83(S) $3.57(S) $3.37(S) $1.83 $4.07(S) $6.19(S) $7.42 $8.84
A,A $2.65(S) $2.51(S) $2.38(S) $2.24(S) $2.13(S) $2.59(S) $4.31(S) $4.84(S) $5.15(S) $5.80(S)
hard totals
5 $6.50 $6.07 $5.60 $5.16 $4.80 $6.51 $7.59 $9.13 $10.20 $10.37
6 $6.68 $6.21 $5.74 $5.28 $4.90 $7.02 $8.17 $9.76 $10.67 $11.06
7 $6.36 $5.90 $5.43 $4.98 $4.63 $5.91 $8.20 $9.73 $10.50 $11.35
8 $5.26 $4.92 $4.55 $4.20 $3.94 $4.13 $5.78 $8.16 $8.82 $9.40
9 $4.24 $4.35(D)
$3.75(D) $3.53(D) $3.36(H) $3.98(H) $5.67 $7.06 $6.69
10 $3.34(D) $3.14(D) $2.95(D) $2.76(D) $2.63(D) $3.20(D) $3.64(D) $4.24(D)
$4.69(H) $4.63(H)
11 $2.92(D) $2.76(D) $2.60(D) $2.45(D) $2.34(D) $2.98(D) $3.40(D) $3.89(D) $4.12(D)
12 $8.65(H) $8.25(H) $7.46 $6.87 $6.35 $8.12 $9.35 $11.06 $11.99 $12.26
13 $8.93 $8.18 $7.46 $6.88 $6.40 $9.29 $10.65 $12.33 $13.61 $13.83
14 $9.07 $8.27 $7.55 $6.91 $6.37 $10.34 $11.57 $13.52 $14.78 $15.16
15 $9.02 $8.26 $7.54 $6.90 $6.37 $11.49 $13.03 $15.18 $16.51(H) $16.98(H)
16 $9.03 $8.27 $7.55 $6.91 $6.42 $12.67 $14.30 $16.59 $16.78(S)
17 $7.21 $6.60 $6.02 $5.55 $5.11 $7.08 $12.90 $14.24 $14.04 $17.75(S)
18 $3.87 $3.63 $3.42 $3.18 $3.01 $1.84 $3.60 $7.66 $7.47 $8.93
19 $1.97 $1.89 $1.80 $1.68 $1.63 $1.00 $0.96 $1.96 $4.27 $3.05
20 $0.80 $0.77 $0.74 $0.70 $0.68 $0.44 $0.41 $0.37 $0.32 $0.69
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